square root of x

anonymous asked:

what are some embarrassing pickup lines mulder would use on scully on valentines day that would totally work

  • he’s used “you’ve abducted my heart” at some point every valentines day since 1993 even though it got markedly less adorable after he was literally abducted
  • “are you made of copper and thallium because you’re cu-te” and she said “you mean tellurium, mulder. thallium is ti not te” but she smiled anyways 
  • he texts her honest to god valentine’s day memes for the whole week leading up to valentine’s day. she has blocked his number 3 times
  • “if you were a triangle all your angles would be less than 90 degrees” “so an acute triangle” “get it scully….acute” 
  • scully once tried to fire back with her own science-inspired valentine’s day pick-up line and it was so complicated that he didn’t even understand what she meant and she had to take 15 minutes to explain it to him
  • “you must be the square root of x because i feel irrational around you” (she told him he was irrational all the time) 
  • “if you were a library book i’d check you out” he actually heard a teenager use this while they were doing research in the back of a library and he repeated it really quietly to scully and she told him his library card had been expired since last june 
  • not even pick up lines but he uses valentine’s day as an excuse to get disgustingly sentimental and he starts every sentence with “scully, love of my life, keeper of my heart, most beautiful woman in the world,” and ends with something mundane like “do you want me to make coffee”
  • (she always does she loves coffee) 
  • anyways!!! i need to stop talking about this now but i love mulder + valentine’s day 
  • ban ryu: alright then han sung. since you say you're that smart, solve this without using any calculator. find the arc length of three x times the square root of seven minus two from x equals zero to one half.
  • han sung: *stares at equation while deeply thinking* well, there are two 'twos' in the equation- minus two and the denominator from the one half. the number two sounds like the letter 'u', and u is between the letters 't' and 'v' in the alphabet.
  • han sung: but tvs aren't really relevant anymore because everybody has computers now, so it's kind like... if you have two tvs, what is it even-
  • han sung: *out loud* four.
  • ban ryu:
  • han sung:
  • ban ryu: ... that's right...
Prompt #42 “Sometimes, you fall for someone you didn’t expect but that doesn’t make it wrong”

Originally posted by nirnaetharnoediads

Written by Christina

Category: Angst with fluff. Just your usual fanfic stuff. 

Word Count: 2298

A/N: I had finals last week, so the stress was super high. Hope you all enjoy :) Feel free to message us with any feedback, requests, or comments. We love you all!

Loosely based off #42 fr this list 

Part 2 


You felt tears well in your eyes as you clenched your fists. An F. Again. And in your first class of the day! This math class was going to be the end of you. You pulled three all-nighters and spent every moment of spare time studying for the past week and a half preparing for this test. To fail was the worst feeling ever. Words couldn’t describe the anger, hurt, and disappointment that consumed every molecule of your being. You just wanted this class to end. You loathed it. The teacher sometimes tried to help you, but you were often pushed aside because “they were too busy at the moment”. You needed a tutor. And fast.

You glanced around the classroom, looking to see if anyone looked like they understood what was going on. The teacher was writing an example on the board for the class to complete. Some people were scribbling down the problem as the teacher wrote it. Some people sat back in their chairs and stared at the board, clearly lost. But there was one student with their hand raised. A boy. He sat two rows over and one seat back from you. The teacher turned around, saw the boy and called on him.

Keep reading

School Days

Genre: Slight angst, fluff

Word count: 8k

Originally posted by apgujeon


Drifting lazily above your head, you laid back on the grass and watched the puffy white clouds go by, finding the different shapes within them. One was obviously supposed to be a dragon, releasing a wisping breath of steam as if it were tired of holding it in all this time. It’s eyes were the pale blue of the sky with the smallest fleck of white that seemed to be staring at you. You never tore your eyes from it. What am I supposed to do now? You silently asked the dragon. His eyes seemed to search yours as you waited for the answer to come to you.

Keep reading

Out of My League // {Brett Talbot Imagine}

Out of My League // {Brett Talbot x Reader}

Summary: The reader has a crush on Brett who is extremely popular and way out of her league, she consults her best friend which is considered very popular even though the reader is very shy and tends to avoid different social gatherings.. After their talk things start up with Brett.

A/N: Lately I have been loving Brett and I will probably post a couple of sweet and romantic imagines including him.

Warnings: Recollection of Body Insecurities.

———————————————————

She was always the cute one,

The one that always admired everything from the side wondering how it feels like,

She was the one that always imagined what it is being loved, being social but panicked when it happens in reality,

She never had luck with boys, She wanted someone to love her but was to shy to even say a word to anyone.

Although she was extremely beautiful;

inside and out,

She was never accepting of herself.

She always felt like every girl in the room was prettier than her,

Like she wasn’t enough.

She was always shy,

Watching from the side but never in the middle,

Listning to the conversations but never speaking,

Keeping everything to herself as if it didn’t matter to anyone how she felt.

But opposing to you was your best friend,

She was very popular, probably the most popular girl in your grade,

She was gorgeous, outgoing,

You two had a bond like no other, she knew everything about you, and you knew her.

But you had a problem, you had a crush.

Not too long ago you had fallen in love with a boy, but nothing happened. It broke your heart and you didn’t know how you could possibly fall in love again.

But now you had a new crush, Brett Talbot.

You hated yourself for crushing on him,

Aside from him being extremely close to Y/B/F/N he was also extremely popular, the captain of the lacrosse team, talking to everybody and being friends with everyone, especially girls.

You kept this to your self, not telling a soul beside one of your friends who found out, not even Y/B/F/N knew.

You tried your best getting over him,

Trying to convince yourself he has something with someone else,

That he doesn’t like you,

But nothing worked.

——————

It was a normal day at school,

You wore a pair of skin tight medium dark jeans and a fitted black t-shirt with a blue and white flannel.

You were at your locker taking out some books for your next class,

Y/B/F/N and Y/F/N come up to you.

“Heyy” They both said hugging you and you hugged them back.

“Girls night at 8,You’re coming” your best friend said with a smile plastered on her face.

“I see I don’t have a choice” You said sarcastically.

“You’re right, You don’t. See you at 8” Your best friend said giving you a peck on the cheek and going her way to her next class leaving you and your friend alone.

You suddenly spotted Brett leaning against the lockers a couple feet from you two,

You turned your eyes to him as he looked towards your way, You quickly turned your focus back to your locker.

“Still not over him?” Your friend asked.

“Nope”

“Then go talk to him”

“Yeah right cause I’ll do that”

—AT THE GIRLS NIGHT—

“Girls I have an Idea!” One of your friends said in a excited tone.

It was you, your best friend and five more girls,

You all were some sort of pack but you still had a slight isolated feeling from all of them.

“We should do a question round!”

You all agreed and sat in a circle.

“Okay, so each girl has a turn to ask a question and all of the girls have to answer it”

“Y/B/F/N you ask first since you have the best questions” One of your friends insisted.

“Fine, umm.. Lets see.

Okay, Is there someone you have been interested in lately?”

The girls answered the question each in their turn until it was your turn;

“Umm maybe..” You said avoiding eye contact.

Your best friend had a confused look on her face as if she had no clue what you were talking about.

“What do you mean?” She asked in a slight aggressive tone.

“You didn’t tell her?” Your friend elbowed your rib catching your attention.

“Tell me what?”

“I’ll explain in private” You said taking your best friend to bathroom and locking the door behind you so you could talk alone.

“Y/N whats going on?”

“Well you remember how I told you that for some reason I always need to have crush on someone right?”

“Yeah”

“So after I got over H/N I have a new crush on someone but I haven’t found the right time to tell you who it is and to be honest I don’t even have enough confidence to say his name out loud.”

“Then am I supposed to guess?”

“Well yes but I will give you a clue.. He’s completely and totally out of my league

“Isaac?”

“No”

“Jackson?”

“Nope”

“Theo?”

“No”

“Come on Y/N  just tell me”

“I’ll give you a better clue, He’s one of your best friends”

“Is it Liam?”

“No”

“Brett”

“Maybe" You said quietly as you picked on your nails avoiding eye contact.

“Are you serious? Why didn’t you tell me?”

“Cause its never going to happen” You said slightly raising your voice.

“He’s friends with so many girls who are so much more social and way prettier than me,

I barely know him and he is so popular, why would he even notice a girl like me”

“If I must say you two look like you would fit each other”

“Don’t say that”

“Why?”

“Cause it won’t happen, he doesn’t even know who I am and even if he does I am way to shy to even look at him”

“Fine, But you need to tell me these things.

I’m your best friend, I’m supposed to be here for you no matter what”

You both got up and hugged and went back out to your friends.

“Did you tell her?” Your friend tugged on your arm.

“Yes”

“And..?”

“And that it”

———

It has been a week since that girls night and you were in your chemistry class,

One of the few classes you shared with Brett.

You were focused on your work as you felt this weird feeling, as if someone was watching you.

You lift your head up and turn your focus to the back of the classroom to catch Brett looking t you and turning his head as soon as you catch him.

“It’s just a incident” You thought to your self.

Chemistry was over and you met up with Your best friend for lunch.

As you were eating your focus turns to Brett.

The way his shirt fit him tightly on his toned muscles,

How parts of his hair fell upon his face.

But you then realised the girls he’s with.

A second before you turn back to the conversation you had with Y/B/F/N Brett suddenly looks at you, giving you a small wink.

You smile and turn your head back to your best friend, you feel you cheeks boiling and the butterflies in your stomach going wild.

“It only a coincidence” You thought trying to calm yourself down.

———

Its now Math, actually, you enjoyed math and you were good at it, one of the best in your class.

Another reason you enjoyed it was that it was the only class were you sat somewhere near Brett.

It was in the middle of the class and you were bored out of your mind.

You looked at Brett when he suddenly looks back up to you,

You raise one of your brows with a small smirk on your face,

He does the same and winks at you,

You roll your eyes sarcastically while giving him a small smile as you started blushing again.

As a result you two started exchanging different faces of sarcasm and flirting.

“Hes not into you, forget about it” you thought to yourself trying to get the idea of you two out of your head.

He suddenly leans towards you with his oh-so-known smirk smeared across his lips.

“Could you explain this? Im having a hard time understanding” He said in a slight flirtatious tone.

“Sure” You said with a small smile.

“Okay, so basically to find X you need to find the square root of 5 times 7..”

You showed him how to solve the equation but couldn’t help but notice it wasn’t the problem he was looking at, he was looking at you.

“Thanks” He said with the smirk still on his face as he turned back to his seat.

The bell rang and you quickly took your stuff and went to your locker, fortunately it was your last period and you couldn’t wait to put in your earphones and just walk home.

You close your locker as Brett suddenly appears leaning on it;

“Hey, I was wondering if you would like to walk home together” He asked.

“Sure, Why not” You said starting to blush, you were freaking out on the inside, why would he ask you to walk home? why is he suddenly trying to get your attention?

You two walked out the gate and started walking down a quiet street near the school.

“So I’ve been talking to Y/B/F/N lately..” He stated

“Oh my gosh” You mumbled under your breath.

“And what did she say?” You asked in a slightly insecure tone.

“Well, I’ll ask you first.

Do you like me?“

You were surprised by his question, it completely threw you off guard.

“I’m gonna kill her” you said sarcastically with an irritated look on your face.

“I hope you answer is a yes cause I really like Y/N”

You had a shocked look on your face, you couldn’t believe Brett Talbot just said that to you.

“YOU like ME?” You asked still quite shocked.

“Yeah, I mean you’re beautiful and your smile is just amazing.

I wanted to talk to you after Y/B/F/N told me what you said because you are always so shy and quite I couldn’t have know if you liked me”

“Well then I guess I do” You said trying to avoid eye contact with him.

“But why me? I mean, You’re so popular and you are friends with so many girls who are so much more prettier than me and way more social, and we never even had a conversation before”

“You caught my eye, don’t underestimate yourself. You are so beautiful and probably more than most of the girls I talk to, I can tell you that you are so much hotter than you think you are. I hear the guys talking about you every once in a while after practice”

At this point you really started blushing.

“How about this, I’ll pick you up tomorrow at 7:30?”

“I’d love that”

—————————————————

{Hope you enjoyed and don’t forget to follow for more imagines,

Send me a message if you want a part 2}

XOXO ♡

Real Numbers and the Real Line

Calculus depends on properties of the real number system.

Real numbers are numbers that can be expressed as decimals.

5 = 5.000…
-¾ = -0.75000…
1/3 = 0.333…
√2 = 1.414…
π = 3.141…

In each example above, the three dots “…” indicate that the sequence of decimal digits goes on forever.

For the first three examples above, the pattern of the digits are obvious, where the subsequent digits are easily known. However, for √2 and π, there is no obvious pattern of their decimal digits.

Real Line
The real numbers can be represented geometrically as points on a number line called the real line.

The symbol ℝ is used to denote either the real number system or the real number line.

Properties of Real Numbers
The properties of real numbers fall into three categories: algebraic properties, order properties, and completeness.

The algebraic properties assert that the real numbers can be added, subtracted, multiplied, and divided (except zero) to produce another real number, and so the rules of arithmetic are valid.

Order Properties
The order properties of the real numbers refer to the order the real numbers appears on the number line.

If x lies to the left of y on the real line, then x is less than y, or y is greater than x, written as x < y, y > x, respectively.

The inequality x ≤ y means either x = y or x < y.

The following are order properties of the real numbers:

The symbol => means “implies” while <=> (seen later) means “equivalent to.”

For Rules 1-4 and 6 (for 0 < a), they also hold if < and > are replaced with ≤ and ≥, respectively.

Note that, for Rules 3 and 4, the rules for multiplying or dividing an inequality by a positive number c preserves the inequality. If the number c is negative, the inequality is reversed.

Completeness Property
If A is any set of real numbers having at least one number in the set, and if there exists a real number y with the property x ≤ y for every x in A, then there exists a smallest number y with this same property.

Therefore, there are no holes on the real line, where every point corresponds to a real number.

The study of infinite sequences will use the property of completeness.

Subsets of the Real Numbers
The set of real numbers ℝ has some special subsets.

1. The set of natural numbers ℕ = {1, 2, 3, 4, …}.
2. The set of integers ℤ = {…, -2, -1, 0, 1, 2, …}
3. The set of rational numbers ℚ, which is the set of numbers that can be expressed as a fraction m/n, where m, n ∈ ℤ and n ≠ 0.

Rational Numbers
Rational Numbers are real numbers with decimal expansion that does either of the following:

1. Terminate: ending with an infinite string of zeros, such as ¾ = 0.75000…, or
2. Repeat: ending with a string of digits that repeat infinitely, such as 23/11 = 2.090909… = 2.̄0̄9̄ . The bar over the digits indicate the pattern of repeating digits.

Real numbers that are not rational are called irrational numbers.

The set of all rational numbers possesses all algebraic and order properties of the real numbers, but it does not possess the completeness property. For example, √2 is irrational, so there is a “hole” on the rational line where √2 should be.

Because the real line has no such “holes,” it is the appropriate setting for the study of calculus.

Intervals
A subset of the real line is called an interval if it contains at least two numbers and all real numbers between any two of its elements.

For example, the set of real numbers x such that x > 6 is an interval, but the set of real numbers such that y ≠ 0 is not an interval, because it consists of two intervals.

If a and b are real numbers and a < b:

1. The open interval from a to b, denoted as (a, b), consists of all real numbers x satisfying a < x < b.

2. The closed interval from a to b, denoted as [a, b], consists of all real numbers x satisfying a ≤ x ≤ b.

3. The half-open interval from a to b, denoted as [a, b), consists of all real numbers x satisfying a ≤ x < b.

4. The half-open interval from a to b, denoted as (a, b], consists of all real numbers x satisfying a < x ≤ b.

Note that, hollow dots are used to indicate endpoints that are not included in the interval, and the solid dots are used to indicate endpoints of the interval that are included. The endpoints are also called boundary points.

The above type of intervals are called finite intervals, such that each interval has a finite length of b – a.

Intervals with infinite length are called infinite intervals.

The following are the infinite intervals (a, ∞) and (-∞, a]:

The whole real line ℝ is an infinite interval denoted as (-∞, ∞).

Infinity ∞ does not denote a real number, and so it is never allowed to belong to an interval.

Union and Intersection of Intervals
The symbol ⋃ is used to denote the union of intervals.

A real number is in the union of intervals if it is in at least one of the intervals.

For example, [1, 3) ⋃ [2, 4] = [1, 4]. Even though 3 is not included in the first interval, it is included in the second interval, and so the union of these two intervals is simply from 1 to 4, inclusive.

The symbol ⋂ is used to denote the intersection of intervals.

A real number is in the intersection of intervals if it is in every one of those intervals.

For example, [1, 3) ⋂ [2, 4] = [2, 3). Even though 4 is included in the second interval, and 1 is included in the first interval, they are not included in both intervals.

Whenever “and” is mentioned in conditions for intervals, it will be one interval. Whenever “or” is mentioned in conditions for intervals, it will be a union of intervals.

The Absolute Value
The absolute value, or magnitude, of a number x, denoted as |x|, is defined as the following:

The vertical lines in the symbol |x| are called absolute value bars.

For example, |3| = 3, |0| = 0, and |-5| = 5.

Note that, √a always denotes the non-negative square root of a, and so the alternative definition for |x| is |x| = √x². It is important to remember that √a² = |a| and not just a, unless it is known that a ≥ 0.

Geometrically, |x| represents the non-negative distance from x to 0 on the real line.

In general, |x – y| represents the non-negative distance between x and y on the real line, since this distance is the same as the distance between x – y and 0.

The following demonstrates |x – y| = distance from x to y:

Properties of Absolute Value
The absolute value function has the following properties:

Equations and Inequalities Involving Absolute Values
The equation |x| = D, where D > 0, has two solutions: x = -D and x = D, which are two points on the real line that lie at distance D from the origin 0.

Equations and inequalities involving absolute values can be solved algebraically by using cases according to the definition of absolute value. Another way to solve them is geometrically interpreting absolute values as distances.

For example, the inequality |x – a| < D means the distance from x to a is less than D, and so x must lie between a – D and a + D, or a must lie between x – D and x + D.

If D is a positive number, then:

1. |x| = D <=> either x = -D or x = D
|x – a| = D <=> either x = a – D or x = a + D

2. |x| < D <=> -D < x < D
|x – a| < D <=> a – D < x < a + D

3. |x| ≤ D <=> -D ≤ x ≤ D
|x – a| ≤ D <=> a – D ≤ x ≤ a + D

4. |x| > D <=> either x < -D or x > D
|x – a| > D <=> either x < a – D or x > a + D

PDF reference: 27/1

Objectives

1. Writing repeating decimals.
2. Converting fractions into repeating decimals.
3. Converting repeating decimals into fractions.
4. Solving linear inequalities and graphing the solution set.
5. Solving quadratic inequalities.
6. Solving absolute value equations and inequalities.
7. Using the Triangle Inequality to prove other inequalities.

Show that each of the following numbers is a rational number by expressing it as a quotient of two integers:

a) 1.323232… = 1.3̄2̄
b) 0.3405405405… = 0.34̄0̄5̄

a)

Let x = 1.323232…

Then the non-decimal digit is subtracted from both sides.

x – 1 = 0.323232…

Then 100 is multiplied on both sides of the original equation to get one repeating pattern on the non-decimal side.

100x = 132.323232… = 132 + 0.323232… = 132 + x – 1

Using algebraic techniques forms the decimal into a fraction and hence prove the number is rational.

100x = 132 + x – 1
99x = 131
x = 131/99

b)

Let x = 0.3405405405…

Since the non-repeating digit is in the decimal side, a multiple of 10 must be multiplied to make it into a non-decimal digit.

10x = 3.405405405…

Then the non-decimal digit can be subtracted from both sides.

10x – 3 = 0.405405405…

Then 10000 is multiplied on both sides of the original equation to get one repeating pattern on the non-decimal side.

10000x = 3405.405405405… = 3405 + 0.405405405… = 3405 + 10x - 3

Using algebraic techniques forms the decimal into a fraction and hence prove the number is rational.

10000x = 3405 + 10x – 3
9990x = 3402
x = 3402/9990 = 63/185

Express the following rational numbers as a repeating decimal. Use a bar to indicate the repeating digits:

a) 2/9
b) 1/11

a)

Using long division, it is found that 2/9 = 0.222… = 0.2̄ .

b)

Using long division, it is found that 1/11 = 0.090909… = 0.0̄9̄ .

Express the following repeating decimal as a quotient of integers in lowest terms:

a) 0.1̄2̄
b) 3.27̄

a)

Let x = 0.121212…

Since there are no non-repeating digits, many steps are skipped and now 100 is multiplied on both sides to get one repeating pattern on the non-decimal side.

100x = 12.121212… = 12 + 0.121212 = 12 + x

Using algebraic techniques forms the decimal into a fraction and then simplified into its lowest terms.

100x = 12 + x
99x = 12
x = 12/99 = 4/33

b)

Let x = 3.2777…

Since there is a non-repeating digit on the decimal side, 10 is multiplied on both sides.

10x = 32.777..

The non-repeating digits are subtracted from both sides.

10x – 32 = 0.777…

Now the original equation is multiplied by 100 to get one repeating pattern on the non-decimal side.

100x = 327.777… = 327 + 0.777… = 327 + 10x – 32

Using algebraic techniques forms the decimal into a fraction and then simplified into its lowest terms.

100x = 327 + 10x – 32
90x = 295
x = 295/90 = 59/18

Solve the following inequalities and express the solution sets in terms of intervals. Graph their intervals.

a) 2x – 1 > x + 3
b) -x/3 ≥ 2x - 1
c) 2/(x – 1) ≥ 5

a)

2x – 1 > x + 3
x – 1 > 3
x > 4

Solution: (4, ∞)

b)

-x/3 ≥ 2x – 1
x ≤ -6x + 3
7x ≤ 3
x ≤ 3/7

Solution: (-∞, 3/7]

c)

This inequality has x in the denominator, and so it is possible for x to be undefined at a certain point on the real line.

The inequality will be written such that all terms are on one side and then simplified into one fraction.

2/(x – 1) ≥ 5
2/(x – 1) – 5 ≥ 0
(2 – 5x + 5)/(x – 1) ≥ 0
(7 – 5x)/(x – 1) ≥ 0

The numerator is examined to determine when it equals 0.

7 – 5x = 0
x = 7/5

The denominator is examined to determine when it equals 0.

x – 1 = 0
x = 1

Since the fraction is undefined when x = 1, the interval will have a round bracket on 1 and a square bracket on 7/5.

Solution: (1, 7/5]

Solve the following systems of inequalities:

a) 3 ≤ 2x + 1 ≤ 5
b) 3x – 1 < 5x + 3 ≤ 2x + 15

a)

First, the left inequality is solved:

3 ≤ 2x + 1
2 ≤ 2x
x ≥ 1

Then the right inequality is solved:

2x + 1 ≤ 5
2x ≤ 4
x ≤ 2

Therefore, since x ≥ 1 and x ≤ 2, the interval is [1, 2].

b)

First, the left inequality is solved:

3x – 1 < 5x + 3
-4 < 2x
x > -2

Then the right inequality is solved:

5x + 3 ≤ 2x + 15
3x ≤ 12
x ≤ 4

Since x > -2 and x ≤ 4, the interval is (-2, 4].

Solve the following quadratic inequalities:

a) x² – 5x + 6 < 0
b) 2x² + 1 > 4x

a)

x² – 5x + 6 < 0
(x – 2)(x – 3) < 0
x = 2, 3

Drawing a number line with labeled solutions, points between -∞ and 2 are positive, points between 2 and 3 are negative, and points between 3 and ∞ are positive.

Therefore, (2, 3).

b)

2x² + 1 > 4x
2x² – 4x + 1 > 0

The quadratic formula is used to determine the solutions.

x = 1 ± √2/2

(x - 1 - √2/2)(x - 1 + √2/2) > 0

Drawing a number line with labeled solutions, points between -∞ and 1 - √2/2 are positive, points between 1 - √2/2 and 1 + √2/2 are negative, and points between 1 + √2/2 and ∞ are positive.

Therefore, the solution is the union of the intervals (-∞, 1 - √2/2) ⋃ (1 + √2/2, ∞).

Express the set of all real numbers x satisfying the following conditions as an interval or a union of intervals.

a) x ≥ 0 and x ≤ 5
b) x < 2 and x ≥ -3
c) x > -5 or x < -6
d) x ≤ -1
e) x > -2
f) x < 4 or x ≥ 2

a)

Since “and” is used, the interval must satisfy when x ≥ 0 and when x ≤ 5.

[0, 5]

b)

Since “and” is used, the interval must satisfy when x < 2 and when x ≥ -3.

[-3, 2)

c)

Since “or” is used, the interval must satisfy when x > -5 or x < -6.

(-∞, -6) ⋃ (-5, ∞)

d)

x ≤ -1 means that the interval contains all real numbers such that x is less than or equal to -1.

(-∞, -1]

e)

x > -2 means that the interval contains all real numbers such that x is greater than -2.

(-2, ∞)

f)

Since “or” is used, the interval must satisfy when x < 4 or x ≥ 2, which is just the real line.

(-∞, 4) ⋃ [2, ∞) = (-∞, ∞)

Solve the following inequality and graph the solution set.

3/(x – 1) < -2/x

Bring all terms to one side.

3/(x – 1) + 2/x < 0
(3x + 2x – 2)/x(x – 1) = (5x – 2)/x(x – 1) < 0

Examine the numerator and determine when it is equal to zero.

5x – 2 = 0
x = 2/5

Examine the denominator and determine when it is equal to zero.

x(x – 1) = 0
x = 0, 1

The denominator is undefined when either x = 0 or x = 1 or both.

Testing points between 0, 2/5, and 1 to determine whether it is negative or positive.

Points to the left of zero are negative, points between 0 and 2/5 are positive, points between 2/5 and 1 are negative, and points to the right of one are positive.

Since it is less than zero and not less than or equal to zero, all three endpoints use a round bracket.

(-∞, 0) ⋃ (2/5, 1)

Solve the following inequalities, giving the solution set as an interval or union of intervals.

a) -2x > 4
b) 3x + 5 ≤ 8
c) 5x – 3 ≤ 7 - 3x
d) (6 – x)/4 ≥ (3x – 4)/2
e) 3(2 – x) < 2(3 + x)
f) x² < 9
g) 1/(2 – x) < 3
h) (x + 1)/x ≥ 2
i) x² – 2x ≤ 0
j) 6x² – 5x ≤ -1
k) x³ > 4x
l) x² – x ≤ 2
m) x/2 ≥ 1 + 4/x
n) 3/(x – 1) < 2/(x + 1)

a)

-2x > 4 <=> x < -2 <=> (-∞, -2)

b)

3x + 5 ≤ 8 <=> 3x ≤ 3 <=> x ≤ 1 <=> (-∞, 1]

c)

5x – 3 ≤ 7 – 3x <=> 8x – 3 ≤ 7 <=> 8x ≤ 10 <=> x ≤ 5/4 <=> (-∞, 5/4]

d)

(6 – x)/4 ≥ (3x – 4)/2 <=> 12 – 2x ≥ 12x – 16 <=> -14x ≥ -28 <=> x ≤ 2 <=> (-∞, 2]

e)

3(2 – x) < 2(3 + x) <=> 6 – 3x < 6 + 2x <=> -5x < 0 <=> x > 0 <=> (0, ∞)

f)

x² < 9 <=> x² – 9 < 0 <=> (x – 3)(x + 3) < 0 => x = -3, 3

Drawing a number line with labeled solutions, points between -∞ and -3 are positive, points between -3 and 3 are negative, and points between 3 and ∞ are positive.

Therefore, (-3,3).

g)

1/(2 – x) < 3 <=> 1/(2 – x) – 3 < 0 <=> (1 – 6 + 3x)/(2 – x) <=> (-5 + 3x)/(2 – x) => x = 5/3, 2

Drawing a number line with labeled solutions, points between -∞ and 5/3 are negative, points between 5/3 and 2 are positive, and points between 2 and ∞ are negative.

Since the fraction is undefined when x = 2, 2 is not allowed to be included in the interval.

Therefore, (-∞, 5/3) ⋃ (2, ∞).

h)

(x + 1)/x ≥ 2 <=> (x + 1)/x – 2 ≥ 0 <=> (x + 1 – 2x)/x ≥ 0 <=> (-x + 1)/x ≥ 0 => x = 0, 1

Drawing a number line with labeled solutions, points between -∞ and 0 are negative, points between 0 and 1 are positive, and points between 1 and ∞ are negative.

Since the fraction is undefined when x = 0, 0 is not allowed to be included in the interval.

Therefore, (0, 1].

i)

x² – 2x ≤ 0 <=> x(x – 2) ≤ 0 => x = 0, 2

Drawing a number line with labeled solutions, points between -∞ and 0 are positive, points between 0 and 2 are negative, and points between 2 and ∞ are positive.

Therefore, [0, 2].

j)

6x² – 5x ≤ -1 <=> 6x² – 5x + 1 ≤ 0 <=> 6x² – 3x – 2x + 1 ≤ 0 <=> 3x(2x – 1) – (2x – 1) ≤ 0 <=> (3x – 1)(2x – 1) ≤ 0 => x = 1/3, ½

Drawing a number line with labeled solutions, points between -∞ and 1/3 are positive, points between 1/3 and ½ are negative, and points between ½ and ∞ are positive.

Therefore, [1/3, ½].

k)

x³ > 4x <=> x³ – 4x > 0 <=> x(x² – 4) > 0 <=> x(x – 2)(x + 2) > 0 => x = -2, 0, 2

Drawing a number line with labeled solutions, points between -∞ and -2 are negative, points between -2 and 0 are positive, point between 0 and 2 are negative, and points between 2 and ∞ are positive.

Therefore, (-2, 0) ⋃ (2, ∞).

l)

x² – x ≤ 2 <=> x² – x – 2 ≤ 0 <=> (x – 2)(x + 1) ≤ 0 => x = -1, 2

Drawing a number line with labeled solutions, points between -∞ and -1 are positive, points between -1 and 2 are negative, and points between 2 and ∞ are positive.

Therefore, [-1, 2].

m)

x/2 ≥ 1 + 4/x <=> 0 ≥ 1 – x/2 + 4/x <=> 0 ≥ 0 ≥ (x – x²/2 + 4)/x <=>   0 ≥ (-2/-2)[(x – x²/2 + 4)/x] <=> 0 ≥ (x² – 2x – 8)/(-2x) <=> 0 ≥ (x – 4)(x + 2)/(-2x) <=> (x – 4)(x + 2)/(-2x) ≤ 0 => x = -2, 0, 4

Drawing a number line with labeled solutions, points between -∞ and -2 are positive, points between -2 and 0 are negative, point between 0 and 4 are positive, and points between 4 and ∞ are negative.

Since the fraction is undefined when x = 0, 0 is not allowed to be included in the interval.

Therefore, [-2, 0) ⋃ [4, ∞).

n)

3/(x – 1) < 2/(x + 1) <=> 3/(x – 1) – 2/(x + 1) < 0 <=> (3x + 3 – 2x + 2)/(x - 1)(x + 1) < 0 <=> (x + 5)/(x – 1)(x + 1) < 0 => x = -5, -1, 1

Drawing a number line with labeled solutions, points between -∞ and -5 are negative, points between -5 and -1 are positive, point between -1 and 1 are negative, and points between 1 and ∞ are positive.

Since the fraction is undefined when x = -1 or 1, -1 and 1 are not allowed to be included in the interval.

Therefore, (-∞, -5) ⋃ (-1, 1).

Solve the following:

a) |2x + 5| = 3
b) |3x – 2| ≤ 1

a)

Case 1: x > 0
|2x + 5| = 3 <=> 2x + 5 = 3 <=> x = -1

Case 2: x < 0
|2x + 5| = 3 <=> -(2x + 5) = 3 <=> 2x + 5 = -3 <=> x = -4

b)

Since the question deals with “less than or equal to,” the equivalent form is used.

|3x – 2| ≤ 1 <=> -1 ≤ 3x – 2 ≤ 1

The left inequality is solved first.

-1 ≤ 3x – 2
1 ≤ 3x
x ≥ 1/3

The right inequality is solved last.

3x – 2 ≤ 1
3x ≤ 3
x ≤ 1

Therefore, [1/3,1].

Solve the equation |x + 1| = |x – 3|.

Case 1: x < 0
|x + 1| = |x – 3| <=> -(x + 1) = x – 3 <=> -x – 1 = x – 3 <=> -2x = -2 <=> x = 1

Case 2: x > 0
|x + 1| = |x – 3| <=> x + 1 = x – 3 <=> no solution

What values of x satisfy the following inequality?

Since the inequality uses “less than,” the following equivalent form is used.

-3 < 5 – 2/x < 3 <=> -8 < -2/x < -2 <=> 4 > 1/x > 1

Solve the left inequality first.

4 > 1/x <=> 4x > 1 <=> x > ¼

Solve the right inequality last.

1/x > 1 <=> 1 > x <=> x < 1

Therefore, the values of x that satisfy the above inequality is in the interval (¼, 1).

Solve the following equations:

a) |x – 3| = 7
b) |2t + 5| = 4
c) |1 – t| = 1
d) |s/2 – 1| = 1

a)

|x – 3| = 7

Case 1: x < 0
-(x – 3) = 7 <=> x – 3 = -7 <=> x = -4

Case 2: x > 0
x – 3 = 7 <=> x = 10

Therefore, x = -4, 10.

b)

|2t + 5| = 4

Case 1: x < 0
-(2t + 5) = 4 <=> 2t + 5 = -4 <=> 2t = -9 <=> t = -9/2

Case 2: x > 0
2t + 5 = 4 <=> t = -½

Therefore, t = -½, -9/2.

c)

|1 – t| = 1

Case 1: x < 0
-(1 – t) = 1 <=> 1 – t = -1 <=> t = 2

Case 2: x > 0
1 – t = 1 <=> t = 0

Therefore, t = 0, 2.

d)

|s/2 – 1| = 1

Case 1: x < 0
-(s/2 – 1) = 1 <=> s/2 – 1 = -1 <=> s = 0

Case 2: x > 0
s/2 – 1 = 1 <=> s/2 = 2 <=> s = 4

Therefore, s = 0, 4.

Write the interval defined by the following inequalities:

a) |x| < 2
b) |x| ≤ 2
c) |t + 2| < 1
d) |3x – 7| < 2
e) |x/2 – 1| ≤ 1
f) |2 – x/2| < ½

a)

|x| < 2 <=> -2 < x < 2 <=> (-2, 2)

b)

|x| ≤ 2 <=> -2 ≤ x ≤ 2 <=> [-2, 2]

c)

|t + 2| < 1 <=> -1 < t + 2 < 1 <=> -3 < t < -1 <=> (-3, -1)

d)

|3x – 7| < 2 <=> -2 < 3x – 7 < 2 <=> 5 < 3x < 9 <=> 5/3 < x < 3 <=> (5/3, 3)

e)

|x/2 – 1| ≤ 1 <=> -1 ≤ x/2 – 1 ≤ 1 <=> 0 ≤ x/2 ≤ 2 <=> 0 ≤ x ≤ 4 <=> [0, 4]

f)

|2 – x/2| < ½ <=> -0.5 < 2 – 0.5x < 0.5 <=> -2.5 < -0.5x < 2.5 <=> 5 > x > 3 <=> (3, 5)

Solve the equation |x – 1| = 1 – x.

Case 1: x < 0
-(x – 1) = 1 – x <=> -x + 1 = 1 – x <=> no solution

Case 2: x > 0
x – 1 = 1 – x <=> 2x = 2 <=> x = 1

Additionally, the equation holds if |x – 1| = -(1 – x), since this is when they are always equal to each other. For this to be true, x – 1 < 0, or x < 1.

Therefore, x < 1.

Show that the following inequality holds for all real numbers a and b:

|a – b| ≥ ||a| - |b||

Begin with the Triangle Inequality.

|x + y| ≤ |x| + |y|
<=> |x| + |y| ≥ |x + y|
<=> |x| ≥ |x + y| - |y|

Let x = a – b and y = b.

|x| ≥ |x + y| - |y|
<=> |a – b| ≥ |a – b + b| - |b| = |a| - |b|

Similarly, |a – b| = |b – a| ≥ |b| - |a|.

Then ||a| - |b|| is equal to either |a| - |b| or |b| - |a|, and since |a – b| ≥ |b| - |a| and |a – b| ≥ |a| - |b|:

|a – b| ≥ ||a| - |b||

I’ll always support you no matter what; Tony Stark x teen reader

Hey guys well this was my first Tony Stark oneshot that I had ever done and it was all came from after watching the Janet Jackson’s music video of “Rhythm Nation”. I feel like Tony even though loving that his child is a mini-genius like him, he would always support their dreams no matter if they wanted to go into the same line of work in math/science or do something completely far out from it like dancing or teaching or whatever. No matter what you do in life, never doubt that your parents aren’t gonna be there for you because they will no matter what it is. Be warned of swear words and mean comments.

Originally posted by iwantcupcakes

_______________________________________________

“And so if you take f(x) and divide it by the square root of two you get—” then the bell rang signaling that our instruction was over.  “Okay we’ll pick this lesson up first thing Thursday, and don’t forget to bring in a full advanced statistics equation of your choice for another fellow competitor to solve”. Our coach Professor Gooden said.

I packed up my stuff and put up the lab coats and just before I was about to leave, Professor Gooden stopped me and said,

“Hold on Miss. Stark, could I have a word with you?”

“Umm, now’s not a really good time, I’ve got somewhere else to be right now”.  The man spoke for so long way ahead of normal class time I only had about 10 minutes left.

“No, no this needs to be said now, it won’t take long”.

“Yeah right”. I muttered under my breath as I walked up to him and removed my bag from my shoulder and set it down beside me.

“Miss Stark, lately I haven’t been seeing you coming to our decathlon meetings, just recently last week you showed up and missed every single lesson and exercise we’re planning to do at the Regional’s a few weeks ago. Is there something going on at home? Or anything like that?”

“No sir, everything is fine bye!” I quickly raced out of the building and got into my motorcycle and drove off as fast as I could to the studio.

Keep reading

3

-Anon request (request for Charles adorableness, I think this counts…)

Sometimes -when he was really bored- the professor liked to bend his own rule a bit. Now, Charles Xavier had a terrible habit of *bending* rules, but one in particular: ’Absolutely! I promise that I will never ever read your thoughts without your permission. You can trust me,’- was just too fun to pass up on occasion.

Keep reading

Edmund x reader: Just kiss already!

Anonymous said:
Can I get an Edmund X reader where they’re in a flirtationship? Like they flirt a lot to tease each other, but then one of Edmund’s siblings hear and is just like “just kiss already!” From the other room. I love your blog❤️

~Here it is! I love this prompt, it’s just so cute😍~

“What’s the ordered pair of the square root of seven when X=19?”

You chewed on the end of your pencil, bored out of your mind. “Umm…” You started, straightening up on Edmund’s bed. “Six? No, wait, thirteen. That’s not it, no, it’s forty-”

Edmund interrupted you with a slightly amused sigh. “Y/n, are you sure you’re paying attention?” He asked with a smirk. You rolled your eyes. You knew where this was going.

“I mean, if I were you, I wouldn’t be able to resist this dashingly handsome face either.” Edmund said, raising an eyebrow flirtatiously. “But we DO have to work, you know.”

You groaned and nudged Edmund playfully. “Not only are you dashingly handsome, but also very modest indeed.” You replied sarcastically.

Edmund’s smirk widened. “Oh, but that’s just it,” Edmund began, propping himself up on the bed with one arm in order to look semi-seductive, “I AM modest. But YOU are also quite the cute little button, aren’t you?”

You leaned into Edmund’s pillows, crossing your arms in mock-annoyance. This was normal behavior for the two of you. “But buttons aren’t that cute at all; they’re more plastic-y and stiff than cute.” Edmund sat up, shaking his head and moving his algebra book from the bed.

”Ah, my dear Y/n, you’re just in denial.” He paused, and you knew a cheesy comment was brewing in his head. “In fact, you’re so cute that even Grumpy Cat said yes.”

You laughed at Edmund’s attempt at a pick-up line. “Okay. I see you want to play dirty.” You said, rolling up your sleeves. “Well then. You are so cute that the CEO of Beanie Babies asked if they could name a stuffed toy after you.” Edmund smirked again, prepared to out-do you. “Y/n, you are so cute that-”

“MY GOD!”

The sudden noise from the room across the hall made you both jump.

“Just kiss already, will you?”

Peter.

You both had totally forgotten that he was in the next room revising. “Uh-sorry for bothering you, Pete.” You yelled, loud enough for him to hear through his closed door.

“Yeah, yeah. Why don’t you and Ed just go off and make out somewhere or whatever it is that you do?”

You didn’t even have to look at Edmund to know that his entire face had turned a bright shade of Crimson. It reminded you a bit of a turnip or a ripe tomato. “Uh,” Edmund said, turning to face you and scratching the back of his neck. “N-never mind my brother, he’s an idiot.”

You smiled, looking down to hide your blushing cheeks. “I don’t think he is, actually.” Edmund paused for a second. “What?” You cleared your throat awkwardly. “Well, I um…I think he caught on t-to something.”

Edmund immediately got the hint. In an instant his demeanor changed from that of an embarrassed piglet to that of sly and ambitious fox.

“Well then,” He purred, leaning closer to you so your noses were an inch apart. “I’m sure you won’t mind if we-for once-take Peter’s advice?” You smirked, slowly gaining confidence and leaning in a little yourself. Your noses touched. “Not at all.” And with that, Edmund kissed you.

More Than You Ever Wanted to Know About Math: Solids of Revolution

It’s sometimes useful (or necessary!) to know the volume of an object of irregular shape. There’s a few ways to figure this out. One of them applies to objects that can be classed as solids of revolution - that is, those that have a shape that can be produced by rotating a profile around an axis.

You can think of a solid like this as being a stack of discs of varying sizes. If you slice into it at any point, you get a disc shape whose outer diameter is defined by the uppermost line of the original profile and who inner diameter is defined by the lowermost line of the original profile at that point.

So basically, all you need to find the volume of this solid is to:

  1. Find the volume of a disc, and
  2. Add up all the discs

We know the disc’s outer diameter is defined by the uppermost line of the original profile and the inner diameter by the lowermost line of the original profile. If we have equations for those two lines, we can get a general expression for the area of the disc.

Here, the uppermost line is y=sqrt(x) and the lower line is y=x^2. So at any point along this profile, the outer radius will be the square root of x, and the inner radius will be x squared. Area of a circle is π*r^2, so we can easily get the area of a disc in terms of those equations.

But ultimately, we want the volume of a disc, which means we need to know how thick it is. Really, we want the disc to be as thin as possible - a stack of a lot of thin discs will give us a more accurate total volume than a stack of a few thicker discs. Fortunately, integration allows us to make the discs as thin as we want - we’ll say that each is a slice with an infinitesimal width of dx.

From here, all we need to do is add up the discs by integration. The integral is bounded by the two points where the lines intersect - here, it runs from 0 to 1.

You could also revolve the original shape around the y-axis. If you wanted to do that, you’d have to get your line equations into terms of y and then integrate with respect to y.

Break - 3 (Barry Reader)

Part One Part Two

Originally posted by permeate

Originally posted by smuchshypush

PRESENT

Barry walked into the room they told you were in. You laid there hooked up to three or machines, he couldn’t really tell in his emotional state.

He went over taking your hand tearing up, “Y/N…”

“We have her in a medically induced coma. We’ll keep her that way for a few days so she can heal.” The doctor told him, “It’s going to be touch and go for a little while.”

“Will she recover?” Barry looked at him. The doctor didn’t answer right away, “Is there a chance?”

“There’s always a chance Mr. Allen, but it’s going to depend on how much she wants to fight for it.” The doctor frowned, “I’ve been given authority by her superiors to do whatever it takes.”

Barry nodded looking back to you, “Can I stay?”

“Of course, if her family shows up however…”

“They won’t…they died…” Barry sat down settling in for a long night, “And her Aunt past away a couple years ago…”

Seven Years Ago

“Dr. Wells is going to revolutionize how we think about the world. He’s going to change everything, I just know it.” You listened to Barry talk as you drove him around.

“Okay, whatever you say. I trust your judgement on that,” You told him, “But I’m telling you…there’s this thing in his eyes…gives me the heebeejeebees…”

“Fine…” He smiled at you as you parked, “I guess that sounds reasonable. Maybe he had an off day when you saw.”

“That is a reasonable explination.” You told him as you got out of your car walking toward your house with him. You shut the door watching Barry take off his shoes, “Mom! Dad! Barry and I are going to my room to study! Is it okay if he stays for dinner!?”

“Why can’t you ever just go find them instead of shouting?” You looked at him smiling at you. You could stare at the smile for days and still enjoy it.

“Because I like being a little rebellious from time to time…this just happens to be that time every time.” You told him, “Head up to my room, I’m gonna see what they’re up to.”

“Right.” He started up the stairs, “Can I have glass of water?”

“I’m not your maid!” You glared at him, but again saw that damnable smile, “But I suppose…”

“Thanks, Y/N.” He ran up the rest of the stairs.

You rolled your eyes walking into the kitchen not seeing anyone there, “Huh…”

You got Barry’s water and walked into your father’s office. You frowned seeing the window open, something that was so unlike your father to do. You walked over and shut the window locking it.

You walked into your room handing the water to Barry. He took it as you sat on the bed, “Is it okay if I stay?”

“They’re not home.” You told him pulling your notebook out of your bag.

Barry looked at you, “Is everything okay?”

You looked at him and smiled, “Yeah, I’m sure they just went to the grocery store or something.”

He nodded and reassured you as you both opened your books. You struggled with math and Barry was a genius it seemed. You didn’t struggle so much that you really needed a tutor, but you liked Barry. Like, liked liked him, and no matter what you did to catch his attention he didn’t seem to notice.

“Oh my god my eyes are going to fall out if I keep looking at this book.” You shut your eyes and leaned your head on his shoulder.

“It’s not that bad…” he looked at you, “You just have to find the average of the data set, X.”

“Oh yeah… cause with all these square roots and divisions…it’s easy.” You told him sarcastically looking up into his eyes. You blushed as he smiled and stared into your eyes, “Uh…”

His twinkled at you, “What?”

“Nothing…” You sat up taking your head from his shoulder, “Sorry…I should focus…”

“Breaks are good for the mind. Sometimes it helps you focus better.” His hand fell on yours.

You looked down at your hands then to his face, “Barry…”

“I’m stupid, Y/N…you get Bs on your test. You don’t need help.” He smiled at you, “I like coming over and being around you.”

You blushed and smiled, “Well…I didn’t think you were getting my hints…”

“Oh I got them…” He laughed, “Believe me, I got them.”

“Then…what do we do…now?” Your hand flipped over and you laced your fingers with him.

“Well…” He smiled leaning toward your face, “I’d like to come over more often…without statistics.”

You licked your lips as you felt his hot breath on your lips. You braced yourself for the kiss that was sure to come.

DING DONG

Your eyes sprung open and you both pulled away from one another, “I…should…”

“Yeah…” He nodded watching your get up as he ran a hand through his hair.

You took a deep breath as you ran down the stars. You stopped just outside of the door seeing red and blue flashers. You opened the door seeing Officer Joe, “Uh…are you here for, Barry, Mr. West? I can go get him.”

Joe took a deep breath looking up at the top of the stairs seeing Barry, “No…I’m not here for Barry, Y/N. I’m here to take you to the station.”

You looked at him surprised, “Why?”

“Everything will be explained there, but I need you to come with me.” He told you and looked up at Barry, “Son, you need to get your things and go home.”

“Joe?” Barry walked down looking at him, “What happened?”

You looked at Barry then to Joe, your heart going to your throat, “Did…did something happen to my parents?”

Joe sighed, “Please grab your things Barry…You too Y/N.”

You sighed reaching over for your coat as Barry ran up stairs. You could feel the tears coming already. They didn’t just come and collect you if it wasn’t something bad.

“Joe…” Barry came down with his bag, “I want to come…I won’t get in the way…but…”

“Barry…” Joe started to protest.

“Officer West…” They both looked at you, “I wouldn’t mind having a friend nearby…if it’s okay…”

Joe sighed and nodded, “Alright.”

He loaded you both up in the back of his squad car and drove you to the station. You felt Barry take your hand as you stared out the window. You were glad he was here, he knew this feeling you were sure of it.

You barely remembered walking into the station, just that you were sat facing that awful golden wall. Joe had asked Barry to sit outside until they were done talking to you. You kept seeing him glance over at you. Finally Joe came back to you.

“Y/N…something did happen…” You watched his mouth move catching words like, parents…murdered…suspects caught, “Y/N?”

“They’re dead?” You looked at him blankly, “…I have to go…I…I need to call them.”

“Y/N…” He stood up with you, “I’m so sorry…”

“No…” You shook your head tears coming to your eyes, “No, I need to call them. They’re going to be worried…they need…they need to know where I’m at…”

“Your Aunt is on the way…we didn’t know if they were going to come to the house. She’s going to meet us here, you have to wait.” Joe told you, “Your Aunt is going to identify the bodies…”

You shook your head, “No…no, they can’t …I just saw them this morning.”

Joe took you into his arms as you broke down crying. That was the night everything changed. Your Aunt did come and take guardianship of you. She didn’t have children, so she moved into your home.

Barry tried to visit, but you didn’t really want to see anyone. He tried to talk to you at school, but even there you didn’t want to be around anyone. You pushed everyone out, tested out earlier and ran never looking back.

PRESENT

The heart monitor was what you heard first as your blurry vision started to focus. You looked over at Barry sleeping. You tried to speak but couldn’t.

You reached up feeling the breathing tube. You made a disgruntled noise as you reached for the pager on the bed remote. You sat there staring at the ceiling until a nurse came in.

Barry woke up when the nurse started talking, “There you are sweetie. Just try to relax, I can’t get that out until the doctor approves it. Just wait.”

Barry looked at you and stood up as the nurse left, “Y/N, I was so worried…”

You stared at him and recoiled your hand when he tried to take it. He looked into your eyes finding confusion and fear. When the doctor came in Barry stepped out to let them work. He’d been there for three days. This was not how he expected you waking up.

A few hours later he was allowed back inside. The doctor was surprised by your recovery rate, but you still had a long way to go. You looked over at him in the doorway. He smiled, “Hi…”

“…hi…” He didn’t like how you were looking at him. Something wasn’t right.

“I didn’t mean to scare you earlier.” He stepped inside, “I just…I was so worried…and seeing you awake. I was happy.”

“You…you know who I am?” His eyes widened, “The doctors said I might remember slowly…I had a head trauma, but you know me?”

“Y-yeah.” He nodded, “My name is Barry…we grew up together.”

“Oh…” You nodded slowly, “Thank you for being here…uh…”

He watched you struggle with his name and hurt. He’d just gotten you back, lost you, and now he’s felt like he lost you completely, “Barry…”

Seventeen in class

Wonwoo: *sleeps through whole class*

Mingyu: WHO NEEDS TO GO TO SCHOOL WHEN YOU ARE AS GREAT AS ME?!?!

Vernon: *listens to music instead of doing work* *whispers* Uh, she says she loves my rap…

Jeonghan: *brushing his hair the entire time*

S.Coups: *not even paying attention because he’s staring at Jeonghan*

Dino: *searches through book bag* HYUNG~~~~~!!! I CANT FIND MY MICHAEL JACKSON NOTEBOOK!!! *cries loudly*

Joshua: *comforts Dino because he’s Jisoos 🙏🏻👼🏼*

Jun: *stares off into space*

Seungkwan: *pulls out notebook* *reads board* Find the square root of 59205028 x 30019838 + 4y….

Seungkwan: … *throws book in trashcan* Who needs this when you’re as sassy as me…? BOOYONCE OUT! *struts out the door*

Hoshi: *gets sleepy* *starts nodding off*

DK: *sees Hoshi out the corner of his eye* *whispers* Hoshi fighting!

Hoshi: *jumps out of seat* *screams* FIGHTING!!!!!

The8: *being a good little fairy and takes all of the notes*

Woozi: *is teaching* CAN YOU ALL PAY ATTENTION FOR ONCE?!?!

Vernon: …. why…?

Woozi: *pulls out guitar*

Seventeen: *panics* *runs in all directions*

[Hillwood, 1977]

Miles: So, looks like I’m going to be spend weekend with Pataki. Tutor him in math.

Phil: ….Really?

Gertie: Hmmm…..

Phil: So, you’re allegedly tutoring Pataki in math?

Miles: Yes, sir.

Gertie: Are you good in math?

Phil: What’s the square root of X?!

Miles: Um, I really can’t answer that.

Phil: AHA!

Miles: No see, X is a variable so until you define is parameters the only possible answer is a variable or X, if you prefer. 

Phil: Is that right?

Gertie: Sounds good…will Bob’s parents be home?

Miles: Yes.

Phil: Are they as dumb as he is?!

Miles: I can’t lie. Yes. Yes they are.

Phil: Right answer, that was a trick question. I know they’re dumb. 

Miles: Sooo, I can go?

Phil: You can go. But I’ll be watching the news. And if anything is vandalized, or explodes, or catches on fire, X is gonna equal ME kicking YOUR ass.