Find g(x) if the indefinite integral of f(x) need little help

Find G(x) If The Indefinite Integral Of F(x) Need Little Help

Answers

Answer 1

Answer:

g(x) = 4x² - x

General Formulas and Concepts:

Algebra II

Functions

Function NotationPiecewise Functions

Calculus

Integration

IntegralsIntegral NotationIntegration Constant C

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Step-by-step explanation:

*Note:

Integrating a piecewise function requires you to integrate both parts.

Step 1: Define

Identify.

[tex]\displaystyle f(x) = \left \{ {{8x - 1 ,\ x \leq 4} \atop {31 ,\ x \geq 4}} \right.[/tex]

[tex]\displaystyle \int {f(x)} \, dx = \left \{ {{g(x) + C ,\ x \leq 4} \atop {31x + C ,\ x \geq 4}} \right.[/tex]

Step 2: Find function g(x)

We can see that the 2nd part of the piecewise function already has been integrated:

[Integral] Set up:                                                                                             [tex]\displaystyle \int {f(x)} \, dx ,\ x \geq 4 = \int {31} \, dx ,\ x \geq 4[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]:                 [tex]\displaystyle \int {f(x)} \, dx ,\ x \geq 4 = 31 \int {} \, dx ,\ x \geq 4[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]:                     [tex]\displaystyle \int {f(x)} \, dx ,\ x \geq 4 = 31x + C ,\ x \geq 4[/tex]

To find function g(x), we simply have the same setup:

[Integral] Set up:                                                                                             [tex]\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = \int {8x - 1} \, dx ,\ x \leq 4[/tex][Integral] Rewrite [Integration Rule - Addition/Subtraction]:                       [tex]\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = \int {8x} \, dx - \int {1} \, dx ,\ x \leq 4[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]:               [tex]\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = 8 \int {x} \, dx - \int {} \, dx ,\ x \leq 4[/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]:                   [tex]\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = 8 \bigg( \frac{x^2}{2} \bigg) - x + C ,\ x \leq 4[/tex]Simplify:                                                                                                         [tex]\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = 4x^2 - x + C ,\ x \leq 4[/tex]Redefine:                                                                                                       [tex]\displaystyle g(x) = 4x^2 - x + C ,\ x \leq 4[/tex]

The integration constant C is already included in the answer, so our answer is g(x) = 4x² - x.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration (Applications)


Related Questions

A furniture maker used 2/3 of a can of paint to paint some chairs. He used 1/6 of a can of paint for each chair. How many chairs did he paint?

Answers

Answer:

4 chairs

Step-by-step explanation:

Start with 2/3 can of paint: (2/3)

He used 1/6 of the can to paint each chair: (divided by 1/6)

Now use the 'keep, change, flip' method to get the expression: (2/3x6/1)

Then simplify your answer: (12/3)

Lastly simplify again: (4)

Thus, he painted 4 chairs.

Some help please please

Answers

Answer:

[tex]8\sqrt{2}[/tex]

Step-by-step explanation:

To find the length of an isosceles triangle, you know that the angles of the triangle are 45-45-90, so let's use that triangle theorem.

Therefore, the length of the hypotenuse (BD) is [tex]x\sqrt{2}[/tex], and x is equal to 8 (length of BC).

[tex]x\sqrt{2}[/tex]

x=8

Therefore, [tex]8\sqrt{2}[/tex] would be the length of side BD.

Answer:

oh snap i have this question too sorry cant help :(

Step-by-step explanation:

but i can provide with advice bc is the side down and bd is across us this to your advantage

HELLLLPPPP QUICKKLLLYYYY PLLZZZ VIEW THE QUESTION IN THE PHOTO ATTACHED!!!!

Answers

Answer:

[tex]\sqrt{18a}[/tex]

Step-by-step explanation:

To insert the factor, you must first find its squared value, in this case, 3's squared number is 9 so.....[tex]3=\sqrt{9}[/tex]

Now with square roots, they multiply like any other number

so you end up with[tex]\sqrt{9}*\sqrt{2a} \\\sqrt{9*2a}\\\\\sqrt{18a} <------ ANSWER[/tex]

Please leave a thanks!!!

7/10 of guest were over 25 what is the percentage

Answers

70% of the guests were over 25
70% of the guests were over 25

I am an odd number. Take away one letter and I become even. What number am I?

Answers

Answer:

seven

Step-by-step explanation:

Lol thxx for the points

Pls give brainliest! Also, plz sub to kgirl633 on yt.

The students at Vienna Elementary sold donuts every day at school for 6 months. The table below shows the earnings for the first 6 weeks. If the pattern continues, how much will the students make in week 8?

Pics here

Answers

$100 because it goes 110,100,90,110,100,90

The student made $100 in week 8.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount earned from the first week to 6 weeks.

110, 100, 90, 110, 100, 90

We see that,

Every 3 weeks the amount gets repeated.

So,

7th week = 110

8th week = 100

Thus,

The amount earned in week 8 is $100.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

please help me and solve it

Answers

Answer:

Step-by-step explanation:

I need the correct answer to this problem please

Answers

∫2x+1 =2-5

Answer is ∫2x+1 = -3
This equation has no solutions

Find the equation that represents the proportional relationship in this graph, for y in terms of x.

Answers

Answer:

y = 0.4 x

Step-by-step explanation:

help plsssssssssssssss

Answers

Answer:

Last answer, height is 150 ft

Step-by-step explanation:

from the graph, you can clearly see, when T=3, H=150

Which means The firework is at a height of 150 feet

Answer:

D

Step-by-step explanation:

At 3 seconds, the firework is at a height of 150 feet

Answer is D. third option

The firework is at a height of 150 feet

Which of the following graphs is described by the function given below?
y = 2x2 + 6x + 3
5
101
10
10
-20
20
- 10
10
-10
20-
101
A.
B.
C.
D.
A. Graph A
B. Graph B
O C. Graph C
D. Graph D

Answers

Answer:

Which of the following graphs is described by the function given below?

y = 2x2 + 6x + 3

-A. Graph A

The function y = 2x^2 + 6x + 3 is a quadratic function that has a vertex of (-1.5,-1.5)

How to determine the graph of the function?

The equation of the function is given as:

y = 2x^2 + 6x + 3

Differentiate

y' = 4x + 6

Set to 0

4x + 6 = 0

This gives

4x = -6

Divide by 4

x = -1.5

Substitute x = -1.5 in y = 2x^2 + 6x + 3

y = 2(-1.5)^2 + 6(-1.5) + 3

Evaluate

y = -1.5

This means that the function y = 2x^2 + 6x + 3 has a vertex of (-1.5,-1.5)

See attachment for the graph of y = 2x^2 + 6x + 3

Read more about quadratic graphs at:

https://brainly.com/question/18797214

#SPJ5

Can someone help me? Will make brainiest :)

Answers

Answer:

D

Step-by-step explanation:

BH is perpendicular to AC since an orthocenter is a point at which the three altitudes of a triangle intersect. The altitude of a triangle is that line that passes through its vertex and is perpendicular to the opposite side. Since you know that BH is an altitude due to Point H being an orthocenter, you know that BH is perpedendicular to AC.

I also agree that it is D

What are the steps in multiplying decimals?​

Answers

Answer:

Ignore the decimal points then multiply the numbers that remain. Count the number of decimal places in all of the numbers of the question combined. Place the decimal point so that there are the same number of decimal places in the answer and the question.

Step-by-step explanation:

2/7 divided by 3/4
Amanda

Answers

Answer:

2/7÷3/4=2/7×4/3=8/21

[tex] \rm \ \blue{ \overbrace{ \underbrace{ \tt \color{hotpink} \: \: \: \: \: \: \: \: \: \: answer \: \: \: \: \: \: \: \: \: }}}[/tex]

[tex]\large \color{pink} \frac{8}{21} [/tex]

Step-by-step explanation:

[tex] \huge \color{brown} \frac{2}{7} \div \frac{3}{4} [/tex]

divide by a fraction, multiply by the reciprocal of that fraction

[tex] \large \color{hotpink} \frac{2}{7} \div \frac{4}{3} [/tex]

multiply the fraction

[tex] \huge \color{darkblue} \frac{8}{21} [/tex]

hope it helps

Espai
A house on the market was valued at $224,000. After several years, the value decreased by 9%. By how much did the house's value decrease in dollars? What
is the current value of the house?
Decrease in value:
Current house value:

Answers

Answer:

decrease in value: 20,160

current value: 203,840

Step-by-step explanation:

that is the 9% value decrease of the house


[tex]prove that\ \textless \ br /\ \textgreater \ \frac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \frac { 1 + \sin \theta } { \cos \theta }[/tex]
pls i want the answwr as fast u can
ASAP !


MisterBrainly Answer Please :((((
0r any top user
who will answer correctly he will be a good user
plz answer​

Answers

[tex] \large \bigstar \frak{ } \large\underline{\sf{Solution-}}[/tex]

Consider, LHS

[tex]\begin{gathered}\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } \\ \end{gathered}[/tex]

We know,

[tex]\begin{gathered}\boxed{\sf{  \:\rm \: {sec}^{2}x - {tan}^{2}x = 1 \: \: }} \\ \end{gathered} 

\\ \\ \text{So, using this identity, we get}

\\ \\ \begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - ( {sec}^{2}\theta - {tan}^{2}\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}[/tex]

We know,

[tex]\begin{gathered}\boxed{\sf{  \:\rm \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }} \\ \end{gathered}  \\ [/tex]

So, using this identity, we get

[tex]\begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - (sec\theta + tan\theta )(sec\theta - tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}[/tex]

can be rewritten as

[tex]\begin{gathered}\rm\:=\:\dfrac {(\sec \theta + tan\theta ) - (sec\theta + tan\theta )(sec\theta -tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac {(\sec \theta + tan\theta ) \: \cancel{(1 - sec\theta + tan\theta )}} { \cancel{ \tan \theta - \sec \theta + 1} } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:sec\theta + tan\theta \\\end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1}{cos\theta } + \dfrac{sin\theta }{cos\theta } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1 + sin\theta }{cos\theta } \\ \end{gathered}[/tex]

Hence,

[tex]\begin{gathered} \\ \rm\implies \:\boxed{\sf{  \:\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \:\dfrac{1 + sin\theta }{cos\theta } \: \: }} \\ \\ \end{gathered}[/tex]

[tex]\rule{190pt}{2pt}[/tex]

Pauline wants to sell stainless steel water bottles as a school fundraiser.

She knows that she will maximize profits, and raise $1024, if she sells

the bottles for $28 each. She also knows that she will lose $4160 if she sells the bottles for only $10 each.

Write a quadratic relation to model her profit, P, in dollars, if she sells the bottles for x dollars each.

Answers

Answer:

  P = -16(x -28)² +1024

Step-by-step explanation:

The equation can be written in vertex form as ...

  P = -a(x -h)² +k

where (h, k) is the vertex, and 'a' is a scale factor. We are given the vertex (h, k) = (28, 1024) and another point (x, P) = (10, -4160). Using these points, we can find the value of 'a'.

  -4160 = -a(10 -28)² +1024

  -5184 = -324a . . . . simplilfy

  a = 5184/324 = 16 . . . . divide by the coefficient of 'a'

A suitable quadratic relation is ...

  P = -16(x -28)² +1024

Melllissa owns 4 sets of jewelry. Each set contains 2 earrings, 1 neckles, 1 bracelet, 1 ring. How many pieces of jewelry does Melissa have all together?

Answers

Answer:

The answer is to the problem is 18.

use order of operations 7-2(-7-4)

Answers

Answer:

29

hope this helps

solve this please this equation

Answers

Answer:

x = 80 degrees

Step-by-step explanation:

Draw a line through DG and name the intersection of that line and line AB as K.

By the same side interior angle theorem, GKC is 40 degrees.

By the sum of interior angles of triangle theorem, CGK is 180-70=110 degrees.

By supplementary angle theorem, x = 80 degrees.

line passes through the points (4,-2) and the slope is 5/4 write an equation in slope intercept form

Answers

Answer:

y=5/4x -7

Step-by-step explanation:

Hope this helps!

The sum of the angles of a triangle is 180 degrees. The second angle is 40 degrees more than the first
angle and the third angle is 5 times the measure of the first angle. What is the measure of the largest
angle?

Answers

Answer:

100⁰

Step-by-step explanation:

Let,

First angle = x

Second angle = x + 40

Third angle = 5x

=> x + x + 40 + 5x = 180

=> 7x + 40 = 180

=> 7x = 180 - 40

=> 7x = 140

=> x = 140/7

=> x = 20

Largest angle = 5x = 5(20) = 100⁰

[tex]\huge{\purple{\underline{\underline{\bf{\pink{ANSWER:-}}}}}}[/tex]

First angle = x

Second angle = x + 40

Third angle = 5x

[tex]:\implies\bf{x + x + 40 + 5x = 180} \\ \\ :\implies\bf{7x + 40 = 180} \\ \\ :\implies\bf{7x = 180 - 40} \\ \\ :\implies\bf{7x = 140} \\ \\ :\implies\bf{x = \frac{140}{7} } \\ \\ :\implies\bf{x = 20}[/tex]

The largest angle above is 5x thus,

[tex]:\implies\bf{5x} \\ \\ :\implies\bf{5 \times 20} \\ \\ :\implies\bf{100^°}[/tex]

A jar contains black marbles and green marbles. Sixty percent of the marbles in the jar are green. A number generator simulates randomly selecting 10 marbles from the jar. The number generator is used 12 times and the number of green marbles in each trial is shown in the dot plot.

Which description is correct about the number generator being fair or not?




The number generator is not fair. The dot plot shows 80% of the marbles drawn are green.

The number generator is fair. The dot plot shows a distribution that is skewed right.

The number generator is not fair. In most of the experiments, considerably less than 60% of the selected marbles are green.

The number generator is fair. It shows that 60% of the marbles selected are green most of the time.

Answers

Answer:

The number generator is not fair. In most of the experiments, considerably less than 60% of the selected marbles are green.

Step-by-step explanation:

Run a significant number of times, a fair distribution should be a bell curve  centered on the 6 for 60%

**WILL GIVE BRAINLIEST IF ANSWERED RIGHT** (this is not math but i just put it as math)

Choose all the answers that apply.

Which are benefits of cardiovascular exercise?

decreases the resting heart rate
helps the blood vessels dilate more easily
decreases the stroke volume
weakens the muscles surrounding the lungs
makes the lungs able to fill more completely

Answers

Answer:

Makes the lungs able to fill more

Makes the lungs able to fill more completely and decreases the stroke volume

Let |u| = 10 at an angle of 45° and |v| = 13 at an angle of 150°, and w = u + v. What is the magnitude and direction angle of w?

|w| = 9.4; θ = 72.9°
|w| = 9.4; θ = 107.1°
|w| = 14.2; θ = 72.9°
|w| = 14.2; θ = 107.1°

Answers

Recall that for two vector x and y making an angle θ with each,

x • y = ||x|| ||y|| cos(θ)

If we replace y with x, we see that

x • x = ||x|| ||x|| cos(0) = ||x||²   ⇒   ||x|| = √(x • x)

Using the last identity, the magnitude of w is

||w|| = √(w • w)

but since w = u + v, we have

w • w = (u + v) • (u + v)

The dot product distributes over sums and is commutative, so

w • w = (u • u) + (u • v) + (v • u) + (v • v)

… = ||u||² + 2 (u • v) + ||v||²

… = ||u||² + 2 ||u|| ||v|| cos(θ) + ||v||²

If u has a direction of 45° with the positive x-axis, v has a direction of 150°, then the angle between u and v is |45° - 150°| = 105°. So,

||w|| = √(||u||² + 2 ||u|| ||v|| cos(150°) + ||v||²)

… = √(10² + 2 • 10 • 13 cos(150°) + 13²)

… ≈ 14.2

Using the parallelogram rule for vector addition (see attached sketch), the sum of the angle between w and u and 45° is equal to the direction of w.

If φ is the angle between w and u, then

w • u = ||w|| ||u|| cos(φ)

… = 14.2 • 10 • cos(φ)

but we also have

w • u = (u + v) • u

… = (u • u) + (v • u)

… = ||u||² + ||u|| ||v|| cos(105°)

… = 10² + 10 • 13 • cos(105°)

… ≈ 66.4

Then

14.2 • 10 • cos(φ) ≈ 66.4

cos(φ) ≈ 0.467

φ ≈ 62.1°

and so the direction of w is 62.1° + 45° ≈ 107.1°.

Can someone help Pleasaseee

Answers

Answer:

i think it's 1.8.

Step-by-step explanation:

why? bc if u add 6/20 + 1.5 = 1.8

i think it's 1.8, im not sure, hopefully it's correct!!

Answer:

1.8

Step-by-step explanation:

you just simplify -6/20 into a decimal and you get .3 then you add it to 1.5.

Sue has 100 dimes and quarters. If the total value of the coins is &21.40, how many of each kind of coin does she have?

Answers

Answer:

Let x be the number of dimes and y the number of quarters

x +y = 100

a dime is $0.10 and a quarter is $0.25

0.1x + 0.25y = 21.40 multiply by 100 to remove the decimals

10x + 25y = 2140, From the first equation y = 100 - x and plug it in to the second equation.

10x + 25(100 -x) = 2140

10x + 2500 - 25x =2140

2500 - 15x = 2140

360 = 15x x = 24 and y = 76

There are 24 dimes and 76 quarters

Answer:

76 Quarters = $19.00

24 Dimes = $2.40

$19.00 + $2.40 = $21.40

Step-by-step explanation:

Yaga

PLEASE HELLPPPPPP IDONTKNOWTHISSS

Solve this system of equations using the Substitution method. Don't forget to write your final answer as a coordinate point. You must show all your work.

3x + y = -2

y = 2x + 3

Answers

Solution :

= 3x+y=-2

= Linear equations with two variables have multiple infinite solutions.

= Assuming x=0

then y=-2

= Assuming x=1

then y=-2-3

= y=-5

= Assuming x=2

then y=-2-6

= y=-8

Writing them as coordinate points -

(0,-2),(1,-5),(2,-8)...and so on.

__________________________.

= y=2x+3

Assuming x=0

then y=3

Assuming x=1

then y=2+3

= y=5

Assuming x=2

then y=4+3

= y=7

Writing them as coordinate points -

(0,3),(1,5),(2,7)...and so on.

Answer:

Point Form:

( − 1 , 1 )

Equation Form:

x = − 1 , y = 1

Step-by-step explanation: there you go

One leg of an isosceles right triangle measures 5 inches. Rounded to the nearest tenth, what is the approximate length of the hypotenuse?

2.5 inches
5.0 inches
7.1 inches
9.8 inches
PLZ ANSWER ASAP

Answers

Answer:

C

Step-by-step explanation:

This means that there is another leg of an isosceles triangle that is also 5 inches.

a^2 + b^2 = c^2

a = 5

b = 5

c = ?

c^2 = 5^2 + 5^2                 Combine

c^2 = 25 + 25

c^2 = 50                            Take the square root of both sides.

sqrt(c^2) = sqrt(50^2)

c = sqrt(5 * 5 * 2)                Take out 1 of two factors under the root sign.

c = 5 * sqrt(2)                      The 2 is left over because there is only 1 of them

sqrt(2) = 1.4142

c = 5 * 1.4142

c = 7.07 = 7.1

How do you divide fractions? Can someone please explain step by step to get marked as brainliest!

Answers

When diving fractions, use KFC:

K eep the first fraction the same

F lip the second fraction upside down

C hange the divide sign to a multiply

After, just work it out multiplying the denominators and the numerators together getting your answer

Hope this helped you, have a good day bro cya)

Use KCF:
K: Keep ( keep the first fraction the same)
C: Change (change your division sign to a multiplication sign)
F: Flip (flip your second faction numbers)

Ex.
Equation: 3/5 divided by 2/6
KCF: 3/5 multiplied by 6/2

Hope this helps!
Other Questions
Who did the ram caught in the thicket (Genesis 22:13) represent? which statement best expresses the reason why the southern states decided to secede from the union after the election of 1860? 2. How many different hands of 3 cards hands be chosen from a deck of 52 cards? Ann and Betty shared a sum of money in the ratio 2:3 respectively. Ann Received $120. What was Bettys share? A cable is 40 decimeters long how long is the cable in meters and be sure to include the correct unit Read the excerpt from Good Country People. Mrs. Hopewell liked to tell people...how she had happened to hire the Freemans in the first place and how they were a godsend to her and how she had had them four years. The reason for her keeping them so long was that they were...good country people ...Before the Freemans she had averaged one tenant family a year...Mrs. Hopewell, who had divorced her husband long ago, needed someone to walk over the fields with her; and when Joy had to be impressed for these services, her remarks were usually so ugly and her face so glum... that Mrs. Hopewell would say, If you cant come pleasantly, I dont want you at all, to which the girl, standing square and rigid-shouldered with her neck thrust slightly forward, would reply, If you want me, here I amLIKE I AM. Based on the excerpt, what inferences can be made about the storys setting? Ella ensea y t y tus amigos (52.) __________ en las sillas. Yo (53.) ________ con unos amigo y t (54.)________ al lado de la puerta.Finish the sentence! ram said " why did you help me?" into indirect In the context of the poem, how has America changed over time?Consider the poem's references to Rosa Parks refusing to leave her seat, the murder of Emmett Till and Brown vs Board of Education, and contrast this with the current climate and race relations within America today. How have things changed? In what way have circumstances changed for the better, remained the same or even grown worse?Rosa ParksBY NIKKI GIOVANNIThis is for the Pullman Porters who organized when people saidthey couldn't. And carried the Pittsburgh Courier and the ChicagoDefender to the Black Americans in the South so they wouldknow they were not alone. This is for the Pullman Porters whohelped Thurgood Marshall go south and come back north to fightthe fight that resulted in Brown v. Board of Education becauseeven though Kansas is west and even though Topeka is the birth-place of Gwendolyn Brooks, who wrote the powerful "TheChicago Defender Sends a Man to Little Rock," it was thePullman Porters who whispered to the traveling men boththe Blues Men and the "Race" Men so that they both wouldknow what was going on. This is for the Pullman Porters whosmiled as if they were happy and laughed like they were tickledwhen some folks were around and who silently rejoiced in 1954when the Supreme Court announced its 90 decision that "sepa-rate is inherently unequal." This is for the Pullman Porters whosmiled and welcomed a fourteen-year-old boy onto their train in1955. They noticed his slight limp that he tried to disguise with adoo-wop walk; they noticed his stutter and probably understoodwhy his mother wanted him out of Chicago during the summerwhen school was out. Fourteen-year-old Black boys with limpsand stutters are apt to try to prove themselves in dangerous wayswhen mothers aren't around to look after them. So this is for thePullman Porters who looked over that fourteen-year-old whilethe train rolled the reverse of the Blues Highway from Chicago toSt. Louis to Memphis to Mississippi. This is for the men who kepthim safe; and if Emmett Till had been able to stay on a train allsummer he would have maybe grown a bit of a paunch, certainlylost his hair, probably have worn bifocals and bounced his grand-children on his knee telling them about his summer riding therails. But he had to get off the train. And ended up in Money,Mississippi. And was horribly, brutally, inexcusably, and unac-ceptably murdered. This is for the Pullman Porters who, when thesheriff was trying to get the body secretly buried, got Emmett'sbody on the northbound train, got his body home to Chicago,where his mother said: I want the world to see what they didto my boy. And this is for all the mothers who cried. And this isfor all the people who said Never Again. And this is about RosaParks whose feet were not so tired, it had been, after all, an ordi-nary day, until the bus driver gave her the opportunity to makehistory. This is about Mrs. Rosa Parks from Tuskegee, Alabama,who was also the field secretary of the NAACP. This is about themoment Rosa Parks shouldered her cross, put her worldly goodsaside, was willing to sacrifice her life, so that that young man inMoney, Mississippi, who had been so well protected by thePullman Porters, would not have died in vain. When Mrs. Parkssaid "NO" a passionate movement was begun. No longer wouldthere be a reliance on the law; there was a higher law. When Mrs.Parks brought that light of hers to expose the evil of the system,the sun came and rested on her shoulders bringing the heat andthe light of truth. Others would follow Mrs. Parks. Four youngmen in Greensboro, North Carolina, would also say No. Greatvoices would be raised singing the praises of God and exhortingus "to forgive those who trespass against us." But it was thePullman Porters who safely got Emmett to his granduncle and itwas Mrs. Rosa Parks who could not stand that death. And in notbeing able to stand it. She sat back down. sin(3x)+sin(x)=0 solve for x As a result of the belief in Manifest Destiny in the mid-1800s, westward expansion increased dramatically. Slowed significantly. Neither increased nor decreased. First decreased, then increased. Someone please help i forgot how to do math aaaaaaaaaa Use the claim to answer the question. Claim: Schools should improve the nutritional value of lunches served at school. Which source would provide the most relevant information for someone conducting research before writing a persuasive essay supporting this claim? Can somebody please help me with this true or false algebra 1 question?A relation that pairs each input with exactly one output is a function.True or False The interior angle of a regular polygon IS 180.find the value if its exterior regular polygon which set of integers is in the correct order, from Least to greatest? A. |-8|, 4, -3, 0,1.B. 0, 1, -3, 4, |-8|.C. -3, 0, 1, 4, |-8|.D. |-8|, -3, 0, 1, 4. Write 2^100 as a power with the following base of 32. Please help and quickly please and 20 points with brainelest Thank you I need help i am writing a mystery story and need a title and character names and descriptions. descriptions are so people get a clue of what they look like and do 25.0g of iron is heated to 100.0 and then placed in 50.0 g of water in a insulated calorimeter. the initial temperature of the water is 38.00. the specific heat of water is 4.181j/g and the specific heat if iron is 0.45j/g. what is the final temp of the water and the iron?