Following the beginning of the lecture, define the area function A(z) under y = t4 between the lines t = 2 and t = x. Sketch a proper graph. Explain and find the formula for A(x).

Answers

Answer 1

The area function A(x) under y = t⁴ between the lines t = 2 and t = x is given by A(x) = ∫[2,x] t⁴ dt.

How to find the area?

The area function A(x) represents the area under the curve y = t⁴ between the lines t = 2 and t = x.

To find the formula for A(x), we integrate the function y = t⁴ with respect to t over the interval [2, x].

We start by calculating the definite integral of t⁴ with respect to t:

∫[2,x] t⁴ dt = [(1/5) * t⁵] evaluated from 2 to x

= (1/5) * x⁵ - (1/5) * 2⁵

= (1/5) * x⁵ - 32/5

Therefore, the formula for the area function A(x) is given by A(x) = (1/5) * x⁵- 32/5.

Learn more about area

brainly.com/question/1631786

#SPJ11


Related Questions

What is the image of M(11,-4) using the translation (x,y) →x-17, y + 2?
A. M'(-6,-2)
B. M'(6,2)
C. M'(-11,4)
D. M'(-4,11)​

Answers

Answer:

https://cdn.kutasoftware.com/Worksheets/PreAlg/Reflections%20of%20Shapes.pdf

Step-by-step explanation:

pls search this

Answer:

A. M'(-6,-2)

Step-by-step explanation:

11. Justin needs to rent a car to go on vacation. EnvoCar charges $65 and $0.10 per mile. FreedomRide charges $80 and $0.05 per mile.
_________________________
a. How much more does Freedom Ride charge for driving m miles than EnvoCar?
_________________________
b. If Justin’s round-trip distance is 250 miles, which car rental company should he rent from? Explain.

Answers

[tex]envo \: car = 65 + 0.10(m)[/tex]

[tex]freedom \: ride = 80 + 0.05(m)[/tex]

//

I honestly don't know how to do a)

//

[tex]envo \: car = 65 + 0.10(250) = 90.00[/tex]

[tex]freedom \: ride = 80 + 0.05(250) = 92.50[/tex]

He should rent from Envo Car because it would be cheaper.

You have three shirts and four pairs of pants. How many outfits consisting of one shirt and one pair of pants can you make?

Answers

Answer:

3

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

3 x 4 = 12

Researchers in plant growth are investigating the proportions of seedlings that sprout under two environmental settings in a lab experiment. Let pˆC represent the sample proportion of seedlings that sprout in garden C, and let pˆH represent the sample proportion of seedlings that sprout in garden H. For random samples of 100 garden C seedlings and 100 garden H seedlings, the sampling distribution of the difference between sample proportions pˆC−pˆH has σpˆC−pˆH≈0.051. Which of the following is the best interpretation of σPˆC−PˆH≈0.051 ?

Answers

Answer:

E

Step-by-step explanation:

For all random samples of 100 garden C seedlings and 100 garden H seedlings, the average distance of all possible differences between sample proportions  pˆC−pˆH  from the mean of the sampling distribution is approximately 0.051.

9. Which of these was an example of US industrial mobilization for war? (5.1.B) A. Increased factory production of tanks and planes B. Increased farm production of wheat C. Rationing of products, like copper and rubber D. Increased production of automobiles​

Answers

Answer:

A

Step-by-step explanation:

Tanks are the Backbone of the Military, they are needed to destroy the Axis Powers during WW2, they also used Captured Enemy Tanks for studying and Produce New Tanks to Counter them.

Two rectangles we're used to form the following figure. Which measurement is closest to the area of the shaded region of this figure in square inches

Answers

Answer:

44 cm

Step-by-step explanation:

You have to find the area of the bigger square and find the area of the smaller one. (Width x Height). Then subtract the smaller rectangle from the bigher one

Find the value of x

66°
117°

Answers

Answer:

x = 51 degrees

Step-by-step explanation:

Keep in mind, the angles of a triangle add up to 180 degrees.

A flat line also equals 180 degrees.

First, we should find the lower left angle. We know that 117 plus that angle is going to be 180, since it's a flat line.

180 - 117 = 63

Now, we just need to find angle x. (All 3 of our angles should add up to 180, knowing this, we can put it in an equation)

63 + 66 + x = 180

Then, you solve for x:

(63+66) + x = 180

129       + x = 180

-129             -129

               x = 51

Hope this helps :)

Daniel's school is selling tickets to a choral performance. On the first day of ticket sales the
school sold 1 adult ticket and 3 child tickets for a total of $39. The school took in $87 on the
second day by selling 5 adult tickets and 3 child tickets. Find the price of an adult ticket and the
price of a child ticket.

Answers

Answer:

Your answer.

Adult ticket = 12

Child ticket = 9

Thank you. And give my answer as Brainlist answer. Follow me for more

Step-by-step explanation:

{y=5x-7
y=-2x+7 Solve the system by graphing.

Answers

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer: Put both equation into desmos and the crossing point will be (2,3) and the graph will be there.

Step-by-step explanation: 5x-7 = -2x+7                   y = 5(2) - 7

                                             5x = -2x + 7 + 7.              y = 3

                                             5x = -2x + 14

                                             5x + 2x = 14

                                             7x = 14

                                             x = 2

% of 25 shirts is 8 shirts.

Answers

the answer is 32% KSJDSJJDJDJD

Answer:

32% of 25 is 8

Step-by-step explanation:

Which group contains triangles that are similar for brainliest

Answers

Answer:

its the second one of course

Step-by-step explanation: plz mark brainliest

Answer:A

Step-by-step explanation:

Because yes

Compare the number of friends at the beginning of a month and at the end of that month if it decreased by 60 and increased by 80

Answers

Answer:

plus 20 or positive

Step-by-step explanation:

-60+80= 20

positive

PLS PLS help!
Type an equation of a parabola that is moved down 2 units, stretched vertically by a factor of 3, and moved left 5 units.

Answers

9514 1404 393

Answer:

  y = 3x^2 +30x +69

Step-by-step explanation:

Transformations work this way:

  g(x) = k·f(x) . . . . vertical stretch by a factor of k

  g(x) = f(x -h) +k . . . . translation (right, up) by (h, k)

__

So, the translation down 2 units will make the function be ...

  f(x) = x^2  ⇒  f1(x) = f(x) -2 = x^2 -2

The vertical stretch by a factor of 3 will make the function be ...

  f1(x) = x^2 -2  ⇒  3·f1(x) = f2(x) = 3(x^2 -2)

The horizontal translation left 5 units will make the function be ...

  f2(x) = 3(x^2 -2)  ⇒  f2(x +5) = f3(x) = 3((x +5)^2 -2)

The transformed function equation can be written ...

  y = 3((x +5)^2 -2) = 3(x^2 +10x +25 -2)

  y = 3x^2 +30x +69

__

The attachment shows the original function and the various transformations. Note that the final function is translated down 6 units from the original. That is because the down translation came before the vertical scaling.

is it possible to have triangle with 3 cm 6 cm and 7 cm sides if yes then​

Answers

Answer:

No

Step-by-step explanation:

Step-by-step explanation:

Yes it is possible to have a triangle with 3 cm, 6 cm and 7 cm sides because in order to form a triangle the length of two sides of a triangle should exceed the third side as shown below :

3 + 6 > 7

9 > 7( True) ✔

6 + 7 > 3

13 > 3 ( True) ✔

7 + 3 > 6

10 > 6 ( True) ✔

Hope it will help :)

Classify each pair of numbered angles as corresponding, alternate interior, alternate exterior, or none of these.

Drag and drop the choices into the boxes to correctly complete the table.

corresponding alternate interior alternate exterior none of these

Answers

Answer:

From left to right, top to bottom: 1 and 2 are neither, 1 and 2 are neither, 1 and 2 are neither, 1 and 2 are cooresponding angles, 1 and 2 are alterante interior angles.

Answer:

We will go in order.

first-None of them

second-Alternate exterior

third-None of them

forth-Corresponding

and Fifth-Alternate Interior

Step-by-step explanation:

just took test



whats 3squared correct to 5 decimal places​

Answers

Answer:

9.0000

Step-by-step explanation:

3 squared = 3*3 = 9

9 to 5 decimal places = 9.0000

pls mark as brainliest

Select the equation of the line of symmetry shown at the graph.
Answer choices:
X=3
Y=3
X=4
X=2​

Answers

the answer is x=3
hope this helps !

are 7/18 and -21/-56 are equivalent​

Answers

Answer:

yes they are equivalent. if you simplify -21/-56 by dividing it by 3 you will get -7/-21 which equals to 7/21

Help Plz
You are playing a game that requires flipping a coin twice. Use a sample space to determine whether flipping heads and then tails are independent events.

Answers

Answer:

Yes , it is independent

Step-by-step explanation:

independent

Encierra todo los números que sean mayores a 18,031 2 ​

Answers

no se me alludas a saber cual es

Simplify the mathematical expressions and arrange them in order of their values from least to greatest. ↓ ↓ ↓ ↓

Answers

Answer and Step-by-step explanation:

To simplify algebraic expressions, follow the basic rules:

1. Remove brackets or parentheses by multiplying factors;

2. Use exponent rule to remove grouping, if terms have exponents;

3. Add or subtract like terms;

4. Combine constants;

In the expressions above, there only constants and scientific notations, i.e., exponents elevated on a base 10. So, to simplify, we multiply the numbers and add the exponents:

(4.27 x 10⁸)(9.2 x 10⁻⁵) = 39.28 x 10³

(6.96 x 10⁵)(8.43 x 10⁻²) = 58.67 x 10³

[tex]\frac{(7.25.10^{5})(9.36.10^{-7})}{(7.95.10^{-2})(4.13.10^{-3})}=[/tex] 2.07 x 10³

[tex]\frac{(8.32.10^{4})(9.67.10^{1})}{(7.56.10^{11})(5.79.10^{-8})}[/tex] = 1.84 x 10²

[tex]\frac{(1.89.10^{4})(5.92.10^{3})}{(2.74.10^{-2})(4.67.10^{2})}=[/tex] 0.875 x 10⁷

All the exponents are positive, which means, comma "moves" to the right.

The numbers arranged from least to greatest will be

1.84 x 10² < 2.07 x 10³ < 39.28 x 10³ < 58.67 x 10³ < 0.875 x 10⁷

Susan Marciano invested part of her $27,000 bonus in a fund that paid a 12% profit and invested the rest in stock that suffered a 3% loss. Find the amount of each investment if her overall net profit was $1,590.​

Answers

54,000 it you add up all the profits

There are 6 dogs and 12 cats in the backyard. Write the ratio of cats to total animals In 3 ways, in simplest form.

Answers

Step-by-step explanation:

12:18

12 to 18

12/18 = 2/3

Which problem matches the given inequality? d > 12.75 Chelsea spent $12.75. Chelsea spent about $12.75. Chelsea spent less than $12.75. Chelsea spent more than $12.75.

Answers

Answer:

Chelsea spent more than $12.75

Step-by-step explanation:

To solve this problem we should understand the meaning of signs first.

sign (<) → less than

sign (>) → more than

sign (=) → equal to

sign (≤) → Not more than

sign (≥) → At least

If the statement is,

"Chelsea spent more than $12.75"

d > 12.75

Therefore, Chelsea spent more than $12.75 is the correct statement.

Answer:

Chelsea spent more than $12.75.

Step-by-step explanation:

bc ik.

The means and mean absolute deviations of the amount of rain that fell each day in a local city, last week and this week, are shown below. Means and Mean Absolute Deviations of Rainfall Last Week and This Week Last Week This Week Mean 3.5 in. 2.7 in. Mean Absolute Deviation 1.2 in. 0.5 in. Which expression compares the difference of the two means to this week's mean absolute deviation?

Answers

Answer:

0.8 / 0.5

Step-by-step explanation:

Given :

Deviations of Rainfall :

______Last Week ____ This Week

Mean___ 3.5 in. ________2.7 in

MAD ___ 1.2 in _________ 0.5 in

Mean difference = 3.5 in - 2.7 in = 0.8 in

This week's mean absolute deviation = 0.5 in

Mean difference / this week's mean absolute deviation

= 0.8 / 0.5

Answer:

0.8 / 0.5

Step-by-step explanation:

Solve the equation w=cx-h for x.

Answers

Answer:

That's your answer. Let me know if you need an explanation.

w=cx-h
add h to both sides
w+h = cx
divide both sides by c
(w+h)/c = x

answer:
x = (w+h)/c

x² + 2xy ty = 144
(x+y)³= ?

Answers

Answer:

t=144x3+432x2y+432xy2+144y3−x2

2xy2

Step-by-step explanation:

I NEED THIS RN AS FAST AS POSSIBLE! Your teacher decides to split the class into four equal groups with no more than five students in each group. that represents the number of students in the class.

Answers

Total student are 20

NO ONE IS HELPINNGGGG PLZZZZ 30 PTS +brainliest

Answers

Answer:

360

Step-by-step explanation:

all quadrilateral angle sums are 360° no matter how you change it

The length of a rectangle is three times its width.
If the width is represented by x, what is the
perimeter of the rectangle, in terms of x?

Answers

Answer:

perimeter:- 8x

Step-by-step explanation:

since,

length= 3(width)

length= 3x

and, perimeter= 2(l + b)

= 2(3x + x)

= 2(4x)

perimeter = 8x

Other Questions
Choose the sentence with the correct capitalization.Mother and father are visiting my sister.Mother and Father are visiting my sister. Donte ordered the plans shown to build a skateboard ramp. Each unit represents one foot. He wants to keep the same slope of the ramp and extend the base of the triangle three feet. How tall will the ramp be factor completely6x2+8x+2. Fill in the blanks using the correct sign: 2(3x+ )(x+ ) Where have you seen discrimination take place in Canadian Society? Where have you seen and or experienced racism in our society? Go online: Look up a current article about racism in Canada and describe the situation in the article and why its problematic. Be sure to include the headline and the website. movimientosliterarios con su representante y caractersticas 16 Which equations represent a relationship where is a nonlinear function of x? Select all that apply.A. y= 4xB. x = - 6yC. y = |x| + 1D.y=2+1E. x - 5y = 2F.1 1y = + angle DGF = ________ 234 students in 9 different classrooms. What is the ratio of students to classrooms? Products are sold and/or services are provided Darlene's cat had a litter of southern kittens Three of the kittens were black what fraction of the kittens were not black also right this fraction into a division problem 5x +1=4x +7What is x Which of the following statements best explains the trend shown in the data?a. State governments tend to be more responsive to social movements than the federal government because they are able to test out new programs on a smaller scale.b. The growth of social media has enabled movements to accelerate the acceptance of social change at the state level, because these activities are not as successful at the federal level.c. A social movement needs to be approved by a percentage of the states before the federal government will consider acting on the change because of fear of angering the conservative electorate.d. The federal government refuses to use the federal courts to respond to social-reform movements. 1. Carlos tiene un terreno de 30.000 m2, lvende 3/5 del total del terreno y recibe porla venta $27.000.000.000; en 1/3 delterreno restante va a construir una piscinaque tiene de profundidad desde 1,2 metroshasta 1,8 m en forma descendente; en elresto del terreno va a construir una casa.De la informacin, se puede decir que Carlosvendi cada m2 por un valor deA. $1.500.000B. $1.800.000C. $2.100.000D. $2.400.000PROCEDIMIENTO: Hola amigos y amigas me pueden poner estrsllas y corazones si por favor Which of the following is an example of economic globalization?Aa chicken farm supplying eggs to the neighboring villageB.a mobile grocery selling organic food across New York CityC.an on-demand beauty salon that provides home serviceD.a Japanese store selling tea and spices from South AsiaResetNext fill in the blanks1. Hindu deity known as the Absolute _______________________.2. Hindu deity of knowledge and creativity _____________________.3. Hindu deity that represents transformation of the universe ____________________.4. Demon king mentioned in the Ramayana ___________________.5. Hindu deity the represents the creation of the universe ______________________.6. Hindu deity that represents preservation of the universe _____________________. 7. Hindu deity of good health and prosperity ____________________.8. Hindu deity of love and devotion ______________________. which one is less than and greater 4/5 or 6/8 Which of the following would have the least amount of inertia? Assume all the bags are the same size.bag of rocksbag of feathersbag of bricksbag of sand I need help with this question What is the surface area of the triangular prism?A)144 cmcm2B)216 cm2C)225 cm2D)256 cm