Fundamental theorem of calculus
[tex]g(s)=\int\limits^s_6 {(t-t^4)^6} \, dt[/tex]

Answers

Answer 1

Answer:

[tex]\displaystyle g'(s) = (s-s^4)^6[/tex]

Step-by-step explanation:

The Fundamental Theorem of Calculus states that:
[tex]\displaystyle \frac{d}{dx}\left[ \int_a^x f(t)\, dt \right] = f(x)[/tex]

Where a is some constant.

We can let:
[tex]\displaystyle g(t) = (t-t^4)^6[/tex]

By substitution:

[tex]\displaystyle g(s) = \int_6^s g(t)\, dt[/tex]

Taking the derivative of both sides results in:
[tex]\displaystyle g'(s) = \frac{d}{ds}\left[ \int_6^s g(t)\, dt\right][/tex]

Hence, by the Fundamental Theorem:

[tex]\displaystyle \begin{aligned} g'(s) & = g(s) \\ \\ & = (s-s^4)^6\end{aligned}[/tex]


Related Questions

Easy function or not

Answers

Answer:

Problem 9: No

Problem 10: Yes

Step-by-step explanation:

Hello!

Problem 9:

This is NOT a function because one x-value has only one unique y-value. -2 is seen twice and the outputs, y, are given as 6 and 0.5. To be a function, each input has its own unique output. Two different inputs can have the same output.

Problem 10:

This IS a function, all inputs have unique outputs, and no repeating inputs are shown.

Terms:

x - values are also known as input, abscicca

y - values are also known as output, ordinate.


The length and breadth of a rectangular piece of paper are 18 cm and 15 cm respectively. By how much should be length be reduced keeping breadth constant to make area equal to 134 cm².....​

Answers

Answer:

Area of a rectangle = length x breadth

Given:

area = 134 cm²breadth = 15 cm

⇒ 134 cm² = length x 15cm

⇒ length = 134 ÷ 15

               = 8.93333333... cm

Reduction in length = original length - new length

                                 = 18 cm - 8.93333333... cm

                                 = 9.07 cm (nearest hundredth)

Which is greater: 3.5 or 6/5

Answers

3.5 is greater as 6/5 = 1.2

Answer:

3.5

Step-by-step explanation:

6/5 = 1.2

3.5 > 1.2

Triangle ABC is rotated to form ​△A'B'C'​.

The coordinates of point A are (1, 1), the coordinates of point B are (3, 1), and the coordinates of point C are (1, 4).

Which counter clockwise rotation around the origin results in the transformation of ​△ABC​​ to ​△A'B'C'​?



Select from the drop down arrow to choose the correct rotation.
90 degrees
180 degrees
360 degrees

Answers

Answer:

may be 90 degrees for that question

Answer: Rotation of 90

Step-by-step explanation:

HELP ME OUT PLS!!!!!!!!!

Which purchase are people most likely to regularly save a small amount of money for, and then let the value grow over time?

A) going to the movies

B) retirement

C) buying audiobooks

D) going to a concert​

Answers

Answer:

B) retirement

Step-by-step explanation:

Retirement is the only one that makes sense to me when you regularly save a small amount of money, and then letting the value grow over time.

Hope this helps!!

A) Going to the movies

Explanation: Entertainment purposes

A mountain road drops 5.2 m for every 22.5 m of the road. Calculate the angle at which the road is inclined to the horizontal.​

Answers

Answer:

13°

Step-by-step explanation:

sin(Ф)= opposite/ hypothenuse

sin(Ф) =  5.2/22.5

Ф= sin∧-1 (5.2/22.5)

Ф= 13.36°

what's 3/4 divided by 1 1/5

Answers

15/44

Step-by-step explanation:

change the division sign to multiple. flip the numbers 11 and 5 around. multiple 3 times 5 then 4 times 11.

Write an equation of the
line that passes through
the given points (-3,-1)
(2, 2)

Answers

Answer:

[tex]y = \dfrac{3}{5}x + \dfrac{4}{5}[/tex]

Step-by-step explanation:

First, find the slope:

m = (change in y) / (change in x) = rise / run

m = (2 - (-1)) / (2 - (-3)) = (2 + 1) / (2 + 3) = 3/5

Then, write the equation of the line in point-slope form:

y - b = m(x - a)  where  (a, b) is a point on the line

y - 2 = (3/5)(x - 2)

Finally, solve for y:

[tex]y = \dfrac{3}{5}(x - 2) + 2[/tex]

[tex]y = \dfrac{3}{5}x - \dfrac{6}{5} + 2[/tex]

[tex]y = \dfrac{3}{5}x + \dfrac{4}{5}[/tex]

Decide which other to give him prices is better and explain why. Storage locker A rents for $32/yd2 per month. Storage locker B rents for $1.58/ ft2 per week. Assume 1 month = 4 weeks. Which one is better and why.

Answers

Answer:

Locker B

Step-by-step explanation:

When you divide 32 by 3 you get 10.667. Then when you divide that by 4 you get $2.667/ft2 per week.

The Davis family purchased a house last year. They put $20,000 towards a down payment and took out a $265,000 mortgage. Because it was a new home, all the repairs and maintenance were covered under the builder’s warranty, but the Davises want to budget this coming year for unexpected expenses. When estimating costs for home repair and maintenance, a good estimate is to budget 1% of the purchase price of a house. What would be a good yearly estimate of repairs and maintenance for the Davis family’s home? a. $28,500 b. $2,650 c. $2,850 d. $200

Answers

Answer:

2,850

Step-by-step explanation:

I'm not very good with percentages, so this may be incorrect, but 1 ℅ of the total purchase price would be 2850 because 1 ℅ is essential 0.01 x 285,000. 285,000 would be adding the down-payment to the mortgage.

hope this helps

Can someone help me figure out angle a in this circle? thank you!

Answers

Answer:

[tex]m \angle a = 116 \degree[/tex]

Step-by-step explanation:

By inscribed angle theorem:

[tex]m \angle a = \frac{1}{2} \times m \widehat{(BD)} \\ \\ \implies m \angle a = \frac{1}{2} \times 232 \degree\\ \\ \implies \huge { \orange{m \angle a = 116 \degree}}[/tex]

I need help please and please explain your answer.

Answers

Answer:

I think it is B or D

actually it is B i got 100%

Step-by-step explanation:

look at the number line below what point is marked on the number line​

Answers

Answer:

-2.5

Step-by-step explanation:

The point is between -2 & -3

What is the horizontal difference between (4, 8) and (-2, 2)?

Answers

Answer:

6 units

Step-by-step explanation:

the horizontal difference is the distance between the x values of both points. we know the distance between 4 and -2 is 6.

If a boat 26’ long by 8.5’ wide and a can is 4.75” tall by 2.4” wide how many cans can fill the boat?

Answers

Answer:

19

Step-by-step explanation:

what is (1/8) to the power of 8

Answers

Answer:

5.96 when rounded to the nearest hundredth

Step-by-step explanation:

A bag of apples weighs
4.25 pounds. How many
ounces
does the bag of apple
weigh?

Answers

Answer:

68 ounces

Step-by-step explanation:

Since 1 pound is 16 ounces, if you use the comparison 1 lb/16 oz=4.25 lb/x oz, you could see that by multiplying 4.25x1, you get 4.25 lbs. So you do the same for the ounces. 16x4.25=68 oz.

The bag of apple weigh is 68 ounces .

What is unit of measurement?

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

According to question

A bag of apples weighs = 4.25 pounds

and  1 pounds = 16 ounces

Therefore ,

4.25 pounds = 16*4.25 ounces

                     = 68 ounces

Hence, the bag of apple weigh is 68 ounces .

To know more about unit of measurement here :

https://brainly.com/question/15402847

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Pls help me get this. Right

Answers

Answer:

26 units

Step-by-step explanation:

so the horizontal distance between the two points is 24 units while the vertical distance is 10 units.

hence, we can use the pythagorean theorem to find the length of the diagonal.

the answer is equal to sqrt( 24^2 +10^2)

the answer is 26 units

also you should always remember that the diagonal is always greater in length than both the vertical and horizontal sides.

make sure to ask if you need any further guidance :)

The answer is C
26 units

Joel is selling a motorcycle for $2,535. He bought the
motorcycle two years ago and paid $4,721 for it. It depreciated
35% during the two years. Is he losing money or making money
on this sale?
18. Willa is buying flowers for a large garden project. She plans

Answers

Answer:

Joel is losing money.

Step-by-step explanation:

4,721-35%=?

First, convert the percentage into a decimal.

35%=35/100=.35

Then multiply 4721 by .35 which is 1652.35

At last, subtract 4,721 by 1652.35= 3068.65

Using the information in the table, draw a
graph of the relationship between t, the
time, and d, the total distance traveled by
the train, for a trip that lasted from 0 to 7
hours.

Answers

Answer:

Step-by-step explanation:

Given y = 2x2 - 5x - 9, what is the value of y when x = 2?

Answers

Answer:

Step-by-step explanation:

y = 2(2)2 - 5(2) - 9

= 8 - 10 - 9

= -11.

Find the reciprocal of [tex]$\frac{1}{-2} \cdot \left(-\frac{1}{3}\right) \cdot \frac{1}{-4} \cdot \left( -\frac{1}{5} \right)$.[/tex]

Answers

Answer:

120

Step-by-step explanation:

Lets take it step by step!

Step 1 : first mutiply -1/2 * -1/3

-1/2 * -1/3 = 1/6

(remember to mutiply fractions we have to mutiply there denominator and numerator together)

Step 2 : then move on and multiply 1/6 * -1/4

1/6 * -1/4 =

-1/24

Step 3 :  Next we have to go and multiply -1/24 by -1/5

-1/24 * -1/5 =

1/120

Step 4 :  Finally we switch the numerator and denominator to find its reciprocal which is :

120!

A company rents moving trucks for $45 plus $0.75 per mile. write an equation that relates the cost C and the miles driven, x. Calculate the cost of
renting a truck for one day, and driving it 110 miles.

Answers

The equation we would use here would be 45 + 0.75x = C

This is because we have a flat fee of $45 and you are being charged $0.75 per mile, so it depends on how many miles were driven.

To find out how much it would cost if it were to drive 110 miles, we simply put 110 in place of x;

45 + 0.75(110) = C

And now we solve!

45 + 82.50 = C

$127.50

Hope this helps!


What is the distance between points (-6, -7) and (-1,5) on the coordinate plane?

Answers

Answer:

The answer is C. 13

Step-by-step explanation:

What happens to the mode of the data set shown below if the number 8 is added to the data set?

12,8,13,9,10,10,15,14,13,6,40,11,15,15,8,7

A. There is no mode.
B. The mode will not change.
C. There will be two modes.
D. The mode increases by 6.
PLEASE HURRY

Answers

Answer:

d the mode increase by 8

Step-by-step explanation:

mode is affected due to change in origin by same constant value

Answer:

C

Step-by-step explanation:

There will be 2 modes because 15 and 8 would both repeat 3 times.

GUYS HELP ASAP
CHECK THE ATTACHED PHOTO

Answers

Answer:

As they triangles are congruent, we can say that, angle A = angle O

So, angle A = 105+25 =130

A = 180 - 130 = 50° all angles in a triangle add up to 180)

Soo 50° is the answer,

I'm not too sure about it but I think this is correct, hope this helps, correct me if I'm wrong....

Which numbers are perfect squares? Check all that apply.
1
2
16
18
32
44
94
100

Answers

Answer:

1, 16, 100

Step-by-step explanation:

Answer:

other persons right i took the test and got it right so 1, 16, and, 100

Step-by-step explanation:

Brent plays three sports: basketball, baseball, and soccer. He calculated the mean absolute deviation of the points he scored in each season.

basketball: mean absolute deviation of 4.6

baseball: mean absolute deviation of 3.5

soccer: mean absolute deviation of 1.2

In which sport were his scores the most spread out?


baseball

soccer

basketball

Answers

Answer:

basketball

I hope this is useful

Answer: (C) Basketball

Step-by-step explanation: I took the test and that is the answer.

How to solve by completing the square??

x^2 +8x=33

Answers

We are given the equation x² + 8x = 33, and we need to solve it from completing the square, for which we will be following the below steps

Step 1 :- First, notice, what's the coefficient of x², if it's 1, then proceed to step 2, if not then divide both sides by the coefficient of x²

[tex]{:\implies \quad \sf x^{2}+8x=33}[/tex]

Step 2 :- Here, we need to develop a whole square in both sides somehow, so we have the coefficient of x, so add the square of half of coefficient of x on both sides :

[tex]{:\implies \quad \sf x^{2}+8x+{\bigg(\dfrac82\bigg)}^{2}=33+{\bigg(\dfrac82\bigg)}^{2}}[/tex]

Simplify both sides now :

[tex]{:\implies \quad \sf x^{2}+8x+(4)^{2}=33+(4)^{2}}[/tex]

Step 3 :- So now, here LHS is in the form of a² + 2ab + b², so we can just replace it by (a + b)², and we will keep simplifying RHS

[tex]{:\implies \quad \sf (x+4)^{2}=33+16}[/tex]

[tex]{:\implies \quad \sf (x+4)^{2}=49}[/tex]

[tex]{:\implies \quad \sf (x+4)^{2}=(\pm 7)^{2}}[/tex]

Step 4 :- As, power on both sides is 2, so we can just equate the bases

[tex]{:\implies \quad \sf x+4=\pm 7}[/tex]

Step 5 :- Equating x + 4 to 7, will yield x = 3, and equating it to -7, will yield x = -11, so we are now left with

[tex]{:\implies \quad \boxed{\bf{x=-11,3}}}[/tex]

A bowling ball has an outside layer, and an inner core. One type of bowling ball has a diameter of 8 inches, and the outside layer is an inch thick. what is the volume of the outsdie layer

Answers

diameter = 8

radius = 4

outside layer is an inch thick so

radius is 3

volume of a bowling ball is

volume of a sphere which is

4/3 * Pi * radius cubed =

(4/3)*Pi*27=

answer = 82447.96 in^3 or inches cubed

socraticorg

The volume of the outsdie layer whose  diameter is of 8 inches is 290 cubic inches.

What is Three dimensional shape?

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that  bowling ball has an outside layer, and an inner core

One type of bowling ball has a diameter of 8 inches

We have to find the volume of the outsdie layer

Radius of the ball is 4 inches.

Volume of sphere = 4/3πr³

=4/3×3.4×4³

=4/3×3.4×64

=290 cubic inches

Hence, the volume of the outsdie layer whose  diameter is of 8 inches is 290 cubic inches.

To learn more on Three dimensional figure click:

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