Jim and two friends are sharing the cost to buy snacks for a birthday party this weekend.

If f is the function given by f(x)= integral from (4 to 2x) of sqrt(t^2-t)dt then f'(2) =?

sammy [17]

Hello,

$f(x)= \int\limits^{2x}_4 {\sqrt{t^2-t} \, dt \\

 \dfrac{df(x)}{dx} = \dfrac{df(x)}{d(2x)} * \dfrac{d(2x)}{dx} =2* \sqrt{(2x)^2-2x} \\

f'(2)=2 * \sqrt{4^2-4} =2* \sqrt{12} =4 \sqrt{3}$

3 0

2 years ago

Read 2 more answers

There are two other ways to write this fraction.<br><br> −15/29<br> List them in the space below.

ludmilkaskok [199]

Answer:

-30/58 & -45/87

Step-by-step explanation:

The first answer is just multiplying the original by 2.

The second one is being multiplied by 3.

The multiplicated moves DO NOT CHANGE THE VALUE OF THE ORIGINAL FRACTION, meaning that they are equivalent. :))

6 0

2 years ago

Suppose that the relation H is defined as follows.

sergiy2304 [10]

Answer:

domain = { 4, -2, 6, 9 }

range = { -3, 6, 0, 9 }

Step-by-step explanation:

(x, y)

x = domain

y = range

5 0

2 years ago

Clark and Lindsey Banks have agreed to purchase a home for $225,000. They make a down payment of 15%. They have obtained a mortg

katrin [286]

Answer:

Mortgage total is $387,400.11.

Step-by-step explanation:

Thee monthly mortgage monthly payment is first calculated using the following formula:

M = P * (r / (1 – (1 + r)^-n)) …………………………. (1)

Where;

M = monthly payment = ?

P = principal = Purchase price * (1 - Down payment percentage) = $225,000 * (1 - 15%) = $191,250

r = monthly interest rate = annual interest rate / 12 = 6.5% / 12 = 0.065 / 12 = 0.00541666666666667

n = number of months = 25 years * 12 months = 300

Substituting the values into equation (1), we have:

M = $191,250 * (0.00541666666666667 / (1 - (1 + 0.00541666666666667)^-300))

M = $191,250 * 0.00675207161347643

M = $1,291.33

Mortgage total can now be calculated as follows:

Mortgage total = Monthly payment * Number of years * Number of months in a year

Mortgage total = $1,291.33 * 25 * 12

Mortgage total = $387,400.11

Therefore, the mortgage total is $387,400.11.

6 0

2 years ago

Joshua started cycling at 5:15 pm By 8:09 pm, he has covered a distance of 7250 mWhat was Joshua's average speed during that tim

vivado [14]

The average speed of Joshua during that time is 2500 m/h.

Explanation:

It is given that Joshua started cycling at 5:15 pm. By 8:09 pm he has covered a distance of 7250 m.

The total time taken by Joshua from 5:15 pm to 8:09 pm is

$2 { h } 54 \text { min }=2 \mathrm{h}+\frac{54}{60} {h}$

Dividing we get,

$2 { h } 54 \text { min }=2 \mathrm{h}+0.9 {h}$

Adding, we have,

$2 { h } 54 \text { min }=2.9 {h}$

Thus, the total time taken by Joshua is $2.9 {h}$

To determine the average speed we use the formula,

$speed=\frac{distance}{time}$

where $distance=7250$ and $time=2.9$

Hence, substituting the values we have,

$speed=\frac{7250}{2.9}$

Dividing, we get,

$speed=2500$

Thus, the average speed of Joshua during that time is 2500 m/h.

5 0

3 years ago