Write a fraction greater than 1 for 6 using 9 as the denominator

Find the average rate of change for the function over the given interval.

jekas [21]

Answer:

The average rate of change for the function over the given integral

$A(x) = \frac{e^{-2} -1}{2}$

Step-by-step explanation:

Explanation

<u>Average rate of a functio</u>n:-

<u>We can define the average rate of change of a function from a to b</u>

<u></u>

$A(x) = \frac{f(b)-f(a)}{b-a}$

Given function f(x) = eˣ

Given interval x = a = -2 and y = b = 0

f(a) = f(-2) = e⁻²

f(b) = f(0) = e⁰

$A(x) = \frac{e^{-2} -1}{0-(-2)}$

The average rate of change for the function over the given integral

6 0

2 years ago

Use the arc length formula to find the length of the curve y = 2 − x2 , 0 ≤ x ≤ 1. Check your answer by noting that the curve is

Lina20 [59]

By using the arc length formula, we will see that the length of the curve is L = 1.48

<h3>How to use the arc length formula?</h3>

Here we have the curve:

y = 2 - x^2 with 0 ≤ x ≤ 1

And we want to find the length of the curve.

The arc length formula for a curve y in the interval [x₁, x₂] is given by:

$L =\int\limits^{x_2}_{x_1} {\sqrt{1 + \frac{dy}{dx}^2} } } \, dx$

For our curve, we have:

dy/dx = -2x

And the interval is [0, 1]

Replacing that we get:

$L =\int\limits^{1}_{0} {\sqrt{1 + (-2x)^2} } } \, dx\\\\L \int\limits^{1}_{0} {\sqrt{1 + 4x^2} } } \, dx\\$

This integral is not trivial, using a table you can see that this is equal to:

$L = (\frac{Arsinh(2x)}{4} + \frac{x*\sqrt{4x^2 + 1} }{2})$

evaluated from x = 1 to x = 0, when we do that, we will get:

$L = \frac{Arsinh(2) + 2*\sqrt{5} }{4} = 1.48$

That is the length of the curve.

If you want to learn more about curve length, you can read:

brainly.com/question/2005046

8 0

2 years ago

The domain for f(x) and g(x) is the set of all real numbers.

Tom [10]

Answer:

Option B

Step-by-step explanation:

=> $f(x) = 3x+5$

=> $g(x) = x^2$

Subtracting both

=> $(f-g)(x) = 3x+5-x^2$

Assembling

=> $(f-g)(x) = -x^2+3x+5$

3 0

2 years ago

multiply. (2.5×10−8)(9×10−10) express your answer in scientific notation. all of the ones with - is to the power of a. 2.25×10−1

svetlana [45]

(2.5 x 10^-8)(9 x 10^-10) = (2.5 x 9) x (10^(-8 + (-10))) = 22.5 x 10^(-8 - 10) = 2.25 x 10^1 x 10^-18 = 2.25 x 10^(1 + (-18)) = 2.25 x 10^(1 - 18) = 2.25 x 10^-17

8 0

3 years ago

Read 2 more answers

What is the value of 0.53?

Marrrta [24]

The value of the decimal, 0.53 is $\frac{53}{100}$ or 53%.

Sure hope this helps you

7 0

2 years ago

Read 2 more answers

Write a fraction greater than 1 for 6 using 9 as the denominator ​

Write a fraction greater than 1 for 6 using 9 as the denominator