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Butoxors [25]
3 years ago
8

Ya'll fr get 50 points if you answer this. What is the rate of change of

" id="TexFormula1" title="f(x)=2^x" alt="f(x)=2^x" align="absmiddle" class="latex-formula">?
Mathematics
1 answer:
Evgesh-ka [11]3 years ago
8 0

Answer:

\dfrac{dy}{dx}=2^x\ln 2

Step-by-step explanation:

**This is a non-linear function and therefore <u>does not have a constant rate of change</u>.  It will have a different slope depending on what points you use in the average rate of change formula:\mathsf{average \ rate \ of \ change = \dfrac{change \ in \ y}{change \ in \ x}}

To calculate rate of change, differentiate.

substitute y for f(x):  

\implies y=2^x

Take natural logs of both sides:

\implies \ln y=\ln 2^x

Apply the log rule  \ln a^b=b \ln a :

\implies \ln y=x\ln 2

Differentiate with respect to x:

\implies \dfrac{1}{y} \frac{dy}{dx}=\ln 2

Mulitply both sides by y:

\implies \dfrac{dy}{dx}=y\ln 2

Replace y with y=2^x

\implies \dfrac{dy}{dx}=2^x\ln 2

Therefore, rate of change of the function is :

\dfrac{dy}{dx}=2^x\ln 2

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Can help me complete this problem please :c
motikmotik

Answer:

A = \dfrac{7}{2}\pi~cm^2

Step-by-step explanation:

There is a formula for the area of a sector given the radius and the angle measure.

A = \dfrac{n}{360^\circ}\pi r

n = angle measure

r = radius

A = \dfrac{140^\circ}{360^\circ}\pi \times (3~cm)^2

A = \dfrac{14}{36}\pi \times 9~cm^2

A = \dfrac{7}{18}\pi \times 9~cm^2

A = \dfrac{7}{2}\pi~cm^2

3 0
3 years ago
Read 2 more answers
Tina paid $6.60 for some $0.15 stamps and some $0.20 stamps. She bought 37 stamps in all. How many of each kind did she buy?
sergiy2304 [10]

Answer:

Let n be the number of 25 cent stamps.Then, 28 - n must be the number of 29 cent stamps.Tim paid $7.60 the stamps.

0.25n + 0.29(28 - n) = 7.60

This means that n stamps at 25 cents a piece plus (28 - n) stamps at 29 cents a piece sum to $7.60.Solve for m.

0.25n + 8.12 - 0.29n = 7.60

-0.04n = -0.52

n = 13

So, Tim bought 13 25-cent stamps and 28 - 13 = 15 29-cent stamps

Step-by-step explanation:

hope this helps:)

4 0
3 years ago
A set of data items is normally distributed with a mean of 240 and a standard deviation of 32. Convert 272 to a? z-score
dem82 [27]

Answer:

z-score = 1

Step-by-step explanation:

Given

Mean= μ=240

SD= σ=32

In order to find the z-score of a value, the mean is subtracted from the value and then divided by standard deviation.

The formula for z-score is:

z-score=(x-μ)/σ

Here x is the value whose z-score is to be found.

In the given question, x = 272

So,

z-score=(272-240)/32

=32/32

=1

So , the z-score for 272 is 1..

7 0
3 years ago
There are (4^9)^5 ⋅ 4^0 books at the library. What is the total number of books at the library?
Sidana [21]
(4^9)^5 \cdot 4^0=4^{9*5} \cdot 1=4^{45}
3 0
3 years ago
Compute a value for t that satisfies the equation below. "-2/3" t - 2 = - 3
Dima020 [189]

Answer:

t = 3/2

Step-by-step explanation:

Instead of randomly guessing values of "t" that will satisfy the equation, you can easily find the correct value by solving the equation in terms of "t". In other words, you can set the equation equal to "t" to find the final answer.

(-2/3)t - 2 = -3                             <----- Original equation

(-2/3)t = -1                                   <----- Add 2 to both sides

t = 3/2                                        <----- Divide both sides by -2/3

You can check this value by plugging it into "t" and determining whether both sides of the equations will be equal.

(-2/3)t - 2 = -3                            <----- Original equation

(-2/3)(3/2) - 2 = -3                      <----- Plug 3/2 into "t"

-6/6 - 2 = -3                               <----- Multiply -2/3 and 3/2

-1 - 2 = -3                                    <----- Simplify -6/6

-3 = -3                                        <----- Subtract

6 0
2 years ago
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