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katrin2010 [14]
3 years ago
5

Differentiating Exponential functions In Exercise,find the derivative of the function. See Example 2 and 3.

Mathematics
1 answer:
nadya68 [22]3 years ago
4 0

Answer:

f'(x)=2(e^4^x)+(x^2+1)(4e^4^x)

Step-by-step explanation:

The derivative of the function:

(x^2+1)e^4^x

The rule for the product of two functions:

f'(x)=g'(x)h(x)+g(x)h'(x)

Therefore

g(x)=x^2+1

g'(x)=2

f(x)=e^4^x

f'(x)=4e^4^x

f'(x)=2(e^4^x)+(x^2+1)(4e^4^x)

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Can u guys PLEASE ANSWER THIS QUESTION ASAP URGENTLY
makvit [3.9K]

Answer:

x^2-4x+3

Step-by-step explanation:

Since the zeroes of the quadratic are 1 and 3, we can set up an equation in factored form:

(x-1)(x-3)

=x^2-4x+3

We can further check that this is the right answer by evaluating it at the vertex:

(2)^2-4*2+3=-1

Since that corresponds to the graph, the answer is x^2-4x+3

3 0
3 years ago
Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and
zloy xaker [14]

Answer:

(0,0)   (4000,0) and (500,79)

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW

\frac{dW}{dt} = -0.02W + 0.00004RW

To solve this, we first equate \frac{dR}{dt} and \frac{dW}{dt} to 0.

So, we have:

0.09R(1 - 0.00025R) - 0.001RW = 0

-0.02W + 0.00004RW = 0

Factor out R in 0.09R(1 - 0.00025R) - 0.001RW = 0

R(0.09(1 - 0.00025R) - 0.001W) = 0

Split

R = 0   or 0.09(1 - 0.00025R) - 0.001W = 0

R = 0   or  0.09 - 2.25 * 10^{-5}R - 0.001W = 0

Factor out W in -0.02W + 0.00004RW = 0

W(-0.02 + 0.00004R) = 0

Split

W = 0 or -0.02 + 0.00004R = 0

Solve for R

-0.02 + 0.00004R = 0

0.00004R = 0.02

Make R the subject

R = \frac{0.02}{0.00004}

R = 500

When R = 500, we have:

0.09 - 2.25 * 10^{-5}R - 0.001W = 0

0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0

0.09 -0.01125 - 0.001W = 0

0.07875 - 0.001W = 0

Collect like terms

- 0.001W = -0.07875

Solve for W

W = \frac{-0.07875}{ - 0.001}

W = 78.75

W \approx 79

(R,W) \to (500,79)

When W = 0, we have:

0.09 - 2.25 * 10^{-5}R - 0.001W = 0

0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0

0.09 - 2.25 * 10^{-5}R = 0

Collect like terms

- 2.25 * 10^{-5}R = -0.09

Solve for R

R = \frac{-0.09}{- 2.25 * 10^{-5}}

R = 4000

So, we have:

(R,W) \to (4000,0)

When R =0, we have:

-0.02W + 0.00004RW = 0

-0.02W + 0.00004W*0 = 0

-0.02W + 0 = 0

-0.02W = 0

W=0

So, we have:

(R,W) \to (0,0)

Hence, the points of equilibrium are:

(0,0)   (4000,0) and (500,79)

4 0
3 years ago
1. Determine the approximate measure of angle E.
Naddik [55]

Answer:

1. 81.0

2. I`m trying to figure that out now I will give answers when I can

Step-by-step explanation:

7 0
3 years ago
A local store sells oranges at a price of $9 for 6 oranges. Alison wants to send 24 oranges to her aunt. How much will Alison sp
kodGreya [7K]

Answer $22.50

Step-by-step explanation:

$9 X 2 = 18 and 6 oranges + 6 oranges = 12

if you divide 9 by 6 you get 1.5 so that means its 1.50 for each orange individually.

which makes 15 oranged 22.50

5 0
3 years ago
Read 2 more answers
an author can write an amazing 2 pages of a story in 15 minutes. How many pages can an author write in 120 minutes
MariettaO [177]

Answer:

I think the answer is 16

Step-by-step explanation:

Because

2 divided by 15 is 7.5

so 120 divided 7.5 is 16 pages

I hope you get it right !

Good Luck!


7 0
3 years ago
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