The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time

Integration by Parts Evaluate e-2x cos(2x) dx.

kifflom [539]

Let

$I = \displaystyle \int e^{-2x} \cos(2x) \, dx[/]texIntegrate by parts:[tex]\displaystyle \int u \, dv = uv - \int v \, du$

with

$u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \cos(2x) \, dx \implies v = \dfrac12 \sin(2x)$

Then

$\displaystyle I = \frac12 e^{-2x} \sin(2x) + \int e^{-2x} \sin(2x) \, dx + C$

Integrate by parts again, this time with

$u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \sin(2x) \, dx \implies v = -\dfrac12 \cos(2x)$

so that

$\displaystyle I = \frac12 e^{-2x} \sin(2x) - \frac12 e^{-2x} \cos(2x) - \int e^{-2x} \cos(2x) \, dx + C\\\\ \implies I = \frac{\sin(2x)-\cos(2x)}{2e^{2x}} - I + C \\\\ \implies 2I = \frac{\sin(2x) - \cos(2x)}{2e^{2x}} + C \\\\ \implies I = \boxed{\frac{\sin(2x) - \cos(2x)}{4e^{2x}} + C}$

6 0

2 years ago

How many bus can fit in a room

RSB [31]

Answer: depending on the size of the room and what kind of bus

Step-by-step explanation:

8 0

3 years ago

A baseball team had $1,000 to spend on supplies. The team spent $185 on a new bat. New baseball cost $4 each. The inequality 185

Marta_Voda [28]

This question is incomplete

Complete Question

A baseball team had $1,000 to spend on supplies. The team spent $185 on a new bat. New baseballs cost $4 each.

The inequality 185 + 4b ≤ 1,000 can be used to determine the number of new baseballs (b) that the team can

purchase. Which statement about the number of new baseballs that can be purchased is true?

A. The team can purchase 204 new baseballs.

B. The minimum number of new baseballs that can be purchased is 185.

C. The maximum number of new baseballs that can be purchased is 185.

D. The team can purchase 185 new baseballs, but this number is neither the

maximum nor the minimum.

Answer:

D. The team can purchase 185 new baseballs, but this number is neither the maximum nor the minimum.

Step-by-step explanation:

The first step would be to solve the given equation:

185 + 4b ≤ 1000

4b ≤ 1000 - 185

4b ≤ 815

Divide both sides by 4

b ≤ 203.75

The maximum amount of baseballs the team can buy is 203. This means that they can buy 203 or less than that amount.

Of all the options give, option D is the correct option because the team can purchase 185 new baseballs, but this number is neither the maximum nor the minimum.

The maximum number of ball they can buy is 203 balls and the minimum is zero.

8 0

3 years ago

Solve the equation N/-2=-15

otez555 [7]

Answer:

30

Step-by-step explanation:

N/-2=-15

N= -15 times -2

N= 30

4 0

3 years ago

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Using the method described in part F, help Kevin change 9/2= x/24 to an equation without fractions. Show your work. Don't solve

soldi70 [24.7K]

Answer:

108 = x

Step-by-step explanation:

multiple both sides by 24 and simplify

9 x 24 = 216/2=x

108 = x

3 0

3 years ago

Read 2 more answers