PLEASE HELP Which of the following questions are correct? Select all that apply.

Mathematics

1 answer:

gregori [183]3 years ago

5 0

Answer:

I think A and D are both correct

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Integrate e^x(sin(x) cos(x))

Karo-lina-s [1.5K]

$I=\int e^x(\sin(x)\cos(x))dx=\int e^x(\frac{1}{2}\sin(2x))dx=\frac{1}{2}\int e^x\sin(2x)dx$

$\text{If }u=\sin(2x)\to du=2\cos(2x)dx~\text{and}~dv=e^xdx\to v=e^x:\\\\
\text{Using }\int u\,dv=uv-\int v\,du:\\\\
I=\frac{1}{2}(e^x\sin(2x)-\int e^x(2\cos(2x))dx)\\\\
2I=e^x\sin(2x)-2\underbrace{\int e^x\cos(2x)dx}_{I_2}$

Looking for $I_2$ :

$\text{If}~u=\cos(2x)\to du=-2\sin(2x)dx~\text{and}~dv=e^xdx\to v=e^x:\\\\
I_2=e^x\cos(2x)-\int e^x(-2\sin(2x))dx\\\\ I_2=e^x\cos(2x)+2\int e^x(\sin(2x))dx\\\\ I_2=e^x\cos(2x)+2\int e^x(2\sin(x)\cos(x))dx\\\\ I_2=e^x\cos(2x)+4\int e^x(\sin(x)\cos(x))dx=e^x\cos(2x)+4I$

Replacing:

$2I=e^x\sin(2x)-2I_2\iff\\\\2I=e^x\sin(2x)-2(e^x\cos(2x)+4I)\iff\\\\
2I=e^x\sin(2x)-2e^x\cos(2x)-8I\iff\\\\
10I=e^x\sin(2x)-2e^x\cos(2x)\iff\\\\
I=\dfrac{e^x}{10}(\sin(2x)-2\cos(2x))\\\\
\boxed{\int e^x(\sin(x)\cos(x))dx=\dfrac{e^x}{10}(\sin(2x)-2\cos(2x))+C}$

6 0

3 years ago

EASY 6TH GRADER MATH

Rudik [331]

Answer:

Step-by-step explanation:

She is wrong the answer is 27, all you have to do is multiply the number by the percentage as a decimal (.45)

8 0

2 years ago

Check my work:<br><br><br> Does it x = -4?

Ne4ueva [31]

The equation given in the question is
(5x + 2)/2 = 2x - 1
5x + 2 = 2(2x - 1)
5x + 2 = 4x - 2
5x - 4x = - 2 - 2
x = -4
So the value of the unknown variable comes out to be -4. Yes your calculation is correct it seems from the answer that you have given. I hope i have been able to help you in this regard.Only be careful about the cross multiplication part.

3 0

3 years ago

What is the value of S? Please hurry-

Tpy6a [65]

Answer: 8 root 2 or 11.3

Step-by-step explanation:

square 16 and divide by two to find square of other sides. Then root it to find answer

8 0

2 years ago

An angle measures 130° more than the measure of its supplementary angle. What is the measure of each angle?

andrey2020 [161]

Answer:

An angle measures 130° more than the measure of its supplementary angle.

Therefore the required angle is (180°-130°)°=50°

<h3>50° is the right answer.</h3>

4 0

2 years ago