Express using algebra A inscreased by 15%

Mathematics

1 answer:

Karolina [17]2 years ago

5 0

Answer:

A(1.15)

Step-by-step explanation:

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How did the National Woman Suffrage Association (NWSA) differ from the American Woman Suffrage Association (AWSA)?

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The National Woman Suffrage Association advocated for a range of reforms to make women equal members of society, such as the right to own property, etc. The American Woman Suffrage Association lobbied state governments to enact laws granting or expanding women's right to vote in the United States.

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In a diagram, X is the midpoint of Segment VZ. VW =5, and VY =20. Find the coordinates of W,X, and Y.

guapka [62]

solution:

$x(a_{x},b_{x})is midpoint of vz\\
a_{x}=\frac{a_{v}+a_{z}}{2}=\frac{-12+22}{2}=\frac{10}{2}=5\\
b_{x}=\frac{b_{v}+b_{z}}{2}=\frac{0+0}{2}=0\\
and,\\
x(5,0)\\
w(a_{w},b_{w}),v_{w} and w is on the right of v.\\
a_{w}-a_{v}=5\\
a_{w}-(-12)=5\\
a_{w}+12=5\\
a_{w}=5-12=-7\\
w(-7,0)\\
y(a_{y},b_{y})=20 and y is on the right of v.\\
a_{y}-a_{v}=20\\
a_{y}-(-12)=20\\
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I got 10! [_-_]-{-_-}-(_-_)

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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:

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

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3 years ago