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Zigmanuir [339]
2 years ago
5

Find WX. 144 V 37 W X

Mathematics
1 answer:
Viktor [21]2 years ago
4 0

9514 1404 393

Answer:

  WX = 107

Step-by-step explanation:

The sum of the segment lengths is the overall length.

  37 +WX = 144

  WX = 144 -37 . . . . . subtract 37

  WX = 107

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Answer and Step-by-step explanation:

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The coordinates of the drop off would be (-2,2)
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3 years ago
There are 4 jacks and 13 clubs in a standard, 52-card deck of playing cards. What is the probability that a card picked at rando
ale4655 [162]

Answer:

16/52, or 4/13.

Step-by-step explanation:

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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:\\\\&#10;\text{Using }\int u\,dv=uv-\int v\,du:\\\\&#10;I=\frac{1}{2}(e^x\sin(2x)-\int e^x(2\cos(2x))dx)\\\\&#10;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:\\\\&#10;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

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2I=e^x\sin(2x)-2I_2\iff\\\\2I=e^x\sin(2x)-2(e^x\cos(2x)+4I)\iff\\\\&#10;2I=e^x\sin(2x)-2e^x\cos(2x)-8I\iff\\\\&#10;10I=e^x\sin(2x)-2e^x\cos(2x)\iff\\\\&#10;I=\dfrac{e^x}{10}(\sin(2x)-2\cos(2x))\\\\&#10;\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
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