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3 years ago

Determine the distance between the points (2,7) and (-4,15)

Mathematics

1 answer:

Nikolay [14]3 years ago

4 0

Answer:

option C

Step-by-step explanation:

$distance = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

$=\sqrt{(-4-2)^2+(15-7)^2} \\\\=\sqrt{(-6)^2 + 8^2}\\\\=\sqrt{36 + 64 }\\\\= \sqrt{100} \\\\= 10$

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2 years ago

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

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I=\frac{1}{2}(e^x\sin(2x)-\int e^x(2\cos(2x))dx)\\\\
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Looking for $I_2$ :

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