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3 years ago

How would you express the area of the rectangle using the Distributive Property?

Mathematics

2 answers:

andreyandreev [35.5K]3 years ago

5 0

Answer:

The area of the rectangle can be found using two different expressions: a(b + c) or ab + ac. The equality of these expressions, a(b + c) = ab + ac, is the distributive property.

Inessa05 [86]3 years ago

3 0

Answer:

the answer is c. 3(x+5)

Step-by-step explanation:

because it give and explantion on the question above which say x plus five with a width of three which give the answer of c

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Zigmanuir [339]

Answer:

length: 5 yd

width: 4 yd

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Step-by-step explanation:

1 yd = 3 ft

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3 years ago

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

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

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Looking for $I_2$ :

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

Replacing:

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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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