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Gnoma [55]
2 years ago
14

The diameter of a circle is 10 in. Find its area in terms of pi

Mathematics
2 answers:
elena55 [62]2 years ago
4 0

Answer:

25 pi

Step-by-step explanation:

exis [7]2 years ago
4 0

78.54 is the area in terms of pi

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Consider the force field and circle defined below.
grin007 [14]

By Green's theorem,

\displaystyle\int_{x^2+y^2=9}\vec F(x,y)\cdot\mathrm d\vec r=\iint_D\left(\frac{\partial(xy)}{\partial x}-\frac{\partial(x^2)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=\iint_Dy\,\mathrm dx\,\mathrm dy

where C is the circle x^2+y^2=9 and D is the interior of C, or the disk x^2+y^2\le1.

Convert to polar coordinates, taking

\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta

Then the work done by \vec F on the particle is

\displaystyle\iint_Dy\,\mathrm dx\,\mathrm dy=\int_0^{2\pi}\int_0^3(r\sin\theta)r\,\mathrm dr\,\mathrm d\theta=\left(\int_0^{2\pi}\sin\theta\,\mathrm d\theta\right)\left(\int_0^3r^2\,\mathrm dr\right)=\boxed0

4 0
2 years ago
Twelve pounds of beans are distributed equally into 8 bags to give out at the food bank. How many pounds of beans are in each ba
BaLLatris [955]
There are 1.5 beans in 1 bag
5 0
3 years ago
If x^2 - 16 > 0, which of the following must be true?
zimovet [89]
The left hand side of the equation is a difference of two squares and may be factored out as follows,
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They may be individually taken as,
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The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle. so I believe it is A. True..
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Firewood is often sold by the cord. A cord of wood is a bundle measuring 4 feet by 4 feet by 8 feet. What's the volume of a cord
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To find the volume of the following Firewood, we would do this:

4 * 4 * 8 = 128 cubic feet

Therefore, the volume of the firewood is 128 cubic feet.
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3 years ago
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