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2 years ago

10

A circular arena is lit by 5 lights equally spaced around the perimeter of the arena. What is the measure of each angle formed b

y the lights on the perimeter?

2 answers:

Artyom0805 [142]2 years ago

6 0

Answer:

D. 108 degrees

Step-by-step explanation:

use the formula (n-2)180/n, n being number of sides.

In this case, the number of sides is 5.

plug it into the formula and solve:

(5-2)180/5

(3)180/5

540/5

108 degrees.

Elden [556K]2 years ago

3 0

Answer:

108

Step-by-step explanation:

Use the total angle of the shape by (5-2)180/5 and you get 108.

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The graph shows the amount of water that remains in a barrel after it begins to leak. The variable x represents the number of da

lukranit [14]

Answer:

-2 is your answer hope this helps!

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2 years ago

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Melissa worked to earn $20.00. Alan worked for $12.00 hours. If she earns $2.00 per hour, how many hours did Melissa work?

MissTica

Answer: 10 hours

Step-by-step explanation: so if you do 10 times 2.00 it equals 20 dollars or you can divide 20 and 2

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2 years ago

Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of

kifflom [539]

Looks like we have

$\vec F(x,y,z)=z^2x\,\vec\imath+\left(\dfrac{y^3}3+\sin z\right)\,\vec\jmath+(x^2z+y^2)\,\vec k$

which has divergence

$\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(z^2x)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial z}=z^2+y^2+x^2$

By the divergence theorem, the integral of $\vec F$ across $S$ is equal to the integral of $\nabla\cdot\vec F$ over $R$ , where $R$ is the region enclosed by $S$ . Of course, $S$ is not a closed surface, but we can make it so by closing off the hemisphere $S$ by attaching it to the disk $x^2+y^2\le1$ (call it $D$ ) so that $R$ has boundary $S\cup D$ .

Then by the divergence theorem,

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(x^2+y^2+z^2)\,\mathrm dV$

Compute the integral in spherical coordinates, setting

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

so that the integral is

$\displaystyle\iiint_R(x^2+y^2+z^2)\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^1\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{2\pi}5$

The integral of $\vec F$ across $S\cup D$ is equal to the integral of $\vec F$ across $S$ plus the integral across $D$ (without outward orientation, so that

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\iint_D\vec F\cdot\mathrm d\vec S$

Parameterize $D$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $D$ to be

$\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=-u\,\vec k$

Then we have

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^1\left(\frac{u^3}3\sin^3v\,\vec\jmath+u^2\sin^2v\,\vec k\right)\times(-u\,\vec k)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{2\pi}\int_0^1u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac\pi4$

Finally,

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\left(-\frac\pi4\right)=\boxed{\frac{13\pi}{20}}$

6 0

2 years ago

Paul's MP3 player has a total of 852 songs. He has 4 different groups of songs. If he puts and equal number of songs in each gro

jeka94

Answer:

213

Step-by-step explanation:

You have to divide the 852 songs into the 4 categories.

852/4=

213

7 0

2 years ago

Evaluate 5w-\dfrac wx5w− x w 5, w, minus, start fraction, w, divided by, x, end fraction when w=6w=6w, equals, 6 and x=2x=2x,

Sunny_sXe [5.5K]

Answer:

$5w-\frac{w}{x}=27$ when w=6 and x=2.

Step-by-step explanation:

Given : Expression $5w-\frac{w}{x}$ when w=6 and x=2.

To find : Evaluate the expression ?

Solution :

Expression $5w-\frac{w}{x}$

Substitute, w=6 and x=2

$5w-\frac{w}{x}=5\times 6-\frac{6}{2}$

$5w-\frac{w}{x}=30-3$

$5w-\frac{w}{x}=27$

Therefore, $5w-\frac{w}{x}=27$ when w=6 and x=2.

6 0

2 years ago