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AnnZ [28]
2 years ago
13

I need help with my geometry homework.

Mathematics
1 answer:
wlad13 [49]2 years ago
7 0

Step-by-step explanation:

5x + 80 = 180

x = 20

2x = 40

3x=60

7x=140

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The minute hand of a clock is 8 inches long and moves from 12 to 8 o’clock. How far does the tip of the minute hand move?
ryzh [129]

The minute hand is like an eight inch radius of a circle, whose circumference would equal 2 * PI * 8 = 50.265 inches.  By moving to 8 o'clock, it travels 2/3 of the circumference or 50.265 * 2/3 = 33.510 inches


3 0
3 years ago
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How can Ari simplify the following expression? StartFraction 5 Over a minus 3 EndFraction minus 4 divided by 2 + StartFraction 1
Zielflug [23.3K]

Answer:

-\frac{8}{3}

Step-by-step explanation:

Given

\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}

Required

Simpify

The very first step is to take LCM of the given expression

\frac{-10 -4 - 2}{6}

Perform arithmetic operations o the numerator

-\frac{16}{6}

Divide the numerator and denominator by 2

-\frac{16/2}{6/2}

-\frac{8}{3}

The expression can't be further simplified;

Hence, \frac{5}{-3} - \frac{4}{2} + \frac{1}{-3} = -\frac{8}{3}

8 0
2 years ago
A sphere of radius r is cut by a plane h units above the equator, where
Anika [276]
Consider the top half of a sphere centered at the origin with radius r, which can be described by the equation

z=\sqrt{r^2-x^2-y^2}

and consider a plane

z=h

with 0. Call the region between the two surfaces R. The volume of R is given by the triple integral

\displaystyle\iiint_R\mathrm dV=\int_{-\sqrt{r^2-h^2}}^{\sqrt{r^2-h^2}}\int_{-\sqrt{r^2-h^2-x^2}}^{\sqrt{r^2-h^2-x^2}}\int_h^{\sqrt{r^2-x^2-y^2}}\mathrm dz\,\mathrm dy\,\mathrm dx

Converting to polar coordinates will help make this computation easier. Set

\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\var\phi\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi

Now, the volume can be computed with the integral

\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_0^{\arctan\frac{\sqrt{r^2-h^2}}h}\int_{h\sec\varphi}^r\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta

You should get

\dfrac{2\pi}3\left(r^3\arctan\dfrac{\sqrt{r^2-h^2}}h-\dfrac{h^3}2\left(\dfrac{r\sqrt{r^2-h^2}}{h^2}+\ln\dfrac{r+\sqrt{r^2-h^2}}h\right)\right)
5 0
3 years ago
A ship sails 20km due North and then 35km due East .How far east is it from its starting point?
atroni [7]

Use the Pythagoras' Theorem:

A^2 + B^2 = C^2

20^2 + 35^2 = C^2

400+ 1225=1625=C^2

square root of 1625= C = 40.31 km

6 0
2 years ago
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Help pleas and thank you
solong [7]

Answer:

the last one i think

Step-by-step explanation:

8 0
2 years ago
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