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2 years ago

1) The membership fee of Math Club is P25. What is the total amount

Mathematics

1 answer:

AURORKA [14]2 years ago

5 0

Answer:

it's actually none of those the answer I have is p 31,300

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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

We want to find the zeros of this polynomial:<br> p(x)= 3x^3 – 3x^2– 18x

bulgar [2K]

Answer:

x=0 x=3 x=-2

Step-by-step explanation:

p(x)= 3x^3 – 3x^2– 18x

Factor out the greatest common factor, 3x

p(x)= 3x (x^2 – x– 6)

Factor inside the parentheses

What 2 numbers multiplies to -6 and adds to -1

-3*2 = -6

-3+2 = -1

p(x)= 3x (x-3)(x+2)

Setting the function equal to zero to find the zeros

0 = 3x (x-3)(x+2)

Using the zero product property

3x = 0 x-3 =0 x+2 =0

x=0 x=3 x=-2

3 0

3 years ago

Read 2 more answers

Simplify the rational expression 6x-24/16-x^2

8_murik_8 [283]

The answer would be -x^2 + 6x - 3/2

5 0

3 years ago

Read 2 more answers

Please help me, It's due soon! Giving brainliest too!

ANEK [815]

Answer:

gimme a sec

Step-by-step explanation:

7 0

2 years ago

Toothbrushes are $4.00 each. there is a 10% discount but also 6% sales tax. What is the new price?

Katena32 [7]

Multiply 4 by 10%.
10% ⇒ 0.1

4 × 0.1 = 0.4
Subtract 0.4 from 4.
4 - 0.4 = 3.6 (price with discount)

Multiply 3.6 by 6%.
6% ⇒ 0.06
3.6 × 0.06 = 0.216

Add 0.216 to 3.6.
0.216 + 3.6 = 3.816

Round 3.816 to the hundredths.
3.816 ⇒ 3.82 (price with tax)

The new price of toothbrushes is $3.82.

6 0

3 years ago