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3 years ago

How do I graph 2d + 4p = 28

Mathematics

1 answer:

gayaneshka [121]3 years ago

7 0

I hope this helps you! Have a great day! :)

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Use spherical coordinates. Find the volume of the solid that lies within the sphere x^2 + y^2 + z^2 = 81, above the xy-plane, an

Natasha_Volkova [10]

Answer:

The volume of the solid is 243 $\sqrt{2} \ \pi$

Step-by-step explanation:

From the information given:

BY applying sphere coordinates:

0 ≤ x² + y² + z² ≤ 81

0 ≤ ρ² ≤ 81

0 ≤ ρ ≤ 9

The intersection that takes place in the sphere and the cone is:

$x^2 +y^2 ( \sqrt{x^2 +y^2 })^2 = 81$

$2(x^2 + y^2) =81$

$x^2 +y^2 = \dfrac{81}{2}$

Thus; the region bounded is: 0 ≤ θ ≤ 2π

This implies that:

$z = \sqrt{x^2+y^2}$

ρcosФ = ρsinФ

tanФ = 1

Ф = π/4

Similarly; in the X-Y plane;

z = 0

ρcosФ = 0

cosФ = 0

Ф = π/2

So here; $\dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}$

Thus, volume: $V = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4} \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho ^2 \ sin \phi \ d\rho \ d \theta \ d \phi$

$V = \int \limits^{\pi/2}_{\pi/4} \ sin \phi \ d \phi \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho ^2 d\rho$

$V = \bigg [-cos \phi \bigg]^{\pi/2}_{\pi/4} \bigg [\theta \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3} \bigg ]^{9}_{0}$

$V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ]$

V = 243 $\sqrt{2} \ \pi$

4 0

3 years ago

Select the correct answer.

katen-ka-za [31]

Answer: B

how close their measurements are to each other

Step-by-step explanation:

The students in a science class did not know the length of the board before taking turns to measure the length of a certain board.

The characteristic of their measurements that best indicates

their accuracy will be how close their measurements are to each other.

If the actual length is known before the carry out the measurements, there average value will be neccessarily to determine their accuracy.

Therefore, option B is the best option.

5 0

3 years ago

John made 357$ for 17 hours of work.

yanalaym [24]

Answer: 14 hours

Step-by-step explanation: First I found the unit rate of how much money per hour. So, 357 divided by 17 = 21. So know I know that she earns 21$ per hour. Then, I did 237 divided by 17 which would be 13 remainder 16. Since he only get paid if he works for a full hour, I think the answer would be 14.

3 0

3 years ago

Read 2 more answers

Nicholas can make 6 cupcakes (the y value) with one cup of

masya89 [10]

36 cupcakes if one cup of flour is 6 cupcakes you multiply the amount of flour by 6

4 0

3 years ago

HELP PLEASE I NEED A ANSWER ASAP

nata0808 [166]

Answer:

5x+6+48+81=180°