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2 years ago

Given this proportion, what ratio completes the equivilent proportion a/8?

1 answer:

8 0

To solve this problem you must follow the steps below:

You have a/b=8/15, Then:

1. You must divide in both side of the given proportion by 8:

a/bx8=8/15x8

2. When you simplify, you obtain:

a/8b=1/15

3. Now, you must multiply both sides by "b", as below:

axb/8b=1xb/15

4. Finally, when you simplify, you have:

a/8=b/15

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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

2 years ago

Help again last question

kompoz [17]

Answer:

5 cubes. 5 cubes. 4 cubes 5 cubes

Step-by-step explanation:

is easy and no hard

4 0

2 years ago

you have 5 shirts and 4 four pair of pants. how many different ways can you arrange your shirts and pants to outfits.

iren2701 [21]

I believe it is 20 since I did 4+4+4+4+4 =20 since each shirt has 4 mixes it could have with the pants. Hope I helped

8 0

2 years ago

Read 2 more answers

Which line is parallel to 8x+2y=12

Nat2105 [25]

x=3/2-1/4

8x+2y=12

move the variable to the right side and change the sign.

8x=12-2y

divide both sides of the equation by 8

x=3/2-1/4y

the final solution is

x=3/2-1/4y

4 0

2 years ago

Read 2 more answers

The larger of two numbers is four more than the smaller. if the larger is x what is the smaller?

Lelu [443]

Answer:

x-4

Step-by-step explanation:

Since the larger of two numbers is four more than the smaller one, this means that there is a difference of 4 between the two numbers. In order to find the smaller of both numbers, you can obtain the smaller from the largest by subtracting 4.

4 0

2 years ago