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2 years ago

How long is DE? Any help will be appreciated thank you

Mathematics

1 answer:

lilavasa [31]2 years ago

3 0

Answer: 4

Step-by-step explanation:

solve for the missing angle

the total degrees a triangle can have is 180 so

$180-90-60=30$

use law of sines to solve for x

$\frac{x}{sin30} =\frac{4\sqrt{3} }{sin60}$

cross multiply

$sin60*x=4\sqrt{3} sin30$

divide by $sin60$

$x=\frac{4\sqrt{3}sin30 }{sin60}$

type into calculator with (ALPHA Y= for a fraction on TI-84) MAKE SURE IT IS IN DEGREES

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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

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Vikki [24]

Answer:

angle b is 62 degrees. This is because if we solve for x, by putting the 2 equations equal to each other(because they are vertical angles), than we figure out that x=6. Now plug that into angle b's equation, and you get 62 degrees.

Step-by-step explanation:

7 0

3 years ago

What is the equivalent fraction for 0.3333

lorasvet [3.4K]

0.3333 = 1/3

Answer would be: 1/3

6 0

2 years ago

Can someone please help me?

koban [17]

Answer:

The X intercepts= 1 and -1

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Step-by-step explanation:

It's where the line meets the axis.

7 0

3 years ago

One of the great mysteries of the world is my hotdogs and hotdog buns come in packages of different sizes hotdogs come in packs

V125BC [204]

Answer:

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Step-by-step explanation:

hot dogs come in packs of 8

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so to get equal number

we have to look for the LCM of 8 and 12 = 24

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therefore, 3 pack of hot dogs and 2 pack of buns 24

7 0

3 years ago