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adoni [48]
2 years ago
9

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:

<u>solve for the missing angle</u>

the total degrees a triangle can have is 180 so

180-90-60=30

use <u>law of sines</u> 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 (<em>ALPHA Y= </em>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
I need help with this <br><br> 10 points <br><br> Pls pls pls someone come help me
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:

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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

burns came in packs of 12

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

7 0
3 years ago
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