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3 years ago

Help please i need this now!

Mathematics

1 answer:

riadik2000 [5.3K]3 years ago

5 0

Answer:

All rectangles are similar

Step-by-step explanation:

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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

X+6-5=8-2 <br> x=? <br> solve the following equation. then place the correct number in the box

Valentin [98]

X
+
6
−
5
=
8
−
2

+
6
−
5
=
8
−
2
Solve
1
Subtract the numbers
x
+
6
−
5
=
8
−
2

+
6
−
5
=
8
−
2
x
+
1
=
8
−
2

+
1
=
8
−
2
2
Subtract the numbers
x
+
1
=
8
−
2

+
1
=
8
−
2
x
+
1
=
6

+
1
=
6
3
Subtract
1
1
from both sides
x
+
1
=
6

+
1
=
6
x
+
1
−
1
=
6
−
1

+
1
−
1
=
6
−
1
4
Simplify
Subtract the numbers
Subtract the numbers
x
=
5

=
5

7 0

2 years ago

A cell phone company has three different production sites.

dlinn [17]

Answer:

3/11

Step-by-step explanation:

given that a cell phone company has three different production sites

Site name 1 2 3 Total

Production 60% 30% 10% 100%

Recalled 5% 7% 9%

Prob for recall 0.003 0.021 0.009 0.033