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bezimeni [28]
2 years ago
6

Use spherical coordinates to evaluate the

Mathematics
1 answer:
kotykmax [81]2 years ago
5 0

Answer:

4096π / 5

Step-by-step explanation:

∫∫∫ (x² + y² + z²) dV

In spherical coordinates, x² + y² + z² = r², and dV = r² sin φ dr dθ dφ.

E is the range 0 ≤ r ≤ 4, 0 ≤ φ ≤ π, 0 ≤ θ ≤ 2π.

∫₀ᵖⁱ∫₀²ᵖⁱ∫₀⁴ (r²) (r² sin φ dr dθ dφ)

∫₀ᵖⁱ∫₀²ᵖⁱ∫₀⁴ (r⁴ sin φ) dr dθ dφ

Evaluate the first integral.

∫₀ᵖⁱ∫₀²ᵖⁱ (⅕ r⁵ sin φ)|₀⁴ dθ dφ

∫₀ᵖⁱ∫₀²ᵖⁱ (¹⁰²⁴/₅ sin φ) dθ dφ

¹⁰²⁴/₅ ∫₀ᵖⁱ∫₀²ᵖⁱ (sin φ) dθ dφ

Evaluate the second integral.

¹⁰²⁴/₅ ∫₀ᵖⁱ (θ sin φ)|₀²ᵖⁱ dφ

¹⁰²⁴/₅ ∫₀ᵖⁱ (2π sin φ) dφ

²⁰⁴⁸/₅ π ∫₀ᵖⁱ sin φ dφ

Evaluate the third integral.

²⁰⁴⁸/₅ π (-cos φ)|₀ᵖⁱ

²⁰⁴⁸/₅ π (-cos π + cos 0)

²⁰⁴⁸/₅ π (1 + 1)

⁴⁰⁹⁶/₅ π

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A credit card company charges an annual simple interest rate of 24%. in august, your purchases totaled $956. How much will you p
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I know because I did this problem a few years ago

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Consider two medical tests, A and B for a virus. Test A is 90% effective at recognizing the virus when it is present, but has a
Licemer1 [7]

1

P(V|A) is not 0.95. It is opposite:

P(A|V)=0.95

From the text we can also conclude, that

P(A|∼V)=0.1

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P(B|∼V)=0.05

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What you need to calculate and compare is P(V|A) and P(V|B)

P(V∩A)=P(A)⋅P(V|A)⇒P(V|A)=P(V∩A)P(A)

P(V∩A) means, that Joe has a virus and it is detected, so

P(V∩A)=P(V)⋅P(A|V)=0.01⋅0.95=0.0095

P(A) is sum of two options: "Joe has virus and it is detected" and "Joe has no virus, but it was mistakenly detected", therefore:

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Four balls of wool will make 8 knitted caps. How many balls of wool will malcolm need if he wants to make six caps?
Olenka [21]
I could be wrong but I think it is 2
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An object is launched at 19.6 m/s from a height of 58.8 m. The equation for the height (h) in terms of time (t) is given by h(t)
beks73 [17]
H(t) = Ho +Vot - gt^2/2

Vo = 19.6 m/s
Ho = 58.8 m
g = 9.8 m/s^2

H(t) = 58.8 + 19.6t -9.8t^2/2 = 58.8 + 19.6t - 4.9t^2

Maximun height is at the vertex of the parabole

To find the vertex, first find the roots.

58.8 + 19.6t - 4.9t^2 = 0

Divide by 4.9

12 + 4t - t^2 = 0

Change sign and reorder

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Factor

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The vertex is in the mid point between both roots

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Answer: the maximum height is 78.4 m
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