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3 years ago

Please help me with this i’m stuck

Mathematics

1 answer:

bagirrra123 [75]3 years ago

5 0

Answer:

A ) Substitute the side lengths of a and b in the equation

Step-by-step explanation:

The hypotenuse which is opposite the right angle it always the length of C in the cosine rule.

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Parameterize S by the vector function

$\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle$

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.

Compute the outward-pointing normal vector to S :

$\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle$

The integral of the field over S is then

$\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv$

$\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv$

$\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}$

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2 years ago

The Sun is v kilometers from the upper edge of the Earth's atmosphere and q kilometers from the surface of the Earth. Which of t

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The distance between the Earth's surface and the upper edge of the Earth's atmosphere would be Q - V.

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3 years ago

Read 2 more answers

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3 years ago

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Step-by-step explanation:

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3 years ago

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s344n2d4d5 [400]

Answer:

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Step-by-step explanation:

Through the process of elimination it is not:

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3 years ago