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2 years ago

Find the area of the figure below:

Mathematics

1 answer:

Afina-wow [57]2 years ago

6 0

Answer:

60.75 m^2

Have a great day

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Which statement best describes the equation x^5+x^3-14=0

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3 years ago

What is the probability from a two way table ?

vladimir1956 [14]

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2 years ago

What is the solution to this equation?

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Answer:

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2 years ago

Use spherical coordinates. evaluate (9 − x2 − y2) dv, where h is the solid hemisphere x2 + y2 + z2 ≤ 4, z ≥ 0.

avanturin [10]

In spherical coordinates, we have

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}$

which gives volume element

$\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$

and so the triple integral is given by

$\displaystyle\iiint_H(9-x^2-y^2)\,\mathrm dV$
$=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{\varphi=0}^{\varphi=\pi/2}\int_{\rho=0}^{\rho=2}(9-\rho^2\sin^2\varphi)\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$
$=\displaystyle2\pi\int_{\varphi=0}^{\varphi=\pi/2}\int_{\rho=0}^{\rho=2}(9\rho^2\sin\varphi-\rho^4\sin^3\varphi)\,\mathrm d\rho\,\mathrm d\varphi$
$=\dfrac{592\pi}{15}$

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3 years ago

Can anyone help me with this

trapecia [35]

Answer:

a)$2800 , $0

b)$1600 , $0

c)$2800 , $0

d)$1650 , $0

e)$4400 , $0

f)$1020 , $0

g)$1405 , $0

h)$5400 , $0

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2 years ago