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2 years ago

The square below has a side length of 14 inches. What is the area of the shaded region?

Mathematics

1 answer:

hichkok12 [17]2 years ago

7 0

Answer:

14 square units

Step-by-step explanation:

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Use spherical coordinates. evaluate xyz dv e , where e lies between the spheres ρ = 4 and ρ = 6 and above the cone ϕ = π/3.

sergey [27]

Set

$x=\rho\cos\theta\sin\varphi$

$y=\rho\sin\theta\sin\varphi$

$z=\rho\cos\varphi$

so that the volume element is

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

The integral is then

$\displaystyle\iiint_Exyz\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi/3}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=4}^{\rho=6}\rho^5\cos\theta\sin\theta\sin^3\varphi\cos\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\rho$

$=\displaystyle\left(\int_0^{\pi/3}\sin^3\varphi\cos\varphi\,\mathrm d\varphi\right)\underbrace{\left(\int_0^{2\pi}\cos\theta\sin\theta\,\mathrm d\theta\right)}_0\left(\int_4^6\rho^5\,\mathrm d\rho\right)$

and so evaluates to 0.

3 0

2 years ago

Pls help quickly I’ll give u brainlyist btw it’s 7th grade math

erica [24]

Answer:

2 and 5

Step-by-step explanation:

3 0

3 years ago

Denton owns a bookstore. Today he sold books for $112, $93, $131, $64 and $210. Estimate the total value of the five book sales.

jonny [76]

In the end it should be 610 dollars

6 0

3 years ago

Read 2 more answers

kelly buys 3 video games that cost &18.95 each. she also buys 2 pairs of earbuds that cost $11.50 each. she has a coupon for

monitta

Answer:

The Cashier

Step-by-step explanation:

First you take off $2.00 of every $18.95 of the game and you get $16.95 you add 16.95 three times and after that you add 11.50 twice and then the sum of both the earbuds and the video games and you add both together and you get $73.85

5 0

3 years ago

HELP PLS !!<br><br> Make y the subject in the formula x = 5y – w.

NARA [144]

Answer:

y=x+w/5

Step-by-step explanation:

x=5y-w

step 1: bring the additional letters/numbers next to the "5y" over to the left

x+w= 5y

step 2: divide the numbers and letters on both sides of the "=" by 5 to only get the letter y

x+w/5= y

step 3: swap them over

y= x+w/5

(we can't get an answer from x+w/5 because the terms are unlike, therefore we keep it as a fraction

8 0

2 years ago