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3 years ago

5

A swimming pool is in the shape of a right rectangular prism. The base of the pool has an area of 216 square feet. When the pool

is completely filled, it holds 1,944 cubic feet of water. What is the depth of the water when the pool is completely full?

1 answer:

rjkz [21]3 years ago

6 0

Answer:

Just divide

1944/216=9

9 feet deep

Hope this helps

Step-by-step explanation:

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Evaluate the line integral: Int(x^2 dx +y^2 dy) ∫Cx2dx+y2dy C consists of the arc of the circle x^2+y^2=4 from (2,0) to (0,2) fo

pychu [463]

The first part of the arc $C$ can be parameterized by

$C_1:\mathbf r(t)=\langle 2\cos t,2\sin t\rangle$

with $0\le t\le\dfrac\pi2$ , and the second part by

$C_2:\mathbf s(t)=(1-t)\langle0,2\rangle+t\langle4,3\rangle=\langle4t,2+t\rangle$

with $0\le t\le 1$ .

Now the line integral can be computed.

$\displaystyle\int_{C=C_1\cup C_2}(x^2\,\mathrm dx+y^2\,\mathrm dx)=\int_0^{\pi/2}\left((2\cos t)^2\dfrac{\mathrm d}{\mathrm dt}(2\cos t)+(2\sin t)^2\dfrac{\mathrm d}{\mathrm dt}(2\sin t)\right)\,\mathrm dt+\int_0^1\left((4t)^2\dfrac{\mathrm d}{\mathrm dt}(4t)+(2+t)^2\dfrac{\mathrm d}{\mathrm dt}(2+t)\right)\,\mathrm dt$
$=\displaystyle\int_0^{\pi/2}(-8\cos^2t\sin t+8\sin^2t\cos t)\,\mathrm dt+\int_0^1(64t^2+(2+t)^2)\,\mathrm dt$
$=\displaystyle-8\int_0^{\pi/2}\sin t\cos t(\cos t-\sin t)\,\mathrm dt+\int_0^1(65t^2+4t+4)\,\mathrm dt$
$=\displaystyle-4\int_0^{\pi/2}\sin2t(\cos t-\sin t)\,\mathrm dt+\int_0^1(65t^2+4t+4)\,\mathrm dt$
$=\displaystyle-2\int_0^{\pi/2}(\sin t+\sin3t-\cos t+\cos3t)\,\mathrm dt+\int_0^1(65t^2+4t+4)\,\mathrm dt$
$=\displaystyle-2\left(-\cos t-\frac{\cos3t}3-\sin t+\frac{\sin3t}3\right)\bigg|_{t=0}^{t=\pi/2}+\left(\frac{65}3t^3+2t^2+4t\right)\bigg|_{t=0}^{t=1}$
$=0+\dfrac{83}3$
$=\dfrac{83}3$

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3 years ago

A random sample of 20 married women showed that the mean time spent on housework by them was 29.8 hours a week with a standard d

DanielleElmas [232]

Answer:

95% confidence interval for the mean time spent on housework per week by all married women.

( 26.66 , 32.94)

Step-by-step explanation:

<u><em>Step(i)</em></u>:-

Given random sample size 'n' = 20

Mean of the sample (x⁻ ) = 29.8 hours

Standard deviation of the sample (S) = 6.7

Given Margin of error = 3.14

<u><em>Step(ii):</em></u>-

95% confidence interval for the mean is determined by

$(x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} +t_{0.05} \frac{S}{\sqrt{n} })$

We know that margin of error is determined by

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3 years ago

Russell has a collection of 1,200 pennies. Of these pennies, 25% are dated before 1980, 35% are dated from 1980 to 2000, and the

Svet_ta [14]

40% dated after 2000

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3 years ago

Read 2 more answers

Solve for x in the diagram below

ella [17]

Answer:

20

Step-by-step explanation:

3x + x + 100 = 180 (sum of angles on a straight line)

4x = 180-100

4x=80

divide both sides by 4

x=20

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3 years ago

Will the given side lengths form a right triangle?<br><br> 1, 2, 5

jek_recluse [69]

Step-by-step explanation:

For 3 side lengths of a triangle to form a right triangle, the sum of the squares of the 2 smaller side lengths must be equal to the square of the largest side. (a² + b² = c²)

Since 1² + 2² =/= 5², (5 =/= 25)

it will not form a right triangle.

Another Explanation:

Since 5 > 1 + 2, the sum of the 2 smaller side lengths is less than the largest side. Hence it will not form a triangle => not form a right triangle.

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3 years ago