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hjlf
3 years ago
14

Micheal has a sink that is shaped like a half-sphere. The sink has a volume of 3000/3π in^3. One day, his sink is clogged. He ha

s to use one of two cylindrical cups to scoop the water out of the sink. The sink is completely full when Micheal begins scooping.
A) One cup has a diameter of 6 in and a height of 8 in. How many cups of water must micheal scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.

B) One cup has a diameter of 10 in and a height of 8 in. How many cups of water must micheal scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.
Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
3 0

Answer:

A is 27 i think and B is 15 i think

Step-by-step explanation:

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Find the range of the given data set.<br><br> -4, -3, -1, -1, 0, 1
Dovator [93]

Answer:

5

Step-by-step explanation:

To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

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3 years ago
The candle company is having its semiannual sale. All items are 40 percent off. If the original price of a candle basket is $120
Stells [14]

Answer:

It's C

Step-by-step explanation:

120 x 0.4 = 48

120 - 48 = 72

6 0
3 years ago
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Suppose that \nabla f(x,y,z) = 2xyze^{x^2}\mathbf{i} + ze^{x^2}\mathbf{j} + ye^{x^2}\mathbf{k}. if f(0,0,0) = 2, find f(1,1,1).
lesya [120]

The simplest path from (0, 0, 0) to (1, 1, 1) is a straight line, denoted C, which we can parameterize by the vector-valued function,

\mathbf r(t)=(1-t)(\mathbf i+\mathbf j+\mathbf k)

for 0\le t\le1, which has differential

\mathrm d\mathbf r=-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt

Then with x(t)=y(t)=z(t)=1-t, we have

\displaystyle\int_{\mathcal C}\nabla f(x,y,z)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\nabla f(x(t),y(t),z(t))\cdot\mathrm d\mathbf r

=\displaystyle\int_{t=0}^{t=1}\left(2(1-t)^3e^{(1-t)^2}\,\mathbf i+(1-t)e^{(1-t)^2}\,\mathbf j+(1-t)e^{(1-t)^2}\,\mathbf k\right)\cdot-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt

\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)(t^2-2t+2)\,\mathrm dt

Complete the square in the quadratic term of the integrand: t^2-2t+2=(t-1)^2+1=(1-t)^2+1, then in the integral we substitute u=1-t:

\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)((1-t)^2+1)\,\mathrm dt

\displaystyle=-2\int_{u=0}^{u=1}e^{u^2}u(u^2+1)\,\mathrm du

Make another substitution of v=u^2:

\displaystyle=-\int_{v=0}^{v=1}e^v(v+1)\,\mathrm dv

Integrate by parts, taking

r=v+1\implies\mathrm dr=\mathrm dv

\mathrm ds=e^v\,\mathrm dv\implies s=e^v

\displaystyle=-e^v(v+1)\bigg|_{v=0}^{v=1}+\int_{v=0}^{v=1}e^v\,\mathrm dv

\displaystyle=-(2e-1)+(e-1)=-e

So, we have by the fundamental theorem of calculus that

\displaystyle\int_C\nabla f(x,y,z)\cdot\mathrm d\mathbf r=f(1,1,1)-f(0,0,0)

\implies-e=f(1,1,1)-2

\implies f(1,1,1)=2-e

3 0
3 years ago
Sherlock Holmes discovers some hair fiber at a crime scene. He view the hairs through his magnifying glass from a distance of 6
snow_lady [41]

Answer:

24 cm.

Step-by-step explanation:

If you take 6 cm. and multiply it by 4(magnify it), you get 6 x 4, which is 24.

Hope this helps!

7 0
2 years ago
Cause
son4ous [18]

Answer:

B. Mecca's leaders forced Muhammad to leave the city.

6 0
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