Please need help it’s due today

Mathematics

1 answer:

jeka943 years ago

8 0

Answer:

B. David's sprinkler uses less water per minute.

Step-by-step explanation:

David's sprinkler uses 10 gallons every 5 minutes, which is 2 gallons a minute.

George's sprinkler uses 6 gallons a minute, which means it uses more.

David's sprinkler uses less and it uses exactly 2 gallons a minute.

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A dance school allows a maximum of 15 students per class. If 112 students sign up for dance class, how many classes does the sch

Talja [164]

Answer:

Step-by-step explanation:

Take 112/15

You get 7.4667

We make it 8 because you can't have .4667 of a class

Hope this helps

7 0

3 years ago

Use stokes' theorem to evaluate c f · dr where c is oriented counterclockwise as viewed from above. f(x, y, z = xyi + 5zj + 7yk,

Helga [31]

The intersection can be parameterized by

$C:=\mathbf r(t)=\begin{cases}x(t)=6\cos t\\y(t)=6\sin t\\z(t)=5-6\cos t\end{cases}$

with $0\le t$ .

By Stoke's theorem, the integral of $\mathbf f(x,y,z)=xy\,\mathbf i+5z\,\mathbf j+7y\,\mathbf k$ along $C$ is equivalent to

$\displaystyle\int_C\mathbf f(x(t),y(t),z(t))\cdot\mathrm d\mathbf r(t)=\iint_S\nabla\times\mathbf f\,\mathrm dS$

where $S$ is the region bounded by $C$ . The line integral reduces to

$\displaystyle\int_0^{2\pi}(36\sin t\cos t\,\mathbf i+(25-30\cos t)\,\mathbf j+42\sin t\,\mathbf k)\cdot(-6\sin t\,\mathbf i+6\cos t\,\mathbf j+6\sin t\,\mathbf k)\,\mathrm dt$
$=\displaystyle\int_0^{2\pi}(54(\cos3t-\cos t)-30(3\cos2t-5\cos t+3)+(126-126\cos2t)\,\mathrm dt$
$=\displaystyle\int_0^{2\pi}(36+96\cos t-216\cos2t+54\cos3t)\,\mathrm dt$
$=72\pi$