40 points!! please do not plagiarize, I need this to be original :D

Mathematics

1 answer:

REY [17]3 years ago

5 0

Answer:

4/5

Step-by-step explanation:

4/5 because that would make five tries and he has made 4 with black so he has a 4/5 chance

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Graph the system of linear equations in the coordinate plane below.

fgiga [73]

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3 years ago

Water is poured into a conical paper cup at the rate of 3/2 in3/sec. If the cup is 6 inches tall and the top has a radius of 6 i

Leto [7]

So.. hmm notice the picture below

r = h, due to similar triangles ratio, whatever "h" may be

now, we're given how much water is being poured into the cup per sec
namely dv/dt the volume's rate

so.. hmmm $\bf \textit{volume of a cone}=V=\cfrac{\pi r^2 h}{3}\quad however\implies r=h
\\\\\\
thus\implies V=\cfrac{\pi h^2 h}{3}\implies V=\cfrac{\pi h^3}{3}\\\\
------------------------\\\\
now
\\\\\\
\cfrac{dv}{dt}=\cfrac{\pi }{3}\cdot 3h^2\cdot \cfrac{dh}{dt}\implies \cfrac{dv}{dt}=\pi h^2\cdot \cfrac{dh}{dt}
\\\\\\
\cfrac{\frac{dv}{dt}}{\pi h^2}=\cfrac{dh}{dt}\quad 
\begin{cases}
\frac{dv}{dt}=\frac{3}{2}\\\\
\left. \frac{dh}{dt} \right|_{h=4}
\end{cases}\implies \cfrac{\frac{3}{2}}{\pi 4^2}=\cfrac{dh}{dt}$