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Rufina [12.5K]
3 years ago
8

Solve for the variable shown. Round answers to the nearest hundredth if needed.

Mathematics
1 answer:
Olenka [21]3 years ago
4 0

Answer and Step-by-step explanation:

Question 4:

We need to solve for y, so we need to use the cosine trig function, which is adjacent divided by hypotenuse.

cos(21) = \frac{y}{18}\\\\18(cos(21)) = y = 16.8\\\\\\

Question 5:

We need to use the sine trig function, which is opposite divided by hypotenuse.

sin(43) = \frac{31}{x} \\\\x = \frac{31}{sin(43)} = 45.45

#teamtrees #WAP (Water And Plant)

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Effectus [21]
Given the formula 
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nata0808 [166]

I suspect 4/2 should actually be 4/3, since 4/2 = 2, while 4/3 would make V the volume of a sphere with radius r. But I'll stick with what's given:

\displaystyle \frac{dV}{dr} = \lim_{h\to0} \frac{2\pi(r+h)^3-2\pi r^3}{h}

\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{(r^3+3r^2h+3rh^2+h^3)- r^3}{h}

\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{3r^2h+3rh^2+h^3}{h}

\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} (3r^2+3rh+h^2)

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In Mathematica, you can check this result via

D[4/2*Pi*r^3, r]

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