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Free_Kalibri [48]
3 years ago
5

What is the value of x? 20 35 60 70

Mathematics
1 answer:
Artist 52 [7]3 years ago
5 0
Vertical angles are congruent. So, x+40=3x. 40=2x. 20=x.
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v=\dfrac h{3x}\implies\dfrac{\mathrm dv}{\mathrm dt}=\dfrac{3x\frac{\mathrm dh}{\mathrm dt}-3h\frac{\mathrm dx}{\mathrm dt}}{3x^2}

By the chain rule,

\dfrac{\mathrm dh}{\mathrm dt}=\dfrac{\mathrm dh}{\mathrm dx}\dfrac{\mathrm dx}{\mathrm dt}

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and we're given that x changes at a constant rate of \frac{\mathrm dx}{\mathrm dt}=0.2 thousand people per minute, which means

\dfrac{\mathrm dv}{\mathrm dt}=\dfrac{3x\left(8e^{2x-6}-2x\right)\left(0.2\frac{\text{thousand people}}{\rm min}\right)-3h\left(0.2\frac{\text{thousand people}}{\rm min}\right)}{3x^2}

At the moment x=4 thousand people are in the park, we have h(4)=4e^2-11, so we find

\dfrac{\mathrm dv}{\mathrm dt}=\dfrac{12\left(8e^2-8\right)-3(4e^2-11)}{240}\dfrac{\text{thousand people}}{\rm min}=\dfrac{7(4e^2-3)}{80}\dfrac{\text{thousand people}}{\rm min}

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Because you move the points according to the rule.

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