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Pavlova-9 [17]
4 years ago
8

I don’t feel like typing it out but can you guys help me on this one

Mathematics
2 answers:
vichka [17]4 years ago
7 0

Answer:

The answer is D

Step-by-step explanation:

The hot air balloon loses 1626 m of mass after 15 minutes. So you divide it by 15 to find it's rate per minute, which is 108.4 m. Afterwards, you divide 108.4 by 3000 to find the percentage rate per minute.

lara31 [8.8K]4 years ago
3 0

the answer is 4%

Hope this helps!

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A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 80 ft is given by y =
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Answer:

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Step-by-step explanation:

Here, the given function,

y=150-\frac{1}{40}(x-50)^2

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y'=-\frac{1}{20}(x-50)

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L=\int_{a}^{b} \sqrt{1+y'^2}dx

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Thus, the arc length of the given curve is,

L=\int_{0}^{80} \sqrt{1+(-\frac{1}{20}(x-50)^2}dx

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\implies L=-20\int_{0}^{80} \sqrt{1+tan^2\theta}sec^2\theta d\theta

=-20\int_{0}^{80} (sec \theta ) sec^2\theta d\theta

=-20\int_{0}^{80} (sec \theta ) sec^2\theta d\theta

By integration by parts,

=|-\frac{20}{2}(sec \theta tan\theta +ln|sec\theta +tan\theta |) |^{x=80}_{x=0}

If x = 80, tan \theta = -\frac{1}{20}(30-50)=\frac{3}{2}

sec \theta = \frac{\sqrt{13}}{2}

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sec \theta = \frac{\sqrt{29}}{2}

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=-10(\frac{\sqrt{13}}{2}(-\frac{3}{2}) +ln|\frac{13}{2}-\frac{3}{2}|) + 10(\frac{5\sqrt{29}}{4} + ln |\frac{29}{2} + \frac{5}{2} |)

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