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2 years ago

A hot air balloon descended 3,240 feet in an hour. find the change in altitude per minute.

Mathematics

1 answer:

3241004551 [841]2 years ago

4 0

Answer:

-54ft/min (-54 feet per minute)

Step-by-step explanation:

To solve this, we need to use background knowledge to get one of our missing numbers.

Since we know an hour is 60 minutes, we need to do 3,240/60 to receive our unit rate. So, 3,240/60 would equal 54.

But, the balloon is <u>descending</u> (going down), so we need to make our answer negative (54 -> -54)

Therefore, the hot air balloon is descending 54 feet per minute, or -54ft/min.

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Aleks04 [339]

73.

$f(x)=\frac{3x^4+3x^3-36x^2}{x^4-25x^2+144}$

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But before, we can factor the numerator and the denominator:

$\begin{gathered} \frac{3x^2(x^2+x-12)}{x^4-25x^2+144}=\frac{3x^2((x+4)(x-3))}{(x-3)(x-3)(x+4)(x+4)} \\ so: \\ \frac{3x^2}{(x+3)(x-4)} \end{gathered}$

Now, we can conclude that the vertical asymptotes are located at:

$\begin{gathered} (x+3)(x-4)=0 \\ so: \\ x=-3 \\ x=4 \end{gathered}$

so, for x = -3:

$\lim_{x\to-3^-}f(x)=\lim_{x\to-3^-}-\frac{162}{x^4-25x^2+144}=-162(-\infty)=\infty$ $\lim_{x\to-3^+}f(x)=\lim_{x\to-3^+}-\frac{162}{x^4-25x^2+144}=-162(\infty)=-\infty$

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$\lim_{x\to4^-}f(x)=\lim_{n\to4^-}\frac{384}{x^4-25x^2+144}=384(-\infty)=-\infty$ $\lim_{x\to4^-}f(x)=\lim_{n\to4^-}\frac{384}{x^4-25x^2+144}=384(-\infty)=-\infty$

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