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nordsb [41]
3 years ago
14

The time it takes you to go a certain distance varies inversely with the speed of travel. Suppose it takes you 4 hours to get to

a sports event driving at a rate of 50 miles per hour.
a) Find the constant of variation. Write the particular equation expressing time in terms of speed.




b) How long will it take you to get to the event if you drive at 40 mph?
Mathematics
1 answer:
fgiga [73]3 years ago
3 0
\bf \qquad \qquad \textit{inverse proportional variation}
\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad  y=\cfrac{k}{x}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad  variation
\end{array}\\\\
-------------------------------

\bf \textit{time it takes varies inversely with the speed rate}\qquad \stackrel{time}{t}=\cfrac{k}{\stackrel{rate}{r}}
\\\\\\
\textit{we also know that }
\begin{cases}
t=\stackrel{hrs}{4}\\
r=\stackrel{mph}{50}
\end{cases}\implies 4=\cfrac{k}{50}\implies 200=k
\\\\\\
\boxed{t=\cfrac{200}{r}}
\\\\\\
\textit{if your rate r = 40, what is your distance \underline{t}?}\qquad t=\cfrac{200}{40}
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Write the inverse function for the function, ƒ(x) =1/2x + 4. Then, find the value of ƒ^ -1(4). Type your answers in the box.
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Answer:

f⁻¹(x) = 2x - 8

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Step-by-step explanation:

f(x) = \frac{1}{2} x + 4\\x = \frac{1}{2} f^{-1}(x) + 4\\x - 4 = \frac{1}{2} f^{-1}(x)\\2x - 8 = f^{-1}(x)\\f^{-1}(x) = 2x - 8

Let's test it

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So we do indeed have the inverse function, so using that we can plug in the values requested:

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The sum of a number times 8 and 21 is less than -16.
vodka [1.7K]

Hello.

First of all, let the number be t.

8 times t can be written like this:

\mathrm{8t}

Notice that the number is before the variable and the times sign (×) is not there.

We can write it as 8×t, but we usually write it as 8t.

The sum of means we add:

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Now, "less than" is "<" :

\mathrm{8t+21 < -16}

Therefore, the answer is

\mathrm{8t+21 < -16}

I hope it helps.

Have a nice day.

\boxed{imperturbability}

7 0
2 years ago
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