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Fantom [35]
2 years ago
11

The time it takes to travel a fixed distance varies inversely with the speed traveled. It takes

Mathematics
1 answer:
uysha [10]2 years ago
6 0

first off, let's notice that Purple's time is in minutes, whilst the rate is in miles per hour, the units of both must correspond, so, we can either change the time from minutes to hours or the rate from hours to minutes, hmmm let's change the time to hours.

so 40 minutes, we know there are 60 minutes in 1 hour, so 40 minutes will be 40/60 of an hr, or namely 2/3.

\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill

\stackrel{\begin{array}{llll} \textit{\tiny "t"ime varies}\\ \textit{\tiny inversely with "s"peed} \end{array}}{t = \cfrac{k}{s}}\qquad \textit{we know that} \begin{cases} t=\stackrel{minutes}{40}\to \stackrel{hrs}{\frac{2}{3}}\\ s=\stackrel{m/h}{9} \end{cases} \implies \cfrac{2}{3}~~ = ~~\cfrac{k}{9} \\\\\\ 18=3k\implies \cfrac{18}{3}=k\implies 6=k~\hfill \boxed{t=\cfrac{6}{s}} \\\\\\ \textit{when s = }\stackrel{m/h}{12}\textit{ what is "t"?}\qquad t=\cfrac{6}{12}\implies t=\cfrac{1}{2}

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zheka24 [161]

Answer:

The circumference of the smaller circle is:

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Step-by-step explanation:

We know that for a circle of radius R the circumference is given by:

C = 2*pi*R

where pi = 3.14...

Here we have two circles, A and B, where B is the larger circle and A is the smaller circle.

We know that:

The circumference of B is 3 times the circumference of A.

The radius of circle B is: OB = x

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C(B) = 2*pi*OB = 2*pi*x

The circumference of circle A will be:

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replacing the equations for the circumferences, we get:

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Step by Step:
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