If r varies inversely as t, but directly as the square of m. if r=32 when m=8 and t=2, find r when m=6 and t=5?

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If r varies inversely as t, but directly as the square of m. if r=32 when m=8 and t=2, find r when m=6 and t=5?

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Answer 1 · 2018-02-28T18:14:45

$r = 7.2$ $r = 7.2$

Explanation:

r varies inversely as t, $\Rightarrow r \propto \frac{1}{t}$ $=> r prop 1/t$ ------(1)

but directly as the square of m $\Rightarrow r \propto m^{2}$ $=> r prop m^2$ -------(2)

Combining (1) and (2):

$r \propto \frac{m^{2}}{t}$ $r prop m^2/t$

writing it as a equation (removing proportionality sign):

$\Rightarrow r = k \times \frac{m^{2}}{t}$ $=> r = k xx m^2/t$ ----(3),where $k$ $k$ is the proportionality constant.

$\Rightarrow k = r \times \frac{t}{m^{2}}$ $=>k = r xx t/m^2$

Given that if r=32 when m=8 and t=2, gives the value of $k$ $k$ as:

$\Rightarrow k = 32 \times \frac{2}{8^{2}} = \frac{64}{64} = 1$ $=> k = 32 xx 2/8^2 = 64/64 = 1$

$therefore k = 1$ ------(1)

To find r when m=6 and t=5, substitute value of $k = 1$ :

(3) $=> r = 1 xx 6^2 /5$

$=> r = 36/5 = 7.2$

Answer 2 · 2018-02-28T18:32:18

$r=36/5$

Explanation:

$"the initial statement is "rpropm^2/t$

$"to convert to an equation multiply by k the constant"$
$"of variation"$

$rArrr=kxxm^2/t=(km^2)/tlarrcolor(blue)"k is the constant of variation"$

$"to find k use the given condition"$

$r=32" when "m=8" and "t=2$

$r=(km^2)/trArrk=(rt)/m^2=(32xx2)/64=1$

$"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(r=m^2/t)color(white)(2/2)|)))$

$"when "m=6" and "t=5" then"$

$r=36/5$

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If r varies inversely as t, but directly as the square of m. if r=32 when m=8 and t=2, find r when m=6 and t=5?

2 Answers

Explanation:

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