# 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:

r varies inversely as t,

but directly as the square of m

Combining (1) and (2):

writing it as a equation (removing proportionality sign):

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

To find r when m=6 and t=5, substitute value of

(3)

#### 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#