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
Pallu
Feb 28, 2018

#r = 7.2#

Explanation:

r varies inversely as t, #=> r prop 1/t# ------(1)

but directly as the square of m #=> r prop m^2# -------(2)

Combining (1) and (2):

# r prop m^2/t#

writing it as a equation (removing proportionality sign):

#=> r = k xx m^2/t# ----(3),where #k# is the proportionality constant.

#=>k = r xx t/m^2#

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

#=> 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#

Jim G.
Feb 28, 2018

#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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