How do you write a general formula to describe each variation if z varies directly with the sum of the cube of x and the square of y; z=1 when x=2 and y=3?

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Answer 1 · 2016-10-08T16:37:30

General formula is #z=1/17(x^3+y^2)#

When a variable say #z# varies directly with say #w#

we have #zpropw# i.e. #z=wxxk#, where #k# is a constant.

Here #w# is the sum of the cube of #x# and the square of #y#

Hence #z=(x^3+y^2)xxk# ......................(1)

When #z=1# when #x=2# and #y=3#, (1) becomes

#1=(2^3+3^2)xxk#

or #1=(8+9)xxk#

or #17k=1# i.e. #k=1/17#

Hence, general formula is #z=1/17(x^3+y^2)#