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How do you write a general formula to describe each variation if the cube of z varies directly with the sum of the squares of x and y; z=2 when x=9 and y=4?

Answer 1

The general formula to describe the variation is z = k(x^2 + y^2), where k is the constant of variation. To find the value of k, substitute the given values of z, x, and y into the formula and solve for k. In this case, z = 2, x = 9, and y = 4.

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Answer 2

Avery Alexander

#z^3=8/97(x^2+y^2)#

As #z^3# varies directly with the sum of the squares of #x# and #y# i.e. #x^2+y^2#, we can say

#z^3=kxx(x^2+y^2)#

Now, as when #x=9# and #y=4#, we have #z=2#

#2^3=kxx(9^2+4^2)=kxx(81+16)=97k#

i.e. #k=8/97#

Hence #z^3=8/97(x^2+y^2)#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.