Question 1203019
your problem seems to be that you assumed that the constant of variation was the same in both parts.
it is not.
this apparently didn't apply to the first problem you solved because one of the parts was a constant and didn't involve a constant of variation.
in the second problem, both parts required a constant of variation.
i initially assumed both constants of variation would be the same but ran into trouble
i then went back and assumed that they were different for each part.
this is how i solved it.
you are given that C = a + b, where a = x * t^3 and b = y / t^2.
both x and y are constants of variations for their part.
you are then given that C = 74 when t = 1 and C = 34 when t = 2
your two equations become:
74 = x * 1^3 + y / 1^2 when t = 1
34 = x * 2^3 + y / 2^2 when t = 2
the first equation becomes 74 = x + y
the second equation bcomes 34 = 8x + y/4
you now want to solve these equations simultaneously.
first equation becomes x + y = 74
second equation becomes 32x + y = 136
subtract the first equation from the second to get 31x = 62
solve for x to get x = 2
since x + y = 74, then y must be equal to 72.
you now have x = 2 and y = 72
x is the constant of variation for the first part and y is the constant of vriation for the second part.
they want you to find C when t = 3.
when t = 3, your equation becomes C = 2 * 3^3 = 72 / 3^2.
this becomes C = 2 * 27 + 72 / 9
this becomes C = 54 + 8 which becomes C = 62.


i'm pretty sure i did it right.
your biggest problem appears that you assumed the constant of variation was the same in both parts.
that's what i think.
i also think think that you assumed b was the constant of variation in the first equation.
it was not.