The variable z is directly proportional to x, and inversely proportional to y. when x is 3 and y is 6, z has the value 9.5. what is the value of z when x=8, and y= 12

round to at least thee thousandths place if needed.

Directly proportional to x

z=kx

And inversely proportional to y

z=kx/y  we are given the point (x,y,z) of (3, 6, 9.5) so

9.5=3k/6  now multiply both sides by 6

57=3k  divide both sides by 3

19=k so now that we know the constant of proportionality:

z=19x/y,  and we want to solve for z when x=8 and y=12 so:

z=19(8)/12

z=12 2/3  exact

z≈12.667  (rounded to the nearest thousandth)

Ithink the answer is: it is likely.

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.