Omg im on my ! if z varies inversely as w, and z=4 when w=9, find z when w=12

z=3. If z varies inversely as w, and z=4 when w=9, then when w=12 the value of z is 3.

The key to solve this problem is using reverse proportionality, in which two magnitudes a and b are inversely proportional when there is a constant k such that

a⋅b=k, where constant k is called the proportionality constant.

Then if z varies inversely as w, and z=4 when w=9

z.w=k > 4.9=k > k=36

So, let's find z when w = 12. With k = 36

z.w=K, clear z from the equation

z=k/w > z=36/12 > z=3

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step-by-step explanation:

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.