SOLUTION: When x = 2 and y = 3, z = 42. Write the function that models each of the following relationships. 1. z varies inversely with x and directly with y. (1 point) 2. z varies

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: When x = 2 and y = 3, z = 42. Write the function that models each of the following relationships. 1. z varies inversely with x and directly with y. (1 point) 2. z varies      Log On


   

Question 275518: When x = 2 and y = 3, z = 42. Write the function that models each of the following relationships.
1. z varies inversely with x and directly with y. (1 point)
2. z varies jointly with x and y (1 point)
3. z varies directly with x and inversely with the square of y (1 point)



Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your problem states:

When x = 2 and y = 3, z = 42. Write the function that models each of the following relationships.

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1. z varies inversely with x and directly with y. (1 point)

formula would be z = ky/x

substitute:

x = 2
y = 3
z = 42

formula becomes:

42 = k*3/2 **************************************************

solve for k to get:

k = 2*42/3 = 28

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2. z varies jointly with x and y (1 point)

formula is z = kxy

substitute:

x = 2
y = 3
z = 42

formula becomes:

42 = k*2*3 *******************************************************

solve for k to get:

k = 42/6 = 7

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3. z varies directly with x and inversely with the square of y (1 point)

formula is:

z = kx/y^2

substitute:

x = 2
y = 3
z = 42

formula becomes:

42 = k*2/(3^2) = k*2/9 ************************************************

solve for k to get:

k = 42*9/2 = 189

they did not ask you to solve the equations.

they only asked you to write the functions.

functions with the ****************************************** next to them should be your answers.