A cardboard box without a lid is to have a volume of 16,384 cm3. Find the dimensions that minimize the amount of cardboard used. (Let x, y, and z be the dimensions of the cardboard box.)

The dimensions that minimize the amount of cardboard used is

x = 31 cm ,  y = 34 cm & Z = 15.54 cm

Step-by-step explanation:

Volume of the cardboard = 16,384

The function that represents the area of the cardboard without a lid is given by

------  (1)

Volume of the cardboard with sides x, y & z is

Put this value of z in equation (1) we get

Differentiate above equation with respect to x & y we get

Take

 ------ (2)

 ------- (3)

By solving equation (2) & (3) we get

x = 31 cm

From equation 2

y = 32768 ()

y = 34 cm

Z = 15.54 cm

Thus the dimensions that minimize the amount of cardboard used is

x = 31 cm ,  y = 34 cm & Z = 15.54 cm

answer: what do you mean

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,