For the following exercises, write an equation describing the relationship of the given variables. 23. y varies jointly as x and z and inversely as the square rootof w and the square of t. When x = 3 , z = 1 , w = 25 , a n d t = 2 , t h e n y = 6
For the following exercises, write an equation describing the relationship of the given variables. 23. y varies jointly as x and z and inversely as the square rootof w and the square of t. When x = 3 , z = 1 , w = 25 , a n d t = 2 , t h e n y = 6
The amount of juice in a grapefruit is directly proportional to the cube of its diameter. Let j represent the amount of juice (in fluid ounces) in a grapefruit, let d represent the diameter (in inches) of the grapefruit, and let k be the constant of proportionality. Write an equation that relates j to d.
j =
A grapefruit with a 4-inch diameter contains 6 fluid ounces of juice. Use the equation that relates j to d and the known information to find k.
k =
How many fluid ounces of juice is contained in a grapefruit with a 5-inch diameter? Round to the nearest tenth of a fluid ounce.
-------fl oz
a. DeepSea Challenger's descent was a change in depth of (-4) feet per
second. We can use the equation y = -4x to model this relationship, where
y is the depth and x is the time in seconds that have passed.
How many seconds does this model suggest it would
take
for DeepSea
Challenger to reach the bottom?
Let yy be a Jane's salary (in thousands of dollars) after she has worked xx years at a company. Assume that the equation y=2.5x+26y=2.5x+26 describes the relationship between x and y.
Years at the companyxx
Salary (thousands of dollars)yy
0
1
2
3
4
By how much does Jane's salary increase each year? $
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