Answer:
A. y= [tex]\frac{z*240ft\\\\^{3} }{x}[/tex]
B. z= 2
Step-by-step explanation:
A.
The format for the inverse variation formula is y =
This is a bit different compared to the format of directly variation formula y= kx
In this case, one load of gravel have [tex]240 ft^{3}[/tex]volume. The area is inversely proportional with depth, so formula for the volume is Area x Depth (V= A x D). The inverse variation formula will be: A= V/D
If the number of loads=z, each load is [tex]240 ft^{3}[/tex], area = y and depth = x , then the model will be:
y= [tex]\frac{z*\\k}{x}[/tex]
y= [tex]\frac{z*240ft\\\\^{3} }{x}[/tex]
B.
The play area is a rectangle 40 ft wide and 24 ft long, then the area will be: area = 40ft * 24ft= 960 [tex]ft^{2}[/tex]
We have area(y= 960 [tex]ft^{2}[/tex]) and depth(x= 6 in- 0.5 ft) , now we can find out the number of loads needed(z) by using the equation.
y= [tex]\frac{240ft*z\\\\^{3} }{x}[/tex]
960 [tex]ft^{2}[/tex]= [tex]\frac{z*240ft\\\\^{3} }{x}[/tex]
[tex]480 ft^{2} * z[/tex]= 960 [tex]ft^{2}[/tex]
z= [tex]\frac{960ft^{2} }{480ft^{2}}[/tex]= 2
