Answer:
Part 1) ![x=11](https://tex.z-dn.net/?f=x%3D11)
Part 2)
Part 3) ![y=9.2](https://tex.z-dn.net/?f=y%3D9.2)
Part 4) ![x=2.375](https://tex.z-dn.net/?f=x%3D2.375)
Part 5) ![y=3.3](https://tex.z-dn.net/?f=y%3D3.3)
Part 6) ![k=6.7](https://tex.z-dn.net/?f=k%3D6.7)
Part 7) ![k=115.2](https://tex.z-dn.net/?f=k%3D115.2)
Part 8) ![y=1.4](https://tex.z-dn.net/?f=y%3D1.4)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
or ![y=k/x](https://tex.z-dn.net/?f=y%3Dk%2Fx)
Part 1) y varies inversely with x. If y = 3 and k (the constant of variation) = 33, what is x?
we have
![y*x=k](https://tex.z-dn.net/?f=y%2Ax%3Dk)
![y=3](https://tex.z-dn.net/?f=y%3D3)
![k=33](https://tex.z-dn.net/?f=k%3D33)
substitute and solve for x
![3*x=33](https://tex.z-dn.net/?f=3%2Ax%3D33)
Divide by 3 both sides
![x=33/3](https://tex.z-dn.net/?f=x%3D33%2F3)
![x=11](https://tex.z-dn.net/?f=x%3D11)
Part 2) y varies inversely with x. When y = 11, x = 5.2. What is the value of k, the constant of inverse variation?
we have
![y*x=k](https://tex.z-dn.net/?f=y%2Ax%3Dk)
![y=11](https://tex.z-dn.net/?f=y%3D11)
![x=5.2](https://tex.z-dn.net/?f=x%3D5.2)
substitute and solve for k
![11*5.2=k](https://tex.z-dn.net/?f=11%2A5.2%3Dk)
Part 3) y varies inversely with x, and k (the constant of variation) = 72. What is the value of y when x = 7.8?
we have
![y*x=k](https://tex.z-dn.net/?f=y%2Ax%3Dk)
![x=7.8](https://tex.z-dn.net/?f=x%3D7.8)
![k=72](https://tex.z-dn.net/?f=k%3D72)
substitute and solve for y
![y*7.8=72](https://tex.z-dn.net/?f=y%2A7.8%3D72)
Divide by 7.8 both sides
![y=72/7.8](https://tex.z-dn.net/?f=y%3D72%2F7.8)
![y=9.2](https://tex.z-dn.net/?f=y%3D9.2)
Part 4) y varies inversely with x. If y = 8 and k (the constant of variation) = 19, what is x?
we have
![y*x=k](https://tex.z-dn.net/?f=y%2Ax%3Dk)
![y=8](https://tex.z-dn.net/?f=y%3D8)
![k=19](https://tex.z-dn.net/?f=k%3D19)
substitute and solve for x
![8*x=19](https://tex.z-dn.net/?f=8%2Ax%3D19)
Divide by 8 both sides
![x=19/8](https://tex.z-dn.net/?f=x%3D19%2F8)
![x=2.375](https://tex.z-dn.net/?f=x%3D2.375)
Part 5) y varies inversely with x, and k (the constant of variation) = 23. What is the value of y when x = 7?
we have
![y*x=k](https://tex.z-dn.net/?f=y%2Ax%3Dk)
![x=7](https://tex.z-dn.net/?f=x%3D7)
![k=23](https://tex.z-dn.net/?f=k%3D23)
substitute and solve for y
![y*7=23](https://tex.z-dn.net/?f=y%2A7%3D23)
Divide by 7 both sides
![y=23/7](https://tex.z-dn.net/?f=y%3D23%2F7)
![y=3.3](https://tex.z-dn.net/?f=y%3D3.3)
Part 6) y varies inversely with x. When y = 6.7, x = 1. What is the value of k, the constant of inverse variation?
we have
![y*x=k](https://tex.z-dn.net/?f=y%2Ax%3Dk)
![y=6.7](https://tex.z-dn.net/?f=y%3D6.7)
![x=1](https://tex.z-dn.net/?f=x%3D1)
substitute and solve for k
![6.7*1=k](https://tex.z-dn.net/?f=6.7%2A1%3Dk)
![k=6.7](https://tex.z-dn.net/?f=k%3D6.7)
Part 7) y varies inversely with x. When y = 9.6, x = 12. What is the value of k, the constant of inverse variation?
we have
![y*x=k](https://tex.z-dn.net/?f=y%2Ax%3Dk)
![y=9.6](https://tex.z-dn.net/?f=y%3D9.6)
![x=12](https://tex.z-dn.net/?f=x%3D12)
substitute and solve for k
![9.6*12=k](https://tex.z-dn.net/?f=9.6%2A12%3Dk)
![k=115.2](https://tex.z-dn.net/?f=k%3D115.2)
Part 8) y varies inversely with x, and k (the constant of variation) = 5.6. What is the value of y when x = 4?
we have
![y*x=k](https://tex.z-dn.net/?f=y%2Ax%3Dk)
![x=4](https://tex.z-dn.net/?f=x%3D4)
![k=5.6](https://tex.z-dn.net/?f=k%3D5.6)
substitute and solve for y
![y*4=5.6](https://tex.z-dn.net/?f=y%2A4%3D5.6)
Divide by 4 both sides
![y=5.6/4](https://tex.z-dn.net/?f=y%3D5.6%2F4)
![y=1.4](https://tex.z-dn.net/?f=y%3D1.4)