Question

X and y vary inversely and x=50 when y=5 find y when x=10 what is k?

x and y vary directly and x=6 when y=42 find k what is y when x=12

Answer 1

Part A)

1)
`k=250`

2)
`y=25`

Part B)

1)
`k=7`

2)
`y=84`

Explanation:

Part 1) x and y vary inversely and x=50 when y=5 find y when x=10 what is k?

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
`y*x=k` or
`y=k/x`

step 1

Find the value of k

x=50 when y=5

substitute the values

`y*x=k` ------>
`5*50=k` ----->
`k=250`

The equation is equal to

`y*x=250` or
`y=250/x`

step 2

Find y when x=10

substitute the value of x in the equation and solve for y

`y*(10)=250`

`y=250/10=25`

Part B) x and y vary directly and x=6 when y=42 find k what is y when x=12

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form
`y/x=k` or
`y=kx`

step 1

Find the value of k

x=6 when y=42

substitute the values

`y/x=k` ------>
`42/6=k` ----->
`k=7`

The equation is equal to

`y/x=7` or
`y=7x`

step 2

Find y when x=12

substitute the value of x in the equation and solve for y

`y=7(12)=84`