Answer:
Part A)
1) [tex]k=250[/tex]
2) [tex]y=25[/tex]
Part B)
1) [tex]k=7[/tex]
2) [tex]y=84[/tex]
Step-by-step 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 [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
step 1
Find the value of k
x=50 when y=5
substitute the values
[tex]y*x=k[/tex] ------> [tex]5*50=k[/tex] -----> [tex]k=250[/tex]
The equation is equal to
[tex]y*x=250[/tex] or [tex]y=250/x[/tex]
step 2
Find y when x=10
substitute the value of x in the equation and solve for y
[tex]y*(10)=250[/tex]
[tex]y=250/10=25[/tex]
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 [tex]y/x=k[/tex] or [tex]y=kx[/tex]
step 1
Find the value of k
x=6 when y=42
substitute the values
[tex]y/x=k[/tex] ------> [tex]42/6=k[/tex] -----> [tex]k=7[/tex]
The equation is equal to
[tex]y/x=7[/tex] or [tex]y=7x[/tex]
step 2
Find y when x=12
substitute the value of x in the equation and solve for y
[tex]y=7(12)=84[/tex]
