1.) suppose y varies directly as x.if x=24 when y=8 then what is the constant of variation?
2.) suppose y varies inversely as x if x=4 when y=8 then what is the constant of variation?
I think this is the answer you are looking for: (it is late here and I'm late to bed...lol)
If y varies directly with x, find the constant of variation with x = 24 and y = 8
k = y/x = 8/24 = .333...
If y varies inversely with x, find the constant of variation with x=4 and y = 8
k = xy = 4*8 = 32
I will check back later today. Try to check my answers for me...and make corrections to make sure we have it right for the next person that needs the answers. Thanks
"y varies directly as x" ---> y = kx
if x=24, y= 8
8 = 24k
k = 8/24 = 1/3 <---- answer
so y = (1/3)x
"y varies inversely as x" ---> y = k(1/x) = k/x
for x=4 and y=8
8 = k/4
k = 32 <---- the constant of variation
y = 32/x
Claire was right.
If y varies inversely as X and y=4 when X=2,
What Is the constant of variation
Find y when X=2.
Find X when y=2.
To find the constant of variation in a direct variation problem, you need to find the ratio between the two variables. In this case, y and x are directly proportional, so the ratio between y and x will stay constant.
1.) Given that y varies directly as x, the equation can be written as y = kx, where k is the constant of variation.
To find k, substitute the given values into the equation. When x = 24, y = 8. Plug these values into the equation and solve for k:
8 = k * 24
Divide both sides of the equation by 24:
8/24 = k
Simplify:
1/3 = k
Therefore, the constant of variation (k) is 1/3.
2.) In an inverse variation problem, the product of the two variables will remain constant. This can be written as y * x = k.
Given that y varies inversely as x, substitute the given values into the equation. When x = 4, y = 8:
8 * 4 = k
Simplify:
32 = k
Therefore, the constant of variation (k) is 32.