Question 1074312: If y varies directly as d find the constant of variation in the proportion 4/v=2/d
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! y = kd
this means y varies directly with d.
equation is 4/y = 2/d
cross multiply to get 2y = 4d
divide both sides by 2 to get y = 2d
constant of variation is 2.
what this says is that d is always 2 times the value of y.
to confirm, start with your original equation of 4/y = 2/d
choose a value of d at random.
i chose 556.
since y = 2d, then y must be equal to 1112
your equation of 4/y = 2/d becomes 4/1112 = 2/556
simplify both to get 1/278 = 1/278
you can choose any number for d, and you will find that y will have to be 2 times that for the equation to be true.
another example:
start with 4/y = 2/d
let d = 4
equation becomes 4/y = 2/4
multiply both sides by y and multiply both sides by 4 to get 16 = 2y
divide both sides by 2 to get y = 8
8 is w times the value of 4.
this will always happen when y = 2d.
direct variation form is y = kd.
k is the constant of variation which is equal to 2.
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