Question 1011305: y is directly proportional to x^2. When y = 5, x = 10.
Write down the equation of proportionality with full working
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the direct proportion formula is y = kx.
when x = x^2, the formula becomes y = kx^2.
when y = 5, x = 10 is the statement.
you can use this to solve for k.
you get y = kx^2 becomes:
5 = k*10^2 which becomes:
5 = k*100
solve for k to get k = 5/100 = 1/20 = .05
now that you know the value of k, you can use that value to solve all other problems involving this proportion.
for example:
when y = 50, what is the value of x^2?
you know the value of k is equal to .05.
the formula of y = kx^2 becomes y = .05*x^2
y = 50 so the formula becomes 50 = .05*x^2
divide both sides of this equation by .05 to get 50/.05 = x^2
simplify to get 1000 = x^2
solve for x to get x = sqrt(1000)
the equation becomes 50 = .05 * (sqrt(1000))^2 which becomes 50 = .05 * 1000 which becomes 50 = 50 which is true.
here'e another example:
what's the value of y when x = 25?
the formula is y = kx^2.
k is equal to .05.
when x = 25, the formula becomes y = .05 * 25^2.
simplify to get y = .05 * 625
simplify further to get y = 31.25
the equation becomes 31.25 = .05 * 25^2 which becomes 31.25 = .05*625 which becomes 31.25 = 31.25 which is true.
since these are direct proportions, a/b^2 should be equal to c/d^2 which should be equal to e/f^2
a = 5
b^2 = 100
c = 50
d^2 = 1000
e = 31.25
f^2 = 625
a/b^2 should be equal to c/d^2
replace a/b^2 and c/d^2 with their respective values and you get 5/100 should be equal to 50/1000
cross multiply to get 5*1000 = 100*50
simplify to get 5000 = 5000
this is true.
c/d^2 should be equal to e/f^2
replace c/d^2 and e/f^2 with their respective values andyou get 50/1000 should be equal to 31.25/625
cross multiply to get 50*625 = 1000*31.25
simplify to get 31250 = 31250
this is true.
based on the law of equations that states if x = y and y = z, then x = z, you also get a/b^2 = e/f^2, which will also be true.
that's how the value of k is used to solve direct proportion type problems.
y = kx.
when x = x^2, the formula becomes y = kx^2.
when you know the value of y and and x, you can solve for the value of x^2 and then solve for the value of k.
once you know the value of k, you can solve other problems using the same formula of y = kx^2.
if you know the value of y and k, you can solve for the value of x^2 and then solve for the value of x.
if you know the value of of x and k, you can solve for the value of x^2 and then solve for the value of y
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