G varies directly as the square of H, If G is 4 when H is 3, find H when G = 100
Answer Details
In this problem, we are given that G varies directly as the square of H. This means that if H is multiplied by some factor, then G will be multiplied by the square of that factor. Mathematically, we can write this as:
G ∝ H^2
where the symbol "∝" means "varies directly as".
We are also given that G is 4 when H is 3. Using this information, we can write:
4 ∝ 3^2
To find H when G = 100, we can use the same relationship:
G ∝ H^2
If we let the constant of proportionality be k, we can write:
G = kH^2
To solve for k, we can use the initial condition where G is 4 when H is 3:
4 = k(3^2)
Simplifying, we get:
k = 4/9
Now we can use this value of k to find H when G is 100:
100 = (4/9)H^2
Multiplying both sides by 9/4, we get:
225 = H^2
Taking the square root of both sides, we get:
H = 15
Therefore, the correct answer is (a) 15.
In summary, we used the direct variation relationship between G and H^2 to find the constant of proportionality, and then used that constant and the given value of G to solve for H.