If c varies directly as the square root of d, and c = 14 when d = 64, find c when d = 324.
If c varies directly as the square root of d, and c = 14 when d = 64, find c when d = 324.
To find the value of c when d = 324, we can use the direct variation equation:
c = k * √d,
where k is the constant of variation.
To find the value of k, we can substitute the given values of c and d into the equation:
14 = k * √64.
Simplifying this equation:
14 = k * 8.
Divide both sides by 8 to solve for k:
k = 14/8.
k = 1.75.
Now that we have the value of k, we can use it to find c when d = 324:
c = 1.75 * √324.
Calculating the square root of 324:
c = 1.75 * 18.
Solving for c:
c = 31.5.
Therefore, when d = 324, c is equal to 31.5.
To solve this problem, we can use the concept of direct variation. In direct variation, two variables, in this case, c and the square root of d, are directly proportional to each other. This means that as one variable increases, the other variable increases or decreases by the same ratio.
To find the value of c when d = 324, we need to set up a proportion and solve for c.
First, let's find the constant of variation (k) using the given information where c = 14 when d = 64.
We can set up the proportion as follows:
c / √d = k
Plugging in the given values:
14 / √64 = k
Now, let's solve for k:
14 / 8 = k
k = 1.75
Now that we have the value of k, we can use it to find c when d = 324.
c / √d = k
Plugging in the given value of d:
c / √324 = 1.75
Simplifying the square root:
c / 18 = 1.75
To solve for c, we can multiply both sides of the equation by 18:
c = 1.75 * 18
Simplifying the multiplication:
c = 31.5
Therefore, when d = 324, c is equal to 31.5.
"c varies directly as the square root of d" means:
c=k*sqrt(d)
plug in c=14, d=64 and solve for k.
then plug in 324 for d, and you will get your answer.