If p varies directly as the square root of r and p=3.2 when r=4,find p when r=6.5
p = k sqrt r
p^2 = k^2 r
3.2^2 = k^2 (4)
so
k^2 = 3.2^2/4
p^2 = (3.2^2/4)(6.5)
find p^2 and take the square root
2+2
Answer to my question
To solve this problem, we need to use the concept of direct variation. In direct variation, two variables are related such that when one variable increases (or decreases), the other variable also increases (or decreases) proportionally.
In this case, we are given that p varies directly as the square root of r. Mathematically, this can be represented as:
p = k*√r
Where p is the value of variable p, r is the value of variable r, and k is the constant of variation.
To find the value of k, we can use the given information that p = 3.2 when r = 4:
3.2 = k*√4
3.2 = k*2
k = 3.2/2
k = 1.6
Now that we have the value of k, we can use it to find the value of p when r = 6.5:
p = 1.6*√6.5
To calculate the square root of 6.5, we can use a calculator or approximation methods. The square root of 6.5 is approximately 2.5495.
p = 1.6*2.5495
p ≈ 4.0792
Therefore, when r = 6.5, the value of p is approximately 4.0792.