P varies directly as the square root of q. P=8 when q =25 find p when q = 100
I don't understand
To solve this problem, we can use the direct variation formula:
P = k * √q
where P is the variable we want to solve for, q is the given value, and k is the constant of proportionality.
Given that P = 8 when q = 25, we can substitute these values into the formula to find k:
8 = k * √25
Since the square root of 25 is 5, we can simplify the equation:
8 = 5k
To solve for k, divide both sides of the equation by 5:
k = 8/5
Now that we have the value of k, we can plug it into the direct variation formula and solve for P when q = 100:
P = (8/5) * √100
Simplifying the equation:
P = (8/5) * 10
P = 16
Therefore, when q = 100, P would be equal to 16.
To solve this problem, we need to use the concept of direct variation, which means that when two quantities are directly proportional, their ratio remains constant.
The given information states that P varies directly with the square root of q. Mathematically, we can write this relationship as:
P = k * √q
Where P and q are the variables, k is the constant of variation, and √q represents the square root of q.
To find the value of k, we can use the given information where P = 8 when q = 25. Substituting these values into the equation, we get:
8 = k * √25
8 = 5k
To isolate k, we divide both sides of the equation by 5:
k = 8/5 = 1.6
Now that we know the value of k, we can use it to find P when q = 100. Substituting this value into the equation, we get:
P = 1.6 * √100
P = 1.6 * 10
P = 16
Therefore, when q = 100, P = 16.
The formula for direct variation, which is what is indicated in the problem, is
P = sqrt(q) x A. A is a nonzero value, and finding its value will help create a function. 8 = sqrt(25) x A. Solve this and you will find the value of A. Then plug that value of A into the this equation:
P = sqrt(100) x A.