If P varies jointly with Q and R, and P=420 when Q is 3 and R is 7, what is the value of P when Q is 2 and R is 1? Help me please...thx
P=kQR, so P/QR is constant. Thus, you want P where
P/2 = 420/21
To find the value of P when Q is 2 and R is 1, we can use the concept of joint variation. When two variables vary jointly with another variable, it means that their product remains constant.
Let's set up the equation using the given information:
P varies jointly with Q and R,
P = k * Q * R,
where k is the constant of variation.
We can find the value of k by substituting the given values:
420 = k * 3 * 7.
Now we can solve for k:
k = 420 / (3 * 7) = 20.
Now that we know the value of k, we can use it to find the value of P when Q is 2 and R is 1:
P = 20 * 2 * 1 = 40.
Therefore, the value of P when Q is 2 and R is 1 is 40.
To find the value of P when Q is 2 and R is 1, we can use the concept of joint variation.
When two variables vary jointly, it means that their relationship can be expressed as a direct proportion. In this case, the variation of P with respect to Q and R can be written as:
P = k * Q * R
where k is the constant of variation.
We are given that "P varies jointly with Q and R," therefore we can write the equation as:
P = k * Q * R
Now, we need to find the value of k. We can do this by substituting the given values into the equation:
420 = k * 3 * 7
Simplifying the equation:
420 = 21k
Dividing both sides of the equation by 21:
20 = k
Now that we have the value of k, we can substitute it back into the equation to find the value of P when Q is 2 and R is 1:
P = 20 * 2 * 1
P = 40
Therefore, when Q is 2 and R is 1, the value of P is 40.