p varies directly as the square of q and inversely as r when p=36, q=3 and r=4 calculate q when p=200 and r=2
p = k (q^2)(1/r)
when p=36,q=3,r=4
so:
36 = k(9)(1/4)
k = 36(4)/9 = 16
p = 16q^2/r
when p=200, r=2
200 = 16q^2 /2
q^2 = 400/16
q = 20/4 = 5
p=k(q^2)/r
36=(k*3^2)/4
36=(9*k)/4
9*k=144
k=16
p=16(q^2)/r
200=(16*q^2)/2
16*q^2=400
q^2=400/16
q^2=25
q=√25
q=5
p = kq^2/r, so pr/q^2 = k, a constant.
So, you want to find q such that
200*2/q^2 = 36*4/3^2
400/q^2 = 16
q^2 = 25
q = 5
Why did the chicken join a math club? Because it wanted to improve its calculus skills! Now, let's solve this math problem together, shall we?
Given that p varies directly as the square of q and inversely as r, we can write the equation as:
p = k * (q^2)/r
where k is the constant of variation.
Using the given values, when p = 36, q = 3, and r = 4, we can solve for k:
36 = k * (3^2)/4
36 = k * 9/4
Multiplying both sides by 4/9, we find:
k = 36 * 4/9
k = 16
Now, we can use this value of k to find q when p = 200 and r = 2:
200 = 16 * (q^2)/2
Multiplying both sides by 2 and dividing by 16:
200 * 2/16 = q^2
25 = q^2
Taking the square root of both sides:
q = ±√25
Since q cannot be negative, we have:
q = √25
q = 5
Therefore, when p = 200 and r = 2, q is equal to 5. Keep smiling and solving those math problems!
To solve this problem, we can use the concept of direct and inverse variation.
When a variable is said to vary directly with another variable, it means that as one variable increases, the other also increases by the same factor. In this case, p varies directly with the square of q.
When a variable is said to vary inversely with another variable, it means that as one variable increases, the other decreases by the same factor. In this case, p varies inversely with r.
We are given p=36, q=3, and r=4 when p, q, and r are in their initial values. We need to find the value of q when p=200 and r=2.
Let's start by setting up the equation:
p = k * (q^2) / r
where k is the constant of variation.
Now, substitute the initial values into the equation:
36 = k * (3^2) / 4
Simplifying this equation:
36 = 9k / 4
Cross-multiply:
9k = 36 * 4
9k = 144
Divide both sides by 9:
k = 16
Now, we can use this value of k in the equation to find q when p=200 and r=2:
200 = 16 * (q^2) / 2
Multiply both sides by 2:
400 = 16 * q^2
Divide both sides by 16:
25 = q^2
Take the square root of both sides:
q = ±√25
Since q is a length, we take the positive square root:
q = 5
Therefore, when p=200 and r=2, q will be equal to 5.