p varies directly as q and the square of r and inversely as s
write the equation of the relation
find k if p=40 q=5 r=4 s=6
find p when q=8 r=6 and s=9
find s when p=10 q=5 r=2
"p varies directly as q and the square of r and inversely as s "
-----> p = k(qr^2/s) , where k is a constant
find k if p=40 q=5 r=4 s=6
you are given the values of the 4 variables, sub them into the above equation to solve for k
then rewrite the equation.
let me know what you get for the first one, to make sure you are doing it correctly.
40=k*(5*4^2)/6
40*6=5*16*k
240=80*k
k=240/80
k=3.
p=(3qr^2)/s
To write the equation of the relation, we can use the following information:
p varies directly as q and the square of r, and inversely as s.
This can be expressed as:
p = k * (q * r^2) / s
where k is the constant of variation.
To find k when p = 40, q = 5, r = 4, and s = 6, we can substitute these values into the equation and solve for k:
40 = k * (5 * 4^2) / 6
First, calculate the numerator: (5 * 4^2) = (5 * 16) = 80
Next, substitute the values and solve the equation:
40 = k * 80 / 6
Multiply both sides of the equation by 6:
240 = 80k
Divide both sides of the equation by 80 to solve for k:
k = 240 / 80 = 3
So, k equals 3 in this case.
To find p when q = 8, r = 6, and s = 9, we can substitute these values into the equation and solve for p:
p = 3 * (8 * 6^2) / 9
First, calculate the numerator: (8 * 6^2) = (8 * 36) = 288.
Next, substitute the values and solve the equation:
p = 3 * 288 / 9
Divide 288 by 9:
p = 3 * 32 = 96
So, when q = 8, r = 6, and s = 9, p equals 96.
To find s when p = 10, q = 5, and r = 2, we can rearrange the equation to solve for s:
p = k * (q * r^2) / s
Multiply both sides of the equation by s and divide by p:
s = k * (q * r^2) / p
Substitute the given values into the equation:
s = 3 * (5 * 2^2) / 10
First, calculate the numerator: (5 * 2^2) = (5 * 4) = 20.
Next, substitute the values and solve the equation:
s = 3 * 20 / 10
Divide 20 by 10:
s = 6
So, when p = 10, q = 5, and r = 2, s equals 6.
Is that the answer
The quality R varies directly as the square of S and inversely proportional as the root of T
..
Can you please check my answers? Thanxs! 40=k*(5*4^2)/6
40*6=5*16*k
240=80*k
k=240/80
k=3.
p=(3qr^2)/s