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

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