If p is inversely proportional to the square of q, and p is 30 when q is 10 determine p when q is equal to 5

The value of p = 120 when q = 5

Step-by-step explanation:

We know that if y varies inversely with x, we get the equation

y ∝ 1/x

y = k/x

k = yx

where 'k' is called the constant of proportionality.

In our case,

If p is inversely proportional to the square of q, then

p ∝ 1/q²

p = k/q²

k = pq²

As p is 30 when q is 10, so

substituting p = 30 and q = 10

k = (30) (10)²

k = (30)(100)

k = 3000

Now,

Determining the value of p when q = 5

Using the equation

p = k/q²

now substituting k = 3000 and q = 5

p =  3000 / (5)²

p = 3000/25

p = 120

Therefore, the value of p = 120 when q = 5

sites:

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4