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

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is