In the xy-plane, a parabola defined by the equation y=(x-8)^2 intersects the line defined by the equation y=36 at two points, p and q. what is the length of pq?
a) 8
b) 10
c) 12
d) 14

12

Step-by-step explanation:

Alright so we are asked to find the intersection of y=(x-8)^2 and y=36.

So plug second equation into first giving:  36=(x-8)^2.

36=(x-8)^2

Take square root of both sides:

Add 8 on both sides:

x=8+6=14 or x=8-6=2

So we have the two intersections (14,36) and (2,36).

We are asked to compute this length.

The distance formula is:

.

I could have just found the distance from 14 and 2 because the y-coordinates were the same. Oh well. 14-2=12.

3 ft

step-by-step explanation:

since the triangle is right use pythagoras' identity to solve for a

the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

a² + 8² = ( )²

a² + 64 = 73 ( subtract 64 from both sides )

a² = 9 ( take the square root of both sides )

a = = 3