4. Trevor Olmo dives off the high board. His distance from the surface of the water varies quadratically with the number of seconds that have passed since he left the
board. His distances at times of 1, 2, and 3 seconds since he left the board are 51, 36,
and 5 meters above the water, respectively.
a.) List three data points.
b.) Using the three data points, write the particular equation of the parabola
relating height with time.
c.) How high is the diving board?
d.) When does he hit the water? SHOW ALL WORK!

the line of

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

then say something, tell them they won’t respect you if you don’t even have respect for your self sweetheart you need to lay it on them, all of it : )