Description down below

Question

A baseball is hit, following a path represented by x = 135t and y = 3.3 + 38t − 16t² for 0 ≤ t ≤ 3.

Part A: Find the ordered pairs, (x, y) when t = 0.2, 1.2, and 2.2.

Part B: The fence, which is 10 feet tall, lies 320 feet away from home plate. Does the baseball travel over the fence? Justify your answer mathematically.

Part C: Write a rectangular equation to represent the plane curve.

Answer 1

x=135t=135(.2)= 27

y= 3.3+38t-16t^2=3.3+38(.2)-16(.2)^2=3.3+7.6 -.64= 10.9-.64= 10.26 feet

(27, 10.26)

t=1.2

x=135(1.2)=162

y=3.3+38(1.2)-16(1.2)^2 = 3.3+45.6-16(1.44)= 48.9 -23.04=25.86

(162,25.86)

t=2.2

x=135(2.2)=297

y= 3.3+38(2.2)-16(2.2)^2=9.46

(297, 9.46)

(320, 10+?) x=135(t)=320, t=320/135=64/27, y= 3.3+38(64/27)- 16(64/27)^2=about 3.38<10

nope, doesn't go over the fence

C) t=x/135

y= 3.3+38(x/135)-16(x/135)^2