Question

Type the correct answer in each box. Use numerals instead of words. If necessary, round your answer to the nearest hundredth.
Ana and Taylor are on the lacrosse team and practicing their passes. The vertical height, a(x), of Ana’s pass x feet from where it was thrown is modeled in this table.

0 10 20 30 40 50 60
0 20 32 36 32 20 0
The vertical height, t(x), of Taylor’s pass x feet from where it was thrown is modeled by this equation.
t(x) = -0.05 (x^2 - 50x)

Complete the statements comparing their passes.


The difference of the maximum heights is ___ feet.

The difference of the total distances traveled is ___ feet.

Answer 1

Very quickly
t(x) = -0.05 (x^2 - 50x)
where is Taylor height max?
d/dx (x^2-50) = 0
2 x = 50
x = 25 for max
and that max is
-0.05 ( 625 - 50) = 0.05 (575 ) = 28.75
which is NOT -1,237,500 feet
repair needed desperately !

Answer 2

To find the total distance traveled by Taylor's pass, we can use the same x values. Plugging in x = 0 into the equation t(x) = -0.05(x^2 - 50x), we get t(0) = -0.05(0^2 - 50*0) = 0. Therefore, the starting point of Taylor's pass is at x = 0.

yes,Taylor pass starts at x = 09
where does it end?
It ends when x^2 - 50 x = 0 again
x (x-50) = 0
x = 50 <==================
So it went 50 feet
How high did it go
if x = 25, the vertex
t = -0.05(x^2 - 50x) = -.05 (625 - 1250) = -.05 ( -625) = + 31.25

Answer 3

Whew !!!