Question

The path of a soccer ball is modeled by the function h(x) = -0.005x2 + 0.25x, where h is the height in meters and x is the horizontal distance that the ball travels in meters. What is the maximum height that the ball reaches? ___________ m. Round your answer to the nearest thousandth.

Answer 1

h(-.25/2(-.005))=h(25)

Answer 2

you can also do it with calculus

Answer 3

h(x) = -0.005x2 + 0.25x,
h'(x)= -0.005(2x) +0.25
h'(x) =0
-0.005(2x) +0.25 =0
x=25
max height =h(25)=-0.005(25)^2 + 0.25(25)=3.125

Answer 4

Jamen, are you in calculus, or algebra?

Answer 5

algebra

Answer 6

ok, do you know how to find the vertex of a parabola?

Answer 7

not really im having trouble setting up and the equation and solving it..

Answer 8

Given h(x) = -0.005x2 + 0.25x
diff it once and set it to zero, we can get x that belongs to the vertex (slope of vertex=0)
as the coeff. of x^2 <0,
h(x) opens downward
so we can know that the vertex is the max point
put the x we get into h(x) to find its value

Answer 9

The highway mileage m in miles per gallon for a compact car is approximated by m(s) = -0.025s2 + 2.45s - 30, where s is the speed in miles per hour. What is the maximum mileage for this compact car to the nearest tenth of a mile per gallon? __________ mi/gal. (Enter the number only.)

can u also help me solve this equasion??

Answer 10

The highway mileage m in miles per gallon for a compact car is approximated by m(s) = -0.025s2 + 2.45s - 30, where s is the speed in miles per hour. What is the maximum mileage for this compact car to the nearest tenth of a mile per gallon? __________ mi/gal. (Enter the number only.)

can u also help me solve this equasion??

Answer 11

CoCo, he said he's in algebra, not calculus

Answer 12

Sorry for that. I study both so I cannot really distinguish which topic is belong to which side. Sorry again

Answer 13

jamens you are familiar with quadratics, right? and can identify the values of a,b,c in the expression ax^2+bx+c?

Answer 14

-0.025s^2+2.45s-30
Identify a,b,c

Answer 15

ok i got
-2.45/2(-0.025) -30
how would i solve it

Answer 16

the x-coordinate of the vertex is -2.45/[2(-0.025)]

Answer 17

when you plug the result of this into h(x), you will get your max.
note that it is only a max because the coefficient of a<0
if a>0, plugging in this value would give you a min

Answer 18

so the maximum mileage is m(49)

Answer 19

plug 49 into m(s)

Answer 20

i got 30.025 is that correct

Answer 21

-60.025+120.05-30=30.025??

Answer 22

30.025 is correct

Answer 23

i typed it in and i keeps saying its incorrect..i have online school, so if i round that to the nearest tenth, would it be 30

Answer 24

30.025 to the nearest tenth is 30.0

Answer 25

oh i understand i jus typed in 30 instead of 30.0..thanks for your help