1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
makvit [3.9K]
3 years ago
13

After t seconds, a ball tossed in the air from the ground level reaches a height of h feet given by the equation h = 144t-16t^2

Mathematics
2 answers:
lesantik [10]3 years ago
4 0
144t-16t^2= 16t(9-t)
after 3 seconds (just substitute t=3):
16(3)(9-3)=
16(3)(6)=
16*18=
288
maximum height: find the average of the roots:
the roots of 16t(9-t) are t=0 or t=9
since it's a parabola, the maximum is at t=4.5, at 324 ft
if its height is 224 feet, the equation is 224=144t-16t^2
16t^2-144t+224=0
divide by 16: t^2-9t+14=0
this can be factored as (t-2)(t-7)=0
the roots are t=2 and t=7, so the ball has been in the air for either 2 seconds or 7 seconds
the roots to 144t-16t^2 are 0 and 9, so the ball will hit the ground 9 seconds after being thrown
kaheart [24]3 years ago
4 0
H = -16t^2 + 144t
when you substitute a number in for t, it will tell you how high in the air the ball is after that many seconds. to find the height at three seconds, put in 3 for t.
h = -16*9 + 144*3
h = -144 + 3*144
h = 2*144 (i didn't want to multiply out 3*144 cause im lazy, so i combined like terms as if 144 was a variable.)
h = 288
after 3 seconds, the ball is 288ft in the air.

the maximum height is more complicated (and feel free to skip this paragraph if you think it'll confuse you more.) you could do it with a graphing calculator by graphing the function f(x)=-16x^2+144t and using a maximum feature. you could also use differential calculus to find it. but i think the best way is the way suggested by the person who answered before me, that is, finding the average of the roots. since the parabola's line of symmetry is perpendicular to the x-axis, that means the places the parabola intersects the x-axis (the roots) will be the same distance from the axis of symmetry and therefore the same distance from the vertex (the maximum point of the parabola.)

the roots of the parabola can be found this way:
h = -16t^2 + 144t
0 =  -16t^2 + 144t
0 = t(-16t + 144)
0 = t or 0 = -16t + 144
16t = 144
t = 9
the roots are t=0 and t=9, therefore the line of symmetry (the middle of the parabola) is t=4.5. to find the maximum point of the parabola, plug 4.5 into the function for t and find the resulting height.
h = -16(4.5)^2 + 144(4.5)
h =  -324 + 648
h = 324
so the maximum height happens at t=4.5 seconds, and the maximum height is 324ft.

to find how long it takes for the ball to be at 224 feet in the air, substitute 224 in for h:
h = -16t^2 + 144t
224 = -16t^2 + 144t
56 = -4t^2 + 36t divide by 4
14 = -t^2 + 9t divide by 4 again
t^2 - 9t + 14 = 0 rearrange
(t - 7)(t - 2) = 0
t = 7 and t = 2
at 2 seconds and again at 7 seconds, the ball will be 224ft in the air.

after how many seconds will the ball hit the ground? we already know this. the ball touches the ground just like the parabola touches the x-axis. to find when the ball hits the ground, we just have to find the root of the parabola, and we already know from earlier that the roots are t=0 and t=9. so, the ball will come into contact with the ground at 9 seconds.

hope this helped
You might be interested in
What is X the two numbers are 46 and 71
tino4ka555 [31]
The answer would be 63 bc 46+71= 117 then a triangle usaually equals 180 so 180 -117=63!!
3 0
3 years ago
Find the product. write your answer in exponential form 9²•9-⁶​
enyata [817]

Answer:

9^8

Step-by-step explanation:

9²•9⁶​ = 9^(2+6) = 9^8

3 0
2 years ago
Read 2 more answers
Select the correct answer.
Flura [38]
Nsssmsns shshssnsnnsnnsdnd
5 0
3 years ago
How many total inches are in 7 feet 4 inches and 4 feet 10 inches ??? A) 257 inches B) 130 inches C) 126 inches D) 146 inches wh
Gelneren [198K]
The correct answer is D, 146 inches.
7 x 12 = 84
4 x 12 = 48
84+48+4+10 = 146
5 0
3 years ago
Read 2 more answers
What is the sales tax of a $178.90 video game system is the tax rate is 3.75%
juin [17]
It would be: 178.90 * 3.75%
= 178.90 * 0.0375
= 6.71

In short, Sales tax would be $6.71

Hope this helps!
3 0
3 years ago
Other questions:
  • It takes Maria 59 minutes to walk to her friends house 1 2/3miles away. What is her walking pace in mph?
    5·1 answer
  • Which is the slope of the line that passes through the points (-2, 4) and (5, -1)?
    7·2 answers
  • How many fractions are equivalent to 4/5?
    10·1 answer
  • (2x+5)/3=-7 <br> show all work
    14·1 answer
  • Plz help me answer this question I’m being timed
    5·2 answers
  • What are the ODDS of rolling a number greater than 3 on a six-sided die?<br> (Odds, NOT probability)
    15·2 answers
  • What’s number 2 4 and 5
    6·1 answer
  • The goalie on the Iceblades hockey team saves (blocks) 73% of the opponent's shots. With 10 minutes to go, the Iceblades are ahe
    8·2 answers
  • SOLVE<br>Express in radian<br>(a) 70°<br>​
    11·1 answer
  • A rock is thrown from the top of a 763 feet tall
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!