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
Help pls ............
Anestetic [448]
Well it sounds like a trick question but the answer is simple! If she runs 90 meters per minute, In one minute she will run 90 meters.

Answer 90
3 0
3 years ago
10 POINTS answer ASAP if you can
Dafna1 [17]

Answer:

I think it is

Step-by-step explanation:

t

3 0
2 years ago
(14x2 - 3x3 + 9x4) - (-14 + 13x3 + 11x4) simplify and answer in standard form
FromTheMoon [43]
We have that
(14x2 - 3x3 + 9x4) - (-14 + 13x3 + 11x4)=<span>14x2 - 3x3 + 9x4 +14 - 13x3 - 11x4
</span>(14x2 - 16x3  +14 - 2x4)

then
-2x4-16x3+14x2+14=0--------------> this is the <span>standard form

simplify </span><span>dividing the entire expression by two
</span><span>-x4-8x3+7x2+7=0

the answer is 
</span>-x4-8x3+7x2+7=0<span>

</span>
4 0
3 years ago
Subtract -6x2 – 2x + 5 from 2.x2 + 8.
tekilochka [14]

<em>Look</em><em> </em><em>at</em><em> </em><em>the</em><em> </em><em>attached</em><em> </em><em>picture</em>

<em>H</em><em>ope</em><em> </em><em>it</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>you</em><em>.</em><em>.</em><em>.</em><em>.</em>

<em>G</em><em>ood</em><em> </em><em>luck</em><em> </em><em>on</em><em> </em><em>your</em><em> </em><em>assignment</em>

<em>~</em><em>p</em><em>r</em><em>a</em><em>g</em><em>y</em><em>a</em>

4 0
2 years ago
Q
Tema [17]

Answer:

y = \frac{1}{2} x+7

Step-by-step explanation:

Slope-intercept form: y = mx + b

Slope formula: \frac{y2-y1}{x2-x1}

Given points: (-6, 4), (6, 10)

(-6, 4) = (x1, y1)

(6, 10) = (x2, y2)

To write the equation in slope-intercept form, we need to find the slope(m) and the y-intercept(b) of the equation.

First, let's find the slope. To do this, input the given points into the slope formula:

\frac{10-4}{6-(-6)}

Simplify:

10 - 4 = 6

6 - (-6) = 6 + 6 = 12

\frac{6}{12}=\frac{1}{2}

The slope is \frac{1}{2}.

To find the y-intercept, input the slope and one of the given points(in this example I'll use point (6, 10)) into the equation and solve for b:

10 = \frac{1}{2}(6)+b

10 = 3 + b

7 = b

The y-intercept is 7.

Now that we know the slope and the y-intercept, we can write the equation:

y = \frac{1}{2} x+7

4 0
3 years ago
Other questions:
  • Jen's has current assets of $2,200, cash of $400, and inventory of $1,300. The firm has accounts payable of $300, long-term debt
    6·1 answer
  • **please give me the steps to solve this, will mark brainlyest if leads to correct answer**
    13·1 answer
  • which of the following cannot be the probality of an event a)1/2 b) 10% c) 0.7. d) 3/2. which is the correct option with the sol
    12·1 answer
  • PLEASE HELP!!!!!!!!!!!!!!!
    13·1 answer
  • Find the product of the given polynomials. A. B. C. D.
    12·1 answer
  • An employee puts $3,000 into a retirement fund that offers 7% interest compounded annually. The employee makes no other deposits
    11·1 answer
  • The Tigers lost 10 yards on their first play and gained 2 yards on their next play. What was their net result in yards after the
    9·1 answer
  • What is equivalent to the given expression? 24−3⋅4÷2+6
    13·2 answers
  • This pattern can be<br> represented by the explicit<br> expression of 2n.
    10·2 answers
  • 300 people went on a trip. 20% chose hiking. how many people chose hiking?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!