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
Charra [1.4K]
2 years ago
14

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t) = 52t - 16t^2 . What i

s the maximum height that the ball will reach?
Do not round your answe
Mathematics
2 answers:
ahrayia [7]2 years ago
7 0

Answer:

42.25 feet

Step-by-step explanation:

The height function is a parabola.  The maximum value of a negative parabola is at the vertex, which can be found with:

x = -b/2a

where a and b are the coefficients in y = ax² + bx + c.

Here, we have y = -16t² + 52t.  So a = -16 and b = 52.  The vertex is at:

t = -52 / (2×-16)

t = 13/8

Evaluating the function:

h(13/8) = -16(13/8)² + 52(13/8)

h(13/8) = -169/4 + 169/2

h(13/8) = 169/4

h(13/8) = 42.25

pochemuha2 years ago
6 0

Answer:

42.25 feet.

Step-by-step explanation:

The maximum height can be found by converting to vertex form:

h(t) = 52t - 16t^2

h(t) =   -16 (  t^2  - 3.25t)

h(t) = -16 [ (t - 1.625)^2 - 2.640625 ]

= -16(t - 1.625 ^2) + 42.25

Maximum height = 42.25 feet.

Another method of solving this is by using Calculus:

h(t) = 52t - 16t^2

Finding the derivative:

h'(t) = 52 - 32t

This = zero for  a maximum/minimum value.

52 - 32t = 0

t = 1.625 seconds at maximum height.

It is a maximum because  the  path is a parabola  which opens downwards. we know this because of the  negative coefficient of x^2.

Substituting in the original formula:h(t) = 52(1.625)- 16(1.625)^2

= 42.25 feet.

You might be interested in
1/4 (20x−28) <2(x−3)+2
xeze [42]

Answer:

Step-by-step explanation:

1/4 x 20x - 1/4 x 28<2x - 6 + 2

5x - 28/4<2x - 4

5x - 2x<-4 + 28/4

3x<-4/1 + 28/4

3x<-16 + 28/4

3x<12/4

3x<3

3x/3<3/3

x<1

6 0
2 years ago
TOU
____ [38]
The answer is quadrant 2
7 0
3 years ago
Read 2 more answers
Find the measure of the indicated angle to the nearest degree.
makvit [3.9K]
You would do tan<span>Ɵ = 9/12
tan^-1(9/12) = </span><span>Ɵ
</span><span>Ɵ = 36.87 degress
make sure your calculator is in degree mode

</span>
8 0
2 years ago
Read 2 more answers
Given the slope m=4 what is the perpendicular slope
ELEN [110]
When a line is perpendicular, the slope is the negative reciprocal. Therefore, since the slope is 4, the slope of a line perpendicular is -1/4
8 0
3 years ago
Please help please thanks
alexandr402 [8]
Fraction: 16/75
Decimal: 0.21
8 0
3 years ago
Other questions:
  • Given a sphere with a radius of 5 cm, find its volume to the nearest whole number.
    10·1 answer
  • How do you graph y=-3x+4
    10·1 answer
  • Help please
    8·2 answers
  • Given the following function: f(x) = 4x +7<br> Evaluate -3 • f(9) = ?
    8·1 answer
  • Slope = -1/3 passing through (4,-9) <br> Point- slope form and slope-intercept form
    7·2 answers
  • A line passes through the two given points. Is it vertical, horizontal, or neither? (-8, 3), (-7, 3)
    9·1 answer
  • Solve x=Arctan 1/3 to the nearest degree.
    14·1 answer
  • Is 5 1/2 bigger then 5 3/8
    7·2 answers
  • Reposting because nobody will help me..
    6·1 answer
  • Please help me I will give you the brain thing and extra points. (image below) 4/4
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!