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
Elden [556K]
3 years ago
5

A ball is projected in to the air. Its height at time t is given by the equation

Mathematics
1 answer:
Ksju [112]3 years ago
3 0
The equation gives the height of the ball. That is, h is the height of the ball. t is the time. Since we are looking for the time at which the height is 8 (h=8), we need to set the equation equal to 8 and solve for t. We do this as follows:

h=-16 t^{2} +60t+1
8=-16 t^{2} +60t+1
16 t^{2} -60t-1+8=0
16 t^{2} -60t+7=0

This is a quadratic equation and as it is set equal to 0 we can solve it using the quadratic formula. That formula is:
t= \frac{-bplus minus \sqrt{ b^{2}-4ac } }{2a}
You might recall seeing this as "x=..." but since our equation is in terms of t we use "t-=..."

In order to use the formula we need to identify a, b and c.
a = the coefficient (number in front of) t^{2} = 16.
b = the coefficient of t = -60
c = the constant (the number that is by itself) = 7

Substituting these into the quadratic formula gives us:
t= \frac{-(-60)plus minus \sqrt{ (-60)^{2}-4(16)(7) } }{2(16)}
t= \frac{60plus minus \sqrt{3600-448 } }{32}
t= \frac{60plus minus \sqrt{3152 } }{32}

As we have "plus minus" (this is usually written in symbols with a plus sign over a minus sign) we split the equation in two and obtain:
t=  \frac{60+56.1426}{32} =3.63
and
t=  \frac{60-56.1426}{32} =.12

So the height is 8 feet at t = 3.63 and t=.12

It should make sense that there are two times. The ball goes up, reaches it's highest height and then comes back down. As such the height will be 8 at some point on the way up and also at some point on the way down.


You might be interested in
Hi guys this is my question
sasho [114]

Answers -

statement B, D, E are correct .

Solution -

As figure B is the scaled copy of figure A, so it is smaller than B and its perimeter is also less than that of A.

On the other hand , as B is the smaller replica of A, so it has same number of edges ,angels and sides. Though the length of the sides are not same, the angels are same. so the perimeters of both figures are different but sum of all the angels are same.

5 0
3 years ago
a stainless steel garbage can is in the shape of a right circular cylinder. If its radius is 6 inches and its volume is 864 pi c
lubasha [3.4K]
\bf \textit{volume of a cylinder}=v=\pi r^2 h\qquad 
\begin{cases}
r=radius\\
h=height\\
---------\\
r=6\\
v=864\pi^3
\end{cases}
\\\\\\
864\pi^3=\pi\cdot 6^2\cdot h\impliedby \textit{solve for "h"}
5 0
3 years ago
Read 2 more answers
Parallelogram A B C D is shown. The length of A B is (9 x minus 14) inches and the length of D C is (3 x + 4) inches. In paralle
Ne4ueva [31]

Answer:

Hello, Friend! ^^

The Answer Is 13 Inches <3

_______________________________________________________

Hope this helps! ^^ :3

3 0
3 years ago
The playing life of a Sunshine radio is normally distributed with mean LaTeX: \muμ = 600 hours and standard deviation LaTeX: \si
Hitman42 [59]

Answer:

The probability that a radio selected at random will last from 600 to 700 hours is 0.3413

Step-by-step explanation:

The playing life of a Sunshine radio is normally distributed

Mean =\mu = 600 hours

Standard deviation =\sigma = 100 hours

We are supposed to find the probability that a radio selected at random will last from 600 to 700 hours i.e.P(600<x<700)

Formula:Z= \frac{x-\mu}{\sigma}

At x = 600

Z= \frac{600-600}{100}

Z=0

P(X

At x = 700

Z= \frac{700-600}{100}

Z=1

P(X

P(600

Hence the probability that a radio selected at random will last from 600 to 700 hours is 0.3413

8 0
3 years ago
Function or not a function
Aliun [14]

Answer:

not a function

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Other questions:
  • 1 3/4 miles in twenty minutes
    8·1 answer
  • Which decimal is shown by the model?<br><br> A, 10.0<br> B,1.0<br> C,0.1<br> D,0.01
    11·2 answers
  • What is 5 and 3/7 as an improper fraction
    11·2 answers
  • Help find slope of each line
    8·2 answers
  • Can someone help me with this? please.
    14·1 answer
  • A statistics teacher has 4 periods of introductory statistics. She wants to get students’ opinions on a new homework policy. To
    10·2 answers
  • Which of the following best explains the value of Sine StartFraction pi Over 3 EndFraction on the unit circle below?
    6·2 answers
  • Suppose while at a store, you ask for change for five dollars. You get in return exactly twenty-four coins, all of which are nic
    7·2 answers
  • If y = 16 when x = 4, find<br> Y when x = 6
    13·1 answer
  • 8 decreased by the difference of t and 4
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!