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
charle [14.2K]
3 years ago
7

You are jumping off the 12 foot diving board at the municipal pool. You bounce up at 6 feet per second and drop to the water you

r height h (in feet) above the water in terms of t seconds is given by h(t)=-16t^2+6t+12
When do you hit the water?

What is your maximum height?
Mathematics
1 answer:
NARA [144]3 years ago
6 0

Answer:

When do you hit the water?

1.075 seconds after you jump.

What is your maximum height?

the maximum height is 12.5626 ft

Step-by-step explanation:

The equation:

h(t) = -16*t^2 + 6*t + 12

Is the height as a function of time.

We know that the initial height is the height when t = 0s

h(0s) = 12

and we know that the diving board is 12 foot tall.

Then the zero in h(t)

h(t) = 0

Represents the surface of the water.

When do you hit the water?

Here we just need to find the value of t such that:

h(t) = 0 = -16*t^2 + 6*t + 12

Using the Bhaskara's formula, we get:

t = \frac{-6 \pm \sqrt{6^2 - 4*(-16)*12} }{2*(-16)} = \frac{-6 \pm 28.4}{-32}

Then we have two solutions, and we only care for the positive solution (because the negative time happens before the jump, so that solution can be discarded)

The positive solution is:

t = (-6 - 28.4)/-32 = 1.075

So you hit the water 1.075 seconds after you jump.

What is your maximum height?

The height equation is a quadratic equation with a negative leading coefficient, then the maximum of this parabola is at the vertex.

We know that the vertex of a general quadratic:

a*x^2 + b*x + c

is at

x = -b/2a

Then in the case of our equation:

h(t) = -16*t^2 + 6*t + 12

The vertex is at:

t = -6/(2*-16) = 6/32 = 0.1875

Evaluating the height equation in that time will give us the maximum height, which is:

h(0.1875) =  -16*(0.1875 )^2 + 6*(0.1875) + 12 = 12.5626

And the height is in feet, then the maximum height is 12.5626 ft

You might be interested in
15/60 as a percentage       
Ugo [173]
15/60=1/4=0.25
0.25*100=25
15/60 in % is 25%
3 0
3 years ago
Read 2 more answers
PLEASSEEE HELP AS FAST AS YOU CAN!!! I put the picture. 10 points!!
iogann1982 [59]

Answer:

<h2>x = 129</h2>

Step-by-step explanation:

3 0
3 years ago
This Bar Chart shows the average amount of rainfall in inches that fell in a city in Louisiana one year.
Daniel [21]
C I think because it shows the months and the total
8 0
3 years ago
Read 2 more answers
A college bookstore marks up the price that it pays the publisher for a book by 35 %. If the selling price of a book is $ 87.00
Dimas [21]

Answer:the amount that the bookstore pay the publisher for the book is $64.4

Step-by-step explanation:

Let x represent the amount that the bookstore pay the publisher for the book.

The college bookstore marks up the price that it pays the publisher for a book by 35%. This means that the value of the mark up would be

35/100 × x = 0.35 × x = 0.35x

Therefore, the amount that the bookstore is selling the book would be

x + 0.35x = 1.35x

If the selling price of a book is $ 87.00, then it means that

1.35x = 87

x = 87/1.35 = 64.4

7 0
3 years ago
In the diagram, what is the value of x ?
nexus9112 [7]
Your answer is 98. Is there a multiple choice?
8 0
3 years ago
Read 2 more answers
Other questions:
  • How do you know or what indicates to you that the solution set of an equation is all real numbers?
    9·1 answer
  • If the polynomial p(x) is being divided my x-r, the remainder is p(r) TRUE OR FALSE
    7·2 answers
  • Is a triangle with angle measures 40,30,and 120 possible?
    8·2 answers
  • Answer this question please.
    13·2 answers
  • What is the length of side a? When one side is 16 and the other side 7
    11·1 answer
  • Write the ratio as a fraction in simplest form. 16 dogs to 12 cats
    9·2 answers
  • The values of x and y vary directly and one pair of values are given. Write an equation that relates x and y. x=1,y=0.5
    9·1 answer
  • Why is it not possible to form a right triangle<br> with the lengths 2, 4 and 7?
    11·1 answer
  • Sue baked cookies for a school fundraiser. She sold three-fourths of the cookies during the first two hours of the fundraiser. S
    11·1 answer
  • 16. The graph shows the relationship between the
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!