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
A mini-lottery involves selecting 2 numbers between 1 and 10. What is the probability of correctly picking the two numbers?
Igoryamba

The probability of correctly picking the two numbers is 2/10.

<h3>What is the probability?</h3>

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability of correctly picking the two numbers = (numbers that have to be selected to win / total numbers)

2/10

To learn more about probability, please check: brainly.com/question/13234031

#SPJ1

5 0
2 years ago
Complete the table time and distance
meriva

Answer:

clip clop sponge blanket phone case

Step-by-step explanation:

8 0
3 years ago
Write the linear inequality shown in the graph. The gray area represents the shaded region.
DaniilM [7]

find it like a regular equation. find your slope and y intercept.

y ---- 4x - 2

since the shaded area is on the right and the coefficient is positive it most likely is less than. since the line is dashed it does not include the number (sign will be < or > without the or equal to)

so let's try it

y < 4x - 2

0 < - 2?

no

so shade on opposite side of the line

the answer is correct.

7 0
3 years ago
Read 2 more answers
If the following points create a line,
Nadya [2.5K]
ANSWER:
Y intercept is (0,1)
EXPLANATION
6 0
2 years ago
A line passing through the points (1,5) and (2,8)
pashok25 [27]

Answer:

3

Step-by-step explanation:

Formula: y2-y1/x2-x2 = 8-5/2-1 = 3/1 = 3

6 0
3 years ago
Other questions:
  • What is the answer for h/8=3/12 in algebra
    10·1 answer
  • What is 3.29 as a fraction or mixed number
    6·1 answer
  • With this triangle find the value of x
    10·1 answer
  • Is my answer correct?
    13·2 answers
  • Simon has 20 quarters and 12 dimes.He wants to purchase ice cream for his friends.An ice cream cone cost $1.00.How many cones ca
    15·1 answer
  • If today is friday what day of the week will it be 101 days from today
    9·1 answer
  • Consider the function f(x) = 2(3)^x. which of the function in the graph below represents f(x-4)?
    11·2 answers
  • Please help marking brainlist
    14·2 answers
  • At the Middleton School festival, a tent covers a rectangular space 30 1/2 yards long and 9 1/3 yards wide. What is the area, in
    6·2 answers
  • Please I need help ASAP
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!