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
sesenic [268]
3 years ago
12

I would appreciate it if you could answer the questions please- A ball is thrown upward at 48ft/s from a building that is 100 fe

et high the function h(t)= -16+84t + 100 expresses the balls height,h in feet given the time t, in seconds since the ball was thrown.please answer the questions if you know the answer I would appreciate it

Mathematics
2 answers:
postnew [5]3 years ago
6 0

Problem 8

<h3>Answer:  1.5 seconds</h3>

----------------

Work Shown:

h(t) = -16t^2+48t+100 is the same as y = -16x^2+48x+100, just with different variables.

Compare this to y = ax^2+bx+c to find that a = -16, b = 48, c = 100

Then compute the x coordinate of the vertex -b/(2a) getting

h = -b/(2a)

h = -48/(2*(-16))

h = 1.5

It takes 1.5 seconds for the ball to reach its peak height. The vertex represents the max height since the parabola opens downward.

==============================================

Problem 9

<h3>Answer:  136 feet</h3>

----------------

Work Shown:

Plug the result from problem 8 into the function

y = -16x^2 + 48x + 100

y = -16(1.5)^2 + 48(1.5) + 100

y = 136

The vertex is (1.5, 136)

This means at 1.5 seconds, the ball is 136 feet off the ground at its highest point.

==============================================

Problem 10

<h3>Answer: approximately 4.415 seconds</h3>

----------------

Work Shown:

Plug in y = 0 and solve for x

y = -16x^2 + 48x + 100

0 = -16x^2 + 48x + 100

-16x^2 + 48x + 100 = 0

Apply the quadratic formula

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(48)\pm\sqrt{(48)^2-4(-16)(100)}}{2(-16)}\\\\x = \frac{-48\pm\sqrt{8704}}{-32}\\\\x \approx \frac{-48\pm93.29523032}{-32}\\\\x \approx \frac{-48+93.29523032}{-32}\ \text{ or } \ x \approx \frac{-48-93.29523032}{-32}\\\\x \approx \frac{45.29523032}{-32}\ \text{ or } \ x \approx \frac{-141.2952303}{-32}\\\\x \approx -1.41547593\ \text{ or } \ x \approx 4.41547595\\\\

A negative x value makes no sense because time cannot be negative, so we ignore the first solution. The only practical solution is roughly x = 4.415

It takes approximately 4.415 seconds for the ball to reach the ground.

==============================================

Problem 11

<h3>2 Answers:  At 0.5 seconds and at 2.5 seconds</h3>

----------------

Work Shown:

Use the same idea as problem 10. Instead of y = 0, use y = 120

y = -16x^2 + 48x + 100

120 = -16x^2 + 48x + 100

-16x^2 + 48x + 100 = 120

-16x^2 + 48x + 100-120 = 0

-16x^2 + 48x - 20 = 0

-4(4x^2 - 12x + 5) = 0

4x^2 - 12x + 5 = 0

Now apply the quadratic formula

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-12)\pm\sqrt{(-12)^2-4(4)(5)}}{2(4)}\\\\x = \frac{12\pm\sqrt{64}}{8}\\\\x = \frac{12\pm8}{8}\\\\x = \frac{12+8}{8}\ \text{ or } \ x = \frac{12-8}{8}\\\\x = \frac{20}{8}\ \text{ or } \ x = \frac{4}{8}\\\\x = 2.5\ \text{ or } \ x = 0.5\\\\

There are two moments in time when the ball is 120 feet in the air. Those two moments are at x = 0.5 seconds and at x = 2.5 seconds.

At x = 0.5, the ball is going upward. At x = 2.5, the ball is coming back down.

Ede4ka [16]3 years ago
6 0

Answer:

(I'm not sure if your teacher is nit-picky about significant figures, but here I go...)

8) 1.5 seconds

9) 136 feet

10) 4.415 seconds

11) 2.5 seconds (also 0.5 seconds)

Step-by-step explanation:

See attached screenshot of Desmos graph showing y(t) = -16t² + 48t + 100, y = 120 and respective points.

You might be interested in
 Identify the vertex, the focus, and the directrix of the parabola with the given equation.
Elenna [48]
Vertex: (-4,-3)
Focus: (-4, -11/4)
Directrix: y= -13/4
7 0
3 years ago
Leo needs 10 10 red roses and 15 15 pink daisies for every 5 5 bouquets he makes for a flower shop. Drag red roses and pink dais
____ [38]

he needs 6 roses and 9 pink daises

8 0
3 years ago
Read 2 more answers
What is the answer to this equation |x + 1| = 6
djverab [1.8K]
Wait homfdgjhgbjhfb
6 0
2 years ago
A car wash detailed 288 cars in 9 hours. At what rate did the car wash detail cars in cars per hour? A. 31 cars per hour B. 33 c
natta225 [31]

Divide the number of cars by the number of hours:

288 / 9 = 32 cars per hour.

4 0
3 years ago
PLZ HELP! Determine the value of k. Round your answer to the nearest hundredth if necessary.
Anton [14]

Answer:15

Step-by-step explanation

4 0
2 years ago
Other questions:
  • Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?
    7·2 answers
  • A cake recipe calls for 2 and 5/6 cups of sugar. A caterer has 13 1/2
    10·1 answer
  • Jim, Bob, Mike and Carlos are taking a road trip. At the first gas stop Jim pays $17 for gas. At the second gas stop Bob pays $1
    6·1 answer
  • Find the national root of x^4+3x^3+3x2-3x-4=0
    8·1 answer
  • Solve the equation.<br> 8 – 2x = -8х + 14<br> A) x= -1<br> B) x= -3/5<br> C) x= 3/5<br> D) x= 1
    15·2 answers
  • Help me with this equation!
    8·1 answer
  • The Ring Toss Game at a summer carnival sold 120 tickets for a total of $60. The Bumper Cars Ride made $100 from selling 50 tick
    6·2 answers
  • Math flavored homework is hard so I need help
    13·1 answer
  • Solve for X.<br> 12 km<br> х<br> 20 km
    10·2 answers
  • Arithmetic sequence
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!