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
Nastasia [14]
3 years ago
14

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th

e given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
equation: y=−16x^2+177x+98
Mathematics
1 answer:
irga5000 [103]3 years ago
4 0

Answer:

The rocket hits the ground at a time of 11.59 seconds.

Step-by-step explanation:

The height of the rocket, after x seconds, is given by the following equation:

y = -16x^2 + 177x + 98

It hits the ground when y = 0, so we have to find x for which y = 0, which is a quadratic equation.

Finding the roots of a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

y = -16x^2 + 177x + 98

-16x^2 + 177x + 98 = 0

So

a = -16, b = 177, c = 98

\bigtriangleup = 177^{2} - 4(-16)(98) = 37601

x_{1} = \frac{-177 + \sqrt{37601}}{2*(-16)} = -0.53

x_{2} = \frac{-177 - \sqrt{37601}}{2*(-16)} = 11.59

Since time is a positive measure, the rocket hits the ground at a time of 11.59 seconds.

You might be interested in
A deep sea diving bell is being lowered at a constant rate. After 10 ​minutes, the bell is at a depth of 600 ft. After 40 minute
Degger [83]
<h2>Average rate of lowering per​ minute = 36.67 ft/min</h2>

Step-by-step explanation:

After 10 ​minutes, the bell is at a depth of 600 ft

After 10 minutes

                   Depth of bell = 600 ft

After 40 minutes the bell is at a depth of 1,700 ft.

After 40 minutes

                   Depth of bell = 1700 ft

Time gap = 40 - 10 = 30 minutes

Depth fallen = 1700 - 600 = 1100 ft

We have

           Depth fallen = Average rate of lowering per​ minute x Time gap

           1100 = Average rate of lowering per​ minute x 30

           Average rate of lowering per​ minute = 36.67 ft/min

7 0
3 years ago
A quadrilateral has three angles that measure 90o , 100o, and 120o. Which is the measure of the fourth angle?
Reptile [31]

360 - (100 + 90 + 120)  \\ 360 - 310 = 50
it measures 50


good luck
3 0
3 years ago
What is the missing length??
amid [387]

Answer

The missing length is 10

Step-by-step explanation:

Represent the missing length with x

The sides of the given shape are directly proportional.

Mathematically:

(15 + x) to (12 + 8) and x to 7

Represent as a ratio:

(15 + x) : (12 + 8) = x : 8

15 + x : 20= x : 8

Convert to fraction

\frac{15 + x}{20} = \frac{x}{8}

Cross Multiply:

(15 + x)*8 = 20 * x

120 + 8x = 20x

Collect Like Terms

20x - 8x = 120

12x = 120

Solve for x

x = \frac{120}{10}

x = 10

<em>The length of the missing side is 10</em>

4 0
3 years ago
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
kirza4 [7]

Okay follow these patterns and you will always get your answer

Cone = (13)πr2h, where r is the radius and h is the height.

Cube = s2, where s is the length of the side.

Cylinder = πr2h, where r is the radius and h is the height.

Rectangular prism= l×w×h, where l is the length, w is the width and h is the height.

Sphere = (43)πr3, where r is the radius.

ANSWER: (D) 904.78 cm^3

5 0
3 years ago
Homework Progress 23 / 39 Marks Work out 83 +52​
antoniya [11.8K]

Answer:

2 1/25  or 2.04

Step-by-step explanation:

8 ^ 1/3 + 5 ^ (-2)

Rewriting

(2^3) ^ 1/3 + 1/5 ^2

2 + 1/25

2 1/25

2.04

4 0
3 years ago
Read 2 more answers
Other questions:
  • Find the value of X°<br> a.25°<br> b.85°<br> c.75°<br> d.105°
    14·1 answer
  • Integrate x^2+5 please i need it fast
    6·1 answer
  • What are the domain and range of the function? {(1,2), (-2, 0), (3,0), (4, 6)} Select all that apply (more than one choice is po
    7·1 answer
  • Round 9 1/3 to the nearest whole number.<br><br><br> PLS HELP
    6·1 answer
  • the length of a rectangle is given by 2t+1 and its height is t^(1/2), where t is time in sec. Find the rate of change of the are
    7·1 answer
  • Simplify 6(7x - (3 - 6y + 5x) + 6y)
    8·1 answer
  • There are 16 pool balls on the table. If you shoot all of the solid balls in on the first turn how many different ways can they
    14·1 answer
  • I need help ASAP pls
    13·1 answer
  • 3. In 2008, the population of the United States
    9·1 answer
  • |p+4| ≤ 8<br> Solve using absolute value. Make sure to check the answer with the original equation.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!