Earlier, you were told about a toy rocket fired into the air from the top of a barn. Its height (h) above the
ground in yards after a seconds is given by the function:
h(x) = -52% + 100 + 20
What was the maximum height of the rocket?
Solution
The maximum height was reached by the rocket at one second as you found in part b from the previous
example. It takes second to reach the maximum height. We will substitute that value in for x in our
function and simplify.
The maximum height reached by the rocket was 25 yards. What is the time it takes for the rocket to hit
the ground? (Use a graph or any other method to solve.)
It takes approximately 3.2 seconds for the rocket to hit the ground. (Round to the nearest tenth.)

Earlier, You Were Told About A Toy Rocket Fired Into The Air From The Top Of A Barn. Its Height (h) Above

Answers

Answer 1

Using quadratic function concepts, it is found that:

It takes 1 second to reach maximum height.The maximum height is of 25 yards.It takes approximately 3.2 seconds for the rocket to hit the ground.

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

[tex]h(x) = -5x^2 + 10x + 20[/tex]

Which is a quadratic function with coefficients [tex]a = -5, b = 10, c = 20[/tex].

The maximum height will be a reached at a time of [tex]x_v[/tex], and will be of [tex]y_v[/tex], considering the vertex given by:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{\Delta}{4a}[/tex]

[tex]\Delta = b^2 - 4ac[/tex]

Then:

[tex]x_v = -\frac{10}{2(-5)} = 1[/tex]

[tex]\Delta = 10^2 - 4(-5)(20) = 500[/tex]

[tex]y_v = -\frac{500}{4(-5)} = 25[/tex]

Thus:

It takes 1 second to reach maximum height.The maximum height is of 25 yards.

It hits the ground when [tex]h(x) = 0[/tex], thus:

[tex]-5x^2 + 10x + 20 = 0[/tex]

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-10 + \sqrt{500}}{2(-5)} = -1.2[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{-10 - \sqrt{500}}{2(-5)} = -3.2[/tex]

We want the positive root, so, it takes approximately 3.2 seconds for the rocket to hit the ground.

A similar problem is given at https://brainly.com/question/24705734


Related Questions

Determine whether there a function or not a function

Answers

Answer:

21 is a function but 20 is not

Answer:

20 no

21 yes

if you draw a line parallel with y axes

if it cut graph in two points or more than it's not function

The sum of three numbers is 137. The second number is 4 more than two times the first number. The third number is less than three times the first number. Find the three numbers.

Answers

Answer:

23, 50, 64

Step-by-step explanation:

137 = 23 + 50 + 64

Let the first number be x

Second number: 2x+4

Third number: 3x-5

Write the equation:

x + (2x + 4) + (3x-5) = 137

Solve for "x"

6x - 1 = 137

6x = 138

x = 23

Plug x (23) into the equation:

x + (2x + 4) + (3x-5) = 137

23 + 2(23) + 4 + 3(23) - 5 = 137

(23 + 46 + 4 + 69) - 5 = 137

142 - 5 = 137

what is 34÷6837 show ur work​

Answers

Answer:

Step-by-step explanation:

  If you're allowed to use a calculator, type in 34, the division symbol, 6837, and finally enter:

  34 / 6837 = 0.00497

Answer:

0.00497294135

Step-by-step explanation:

Write the equation of a line going through the points (2,2) and (4,-3) in slope intercept form.

Step 1: Find slope


Step 2: find b



Step by step answer please.

Answers

Answer:

the slope is y2 - y1 over

x2 - x1

which means

[tex]( - 3- 2) = - 5[/tex]

[tex](4 - 2) = 2[/tex]

slope is m= -5/2

then you take a y from the first set of points for b

[tex]y = - \frac{5}{2} x \times 2[/tex]

hope it helps.


I will give brainliest if right, please help!

Which line uses all trochees?
A. Correct, the mall is over there
B. Roadrunners and barbecue
C. Toy store sausages swung by
D. Ask me questions now or later

Answers

Answer:

I believe it is c

Step-by-step explanation:

The metrical pattern of a trochee is said to have a "falling rhythm" because the emphasis comes at the beginning of the foot: "da-dum da-dum." This falling rhythm is the exact opposite of the iambic "rising rhythm" that is more common in both poetry and speech, so the cadence of trochaic meter tends to sound a little unnatural to the ear. While for this reason trochees are relatively rare in most poetry, the "downward" motion and "backward" orientation of trochees actually makes them a popular foot for writing about dark subjects like madness and death.

Answer:

Step-by-step explanation:

I don't understand this but D is the

Please help me with this. Thanks!

Answers

Answer:

the plane is descending at a rate of 8,300 feet per minute

Step-by-step explanation:

31,275 - 22,975 = 9,300

BRAINLIEST PLEASE!

A line has a slope of 9 and passes through the point (0, 5). What is its equation in slope -intercept form?

Answers

Answer:

y = 9x + 5

Step-by-step explanation:

Slope = m = 9

(0 , 5)

Slope intercept form: y = mx + b

y = 9x + b

Plugin x = 0 and y = 5

5 = 0 + b

b = 5

y = 9x + 5

Which of the following is a characteristic of a deferred payment plan? (2 points)
There is an introductory period where no interest is accrued.
The item purchased is used as collateral until the balance is paid in full.
A down payment is always required.
A certain number of payments must be made before the product is owned.

Answers

A characteristic of a deferred payment plan is that the item purchased is used as collateral until the balance is paid in full.

A deferred payment plan is a form of credit purchase, a way to pay for an item in arrears. The payment is usually divided into several installments, which are distributed over a certain period of time. Interest and fees are often added, which in the end makes the purchase considerably more expensive than if you had paid in cash.

Thus, through this payment system, the asset is delivered to the buyer before the payment is completed, thereby constituting the asset itself as an enforceable guarantee of payment compliance.

Learn more in https://brainly.com/question/2130499

Please help me with this math probelm ASAP!! Will give brainliest!! :)

Answers

Answer:

z=21, x=1, y=9

Step-by-step explanation:

3z=63 (a property of a kite)

z= 21

3x-1=2x (another property of a kite)

x=1

y+4=13 (another property of a kite)

y=9

Be sure to know your properties!

if x 60 and 30 find the unknown sizes of angle​

Answers

Answer:

A special right triangle is a right triangle having angles of 30, 60, 90, or 45, 45, 90. Knowledge of the ratio of the length of sides of a special right triangle enables us to solve for any missing part of the triangle. The ratio of the side lengths of a special right triangle with angles of 30, 60, 90 is 1:sqrt(3):2, while the ratio of the side lengths of a special right triangle with angles of 45, 45, 90 is 1:1:sqrt(2).

Please help I really need help.

Answers

u need a protractor

By which rule are these triangles congruent

A. AAS
B. ASA
C. SAS
D. SSS

Answers

Answer:

option D

Step-by-step explanation:

this trianle will be congurent by SSS method easily

Answer:

Option D.SSS These triangles congruent with SSS property

May I please receive help???

Please

Answers

Answer:

sorry i don't know the answer!

Step-by-step explanation:

if i knew i would'v helped..

The answer is 86 - 12= 74

Math question.

I’ll give brainliest, thanks and 5 stars to the correct answer that has been explained properly.

Answers

Answer:

C) 25%

Step-by-step explanation:

let salt be 's'

let water be 'w'

[tex]\frac{s+1}{w+s+1} = 33\frac{1}{3} \\\\\frac{s+1}{w+s+1} = \frac{1}{3} \\\\\frac{w + s + 1}{3} = s+1\\\\3s +3 = w+s+1\\w = 2s+2\\\\\frac{s+1}{w+1+s+1} = \frac{3}{10} \\\\\frac{3(w+s+2)}{10} = s+1\\\\3w+3s+6 = 10s+10\\**w = 2s+2\\3(2s+2) + 3s + 6 = 10s+10\\\\6s+6+3s+6 = 10s+10\\9s+12 = 10s+10\\-s = -2\\s = 2\\\\w= 2s+2\\w=2*2+2\\w = 6\\\\\frac{2}{2+6} = \frac{2}{8} = 0.25[/tex]

0.25 = 25%

if i had 475 connolies and got left with 24 and i sold them for 2.50 how much money did i make.​

Answers

1127.50 money

475-24=451
451 times 2.5

What is the sum of the roots of the equation 2 x^2 + 5 x − 3 = 0?
a)-3.5
b)-2.5
C)-1.5
D)2.5

Answers

Answer:

B) -2.5

Step-by-step explanation:

2x^2 + 5x -3 = 0

(2x - 1)(x + 3) = 0

2x - 1 = 0; 2x = 1, so x = 1/2 = ROOT 1

x + 3 = 0, so x = -3 = ROOT 2

Now add the roots: -3 + 1/2 = - 2 1/2, so the answer is B.

I need help asap plssss

Answers

Answer:

x = -4

Step-by-step explanation:

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

If you expand this, you get:

x^2 - x - 20 = x^2 + 4x

graph similar terms together, the x^2 disappears:

-20 = 5x

x = -20/5 = -4

help me please
i need it

Answers

Answer:

5

Step-by-step explanation:

read your book so that you can know your book

The answer to your question is 5

if the slope of a line 4/9 the slope of a line parallel to this would be

Answers

Answer:

4/9

Step-by-step explanation:

Parallel lines have the same slope.

If the slope of one line is 4/9, the slope of a parallel line is 4/9.

in 2000 the population of India was around 1.053 billion , and in 2016 the population hit 1.327 billion people . if India's population continues to grow at this same rate in what year was the population of India reach 3 billion people. ​

Answers

Answer:

The population of India would reach 3 billion in about 112 years (year 2128)

Step-by-step explanation:

1. subtract 1.327 billion by 1.053 billion  (1.327-1.053)

2. The answer you should get is 274,000,000 (two hundred seventy four million)

3. multiply 274,000,000 by 7 (amount of people required to reach about 3 billion)

4. add the product (ans to multiplication problem) to 1.327 billion. (you should get 3.245 billion (3245000000).

5. multiply 16 by 7 (16x7) to get the number of years to reach 3 billion (maybe 112)

6. Add the product to 2016

7. Therefore you get the year 2128.

Using Cramer's Rule, the solution to the system of equations

6x−5y=−4−7x+3y=−1

can be written in the form (DxD,DyD).

What is the value of Dx?

Answers

Using Cramer's rule it is found that Dx = -34.

In Cramer's rule, we have three matrices.

x is a matrix in which the first column is the coefficients that multiply x, and the second are the coefficients on the right side of the equality.y is a matrix in which the first column is composed by the coefficients on the right side of the equality and the second is the coefficients that multiply y.M is a matrix in which the first column is the coefficients that multiply x, and the second is the coefficients that multiply y.

In this problem, the system is:

[tex]6x - 5y = -4[/tex]

[tex]-7x + 3y = -1[/tex]

Matrix x is given by:

[tex]x = \left[\begin{array}{ccc}6&-4\\-7&-1\\\end{array}\right][/tex]

It's determinant is given by:

[tex]Dx = 6(-1) -(-4)(-7) = -6 - 28 = -34[/tex]

Thus, Dx = -34.

A similar problem is given at https://brainly.com/question/24749091

#2
Are the following triangles similar?
Please help!!

Answers

Answer:

Yes

Because

[tex] \frac{pn}{kr} = \frac{pt}{kg} = \frac{tn}{gr} = \frac{1}{2} [/tex]

Also all angles are equal

Answer:

Yes

Step-by-step explanation:

Angle are equal and the ratio of the sides is 2:1.

What's the equation 3c - 4y =28 on a graph?

Answers

here’s the graph for that equation!!

Evaluate 7 10 × 4 5 Give your answer in its simplest form.

Answers

289254654976 if the 7 10 is to the power of not quite sure what you’re supposed to do with the 7 and 10 and 4 and 5

8(x-2)+9<3(x-1)+5x

a. x<-7
b. x<-3
c. no solution
d. all real numbers

thanks!!

Answers

Answer:

d

Step-by-step explanation:

What’s the domain and range of f(x) = 72 - 1/6x?

Answers

Answer:

Step-by-step explanation:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. A rational function is a function of the form f(x)=p(x)q(x) , where p(x) and q(x) are polynomials and q(x)≠0 .


There is a raffle at a hockey game and 250 tickets are sold. Trenton bought 88 tickets. What percent of the
tickets does Trenton have?

Answers

Answer:

35.2%

Step-by-step explanation:

88/250

88x4=352

250x4=1000

352/1000=35.2/100

is the answer C, E, A, B, or D?​

Answers

Answer:

the answer is B hope this helps

please mark mw brainalist

Bob's Gift Shop sold 500 cards for Mother's Day. One salesman, Robert, sold 2% of the cards sold for Mother's Day. How many cards did Robert sell? Divide/scale down to solve for the missing percent.

Answers

Answer:

Robert sold 10 cards for Mother's Day

Step-by-step explanation:

2% of 500 is exactly like multiplying 0.02 with 500 which is 10

3. Consider the equation 3x + 4 = 8x - 16. Solve for x using the given starting point."
Group 1
Group 2
Group 3
Group 4
Add 16 to both sides
Subtract 3x from both
sides
Subtract 4 from both
sides
Subtract 8x from both
sides

Answers

Answer:

X=-2.4

Step-by-step explanation:

3x+4=8x+16

-5x+4=16

-5x=12

x=-2.4

X=6
3x+4=8x-16
+16 +16
3x+20=8x
-3x -3x
30=5x
/5 /5
6=x
Other Questions
You need to exercise your body in the same what that you are going to use it. 3/4+x=2x-x+ ?(need answer) the condition characterized by the telescoping of one part of the intestine into another is: 12. How does a detergent remove a stain?? 2(x+1)=x3x2 No solution, one solution, or infinite solutions repairs, evenAn RRIM part can be repaired using plastic repair adhesives or by______though it is a thermoset part.1 adhesive 2 welding 3 minor 4 major which idea of Jean-Jacques Rousseau was different from those of thomas hobbes?A. Rousseau believed that education needed changes.B. Rousseau believed that the government should be strong.C. Rousseau believed that humans are naturally good.D. Rousseau believed people should give up freedom. which system represents the graph?A. y + 2x = 12 y = x + 3B. y = -2x + 10 y = 2C. x + y = 3 y = -3 (2x - 1)D. y = 2/3x y = 5/3x - 3 Which four components should be included in a good exercise program?power lifting to maximize muscle masslifting free weights for muscular strengthrunning or jumping for muscular endurancedrinking high-sugar sports beverages to give the body energyaerobics exercise for cardio-respiratory enduranceeating an all-vegetable diet to avoid too much fatstretching to maintain flexibility Do you believe that employees communication helps on a business? what are the coordinates of B and D? what do you think is.meant by the end of the 3rd pargraph beginning with, "only a father in that kind of pain could take a boy's shoe in winter only a gather, flesh and bone, could burn a som with smoking end of a coal shovel" A number is first increased by 20 and then doubled. The result is less than 5 times the number 2.2.2 quiz unit 2 fitness and nutrition Command economies produce goods that how are payroll taxes different from personal income taxes brainly There is ______man waiting for you in ____office If anybody sees this can they help me out?And on that cheek, and oer that brow,So soft, so calm, yet eloquent,The smiles that win, the tints that glow,But tell of days in goodness spent,A mind at peace with all below,A heart whose love is innocent!The rhythm and rhyme scheme of this stanza reflect Question 12 options:A. A heart beating with passionate love B. the pretty features of the woman's face C. The passing of time from day to night D. the calm peace the speaker sees in the woman Re-read the following lines from Edna Millays Love is Not AllLove is not all: it is not meat nor drinkNor slumber nor a roof against the rain;Nor yet a floating spar to men that sinkWhat type of figurative language is present in the lines above?Question 10 options:A. SimileB. Repetition C. HyperboleD. Assonance The reader can infer that the speaker Question 9 options:A. Believes love is the only thing in life that truly mattersB. Believes that love is not necessary for survivalC. Desires to find love more than anythingD. Would rather keep the memory of her love than trade it for something necessary for survival What impact would this have on American trade with China ? Please help !!!! TIADraw Venn diagrams to show the prime factors for each of the following sets of three numbers. a. 12, 14, 70 b. 6, 7, 8