Mathematics College

A rocket fired upward from some initial distance above the ground. Its height (in feet) h, above the ground t seconds after it is fired is given by h(t)=-16t^2+160t+384

What is the rockets maximum height?


After it is fired, The rocket reaches the ground at t=____ seconds

Answers

Answer 1

Answer:

Part A)

784 feet in the air (after five seconds).

Part B)

After 12 seconds.

Step-by-step explanation:

The height h (in feet) of a rocket t seconds after being fired is modeled by the function:

[tex]h(t)=-16t^2+160t+384[/tex]

Part A)

We want to find the rocket's maximum height.

Since our function is a quadratic, the maximum height will occur at its vertex. The vertex of a quadratic is given by:

[tex]\displaystyle \Big(-\frac{b}{2a}\, f\Big(-\frac{b}{2a}\Big)\Big)[/tex]

In this case, a = -16, b = 160, and c = 384.

So, the vertex occurs at:

[tex]\displaystyle t=-\frac{160}{2(-16)}=\frac{160}{32}=5\text{ seconds}[/tex]

The maximum height is reached after five seconds.

Then the maximum height is:

[tex]h(t)_\text{max}=h(5)=-16(5)^2+160(5)+384=784\text{ feet}[/tex]

Part B)

When the rocket reaches the ground, its height h above the ground will be 0. Hence:

[tex]h(t)_\text{ground}=0=-16t^2+160t+384[/tex]

Solve for t. We can first divide both sides by -16:

[tex]t^2-10t-24=0[/tex]

Factor:

[tex](t-12)(t+2)=0[/tex]

Zero Product Property:

[tex]t-12=0\text{ or } t+2=0[/tex]

Solve for each case:

[tex]t=12\text{ or } t=-2[/tex]

Time cannot be negative. Hence, our only solution is:

[tex]t=12\text{ seconds}[/tex]

The rocket reaches the ground 12 seconds after it is fired.

Related Questions

Two angles in a triangle have measures of 35° and 73".
What is the measure of the third angle?
A. 143
B. 108
C. 38
D. 72

Answers

it’s D because every triangle is equivalent to 180 degrees and you just add the two measurements up and then subtract from 180 and you get 72.

Answer:

D. 72

Step-by-step explanation:

the actual length of a Corvette is 15 feet. Using the scale factor 1:3, determine the length of the model Corvette in inches

Answers

The length of the model will be 5”.

15/3=5

What is the Greatest Common Factor of 12 and 36? (1 point)

a

2

b

4

c

6

d

12

Answers

Answer: D) 12

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

The greatest common factor is 12.

Answer:

d.) 12

Step-by-step explanation:

36/12 is equal to 3 and it is the largest number on the list.

12/12 is well one so the answer is "d".

Find the area of a rectangle with a width of 2/3 inches and a height of 8 inches. (*just put the number, square inches)

Answers

Answer:

[tex]\frac{16}{3}in^2[/tex]

Step-by-step explanation:

the area of a rectangle is the multiplication of dimensions.

A = (2/3)in * 8in = (16/3)in^2

How many different meal combinations are possible if he chooses one type of sandwhich, one snack, and one drink ?

Answers

Answer:

12 different possibility

Step-by-step explanation:

1- pbj, cookie, juice

2-pbj, cookie, milk

3-pbj, cookie water

4-pbj,brownie, juice

5-pbj, brownie milk

6-pbj, brownie water

7-turkey, cookie, juice

8-turkey, cookie, milk

9-turkey, cookie, water

10-turkey, brownie, juice

11-turkey, brownie, milk

12-turkey, brownie, water

Convert the following angle from degrees to radians. Express your answer in simplest form. 435^

Answers

Answer:

29π/12.

Step-by-step explanation:

Multiply by π/180

= 435π/180

= 29π/12 radians.

A rectangle’s length is three times its width, w. Its area is 243 square units. Which equation can be used to find the width of the rectangle?

w2 = 3(243)
3w2 = 243
4w2 = 243
3w2 = 3(243)

Answers

Answer:

the second option because it's three times the width so it would be time the W

Step-by-step explanation:

Answer:

the guy above me is correct

Step-by-step explanation:

just did the test got a 100%

What is the volume of a cube with a side length of 2/3 cm? *

Answers

the volume of the cube would be 0.3 cm

A parking garage charges $5 for the first hour and $2 for each additional hour or fraction of an hour. Which point is NOT included in the graph of this step function? A. (3.5, 11) B. (4.2, 11) C. (3.0, 9) D. (4.0, 11)

Answers

Answer:(4.2,11)

Step-by-step explanation:

Find the coordinates of the indicated point after performing the described transformation on triangle ABC

Answers

Answer:

DUDE YOU USE SCHOLOGY!!

Wait is your name andy from the inbox mail tab?? Arent you in 6th grade??

I think I know you man!!

Step-by-step explanation:

giving brainliest to
whoever answers this
correctly


8^2x-3=(1/16)^x-2

Answers

Answer:

x  =  −

6

Step-by-step explanation:

Nearly Positive hope i helped :)

what is the surface area of the pyramid???​

Answers

Answer:

B

Step-by-step explanation:

B is correct

Hope this helps!!!

Simplify the following expression. 10x + 6 + 2(x + 5)

Answers

Answer:

12x+10

Step-by-step explanation:

10x+2(x+5)

10x+2x+10

12x+10

If you are adding a whole to 3/4, how should you write it?

A. 3/4 + 1
B. 3/4 + 3/4
C. 3/4 + 4/4
D. 3/4 + 4
E. 3/4 + 1/1



HELO MEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

i would say "a"

Step-by-step explanation:

essentially, "a" "c" and "e" are all the same thing but most people would write it as "a"

Chris plants25 pumpkin seeds in 5 equal rows. How many seeds does Chris plant in each row? Make an array to-represent the problem then solve the problem

Answers

Answer:

5 seeds in each row

Step-by-step explanation: This is what the array should look like

Which one is greater?
4 yd or 144 in.

Answers

Answer:

4yd

144

Step-by-step explanation:

because 4yd is greater than 144

which of these numbers is irrational?

Answers

Its gotta be C square root of 72

Donna makes 8 dollars for each hour of work write an equation to represent her total pay p after working h hours

Answers

Answer:

8h = P

Step-by-step explanation:

you do the amount she makes and hour (8$) multiply by the number of hou   hours (h), and make it equal the total pay (P). So you would write 8h = P (8$ for each hour equals her total pay for those hours)

Malia ran 7/12 of a mile. Shona ran 3/4 of a mile. Who ran further?

Answers

Answer:

Shona ran farther

Step-by-step explanation:

3/4 *3/3 is 9/12 and 9/12 is bigger than 7/12

Answer:

Shona

Step-by-step explanation:

Both fractions have different denominators. To get a better picture of who ran further, let's have both fractions have the same denominator.

Let's convert the smaller denominator to the bigger one.

In order to do this, we will multiply top and bottom by 3:

[tex]\frac{3}{4} *\frac{3}{3} \\\frac{9}{12}[/tex]

Now, we compare the two fractions by seeing which numerator is closer to denominator.

From this comparison, the converted fraction, [tex]\frac{9}{12}[/tex] is closer to 12.

Therefore, Shona ran further.

PLEASE HELP WILL MARK BRANIEST IF RIGHT

Answers

Answer:

This function has a local minimum at x = 10 with output value -693

and a local maximum at x = 1 with output value 36.

Step-by-step explanation:

see attached desmos graph.

Algebra II Part 1
Triangle ABC is reflected over the x-axis. Triangle ABC has points A (-6, -1), B (-2, -1), and C
(-5, -6). What is the A coordinate?
Be sure to put coordinates
in parentheses

Answers

Answer:

JjKjKjKk

Step-by-step explanation:

A earned wages of ​$34400​, received ​$2300 in interest from a savings​ account, and contributed ​$2900 to a​ tax-deferred retirement plan. was entitled to a personal exemption of ​$3800 and had deductions totaling ​$6090. Find gross​ income, adjusted gross​ income, and taxable income.

Answers

Answer:

53,320 gross income

50,120 adjusted gross income

39,370 taxable income

Step-by-step explanation:

Which is the graph of a logarithmic function?

Answers

Where is the graph ?

Please answer and explain ILL MARK BRAINLIEST

Answers

Answer:

a) x²-x-6

b) 2x²-11x+12

c) x²-4

Step-by-step explanation:

See image!


A line passes through the point (10,8) and has a slope of
5/2

Answers

Answer:

y=5/2x-17

Step-by-step explanation:

The area of the Pacific Ocean is about 6.0061 x 10^7 square miles. The area of the Southern Ocean is about 7.8483 x 10^6 square miles. Approximately how many times larger is the area of the Pacific Ocean than that of the Southern Ocean?

Answers

Answer:

7.653 larger

Step-by-step explanation:

Pacific area/Southern area = (6.0061) * 10^7 / (7.8483) * 10^6

                            = 6.0061/ 7.8483    *    10^7/10^6

                            = 0.7653    *    10^(7-6)

                            = 0.7653   *   10^1

                             = 0.7653 * 10

                             = 7.653

Compared to the Southern Ocean, the Pacific Ocean is about 7.653 times larger.

What are the possible values for m and n

Answers

Answer:

m=4

n=-6

The above is just a possible value you can come up with your own :D.

See below for an explanation.

Step-by-step explanation:

Here you are going to really know the exponent rules. But in jest, you basically need to know that m+n=-2 due to exponent rules.

So?

An example would be

m=4

n=-6

Why?

Because 4-6=-2!

What are the Answers to 1-10?

Answers

Answer:

i can give u 2 10 and 7   acute, acute and straight

Step-by-step explanation:

1. acute
2. acute
3.obtuse
4. obtuse
5.obtuse
6.obtuse
7.straight
8. acute
9.right
10. acute

WILL GIVE EXTRA BRAINLST

HAVE A NICE DAy

Answers

Answer:

They should both be irrational

Step-by-step explanation:

:)

Have a nice day too!

15 / 8 hfhhhfshsfhsfhfshfshfshsfhsf

Answers

Gyfyykfkyxkhxmjxmhxmjxmhxkhditekyelktsbgdngdhnzngz vxmhdkydk
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