A bullet is fired straight upward with an initial speed of 720 ft/s. It’s path is modeled by the equation h=-16t^2 + 720t, where h is the height of the bullet t seconds after it was fired. When does the bullet reach a height of 4,000 feet?

Answers

Answer 1

Answer:

The bullet reaches a height of 4000 feet after 6.49 seconds, and then, coming back down, after 38.5 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

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

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

The height of the bullet after t seconds is given by:

[tex]h(t) = -16t^2 + 720t[/tex]

When does the bullet reach a height of 4,000 feet?

This is t for which [tex]h(t) = 4000[/tex]. So

[tex]4000 = -16t^2 + 720t[/tex]

[tex]16t^2 - 720t + 4000 = 0[/tex]

Dividing by 16

[tex]t^2 - 45t + 250 = 0[/tex]

So [tex]a = 1, b = -45, c = 250[/tex]

[tex]\bigtriangleup = b^{2} - 4ac = (-45)^2 - 4(1)(250) = 1025[/tex]

[tex]t_{1} = \frac{-(-45) + \sqrt{1025}}{2} = 38.5[/tex]

[tex]t_{2} = \frac{-(-45) - \sqrt{1025}}{2} = 6.49[/tex]

The bullet reaches a height of 4000 feet after 6.49 seconds, and then, coming back down, after 38.5 seconds.


Related Questions

I need help with 1 through 10

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Answer:

1) yes

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HELPPPPOMOGMGOGMGOGKM PLS ANSWER THIS CORRECTLY PLZZZ THIS IS FOR A VERY IMPORTANT TEST YOUWILL GET BRAINLIEST HELP

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Answer:

i cant give u the answer but here is an example hope this helps slope  =  "rise over run"  the difference in y values divided by the difference in x values

= 6/-3 = -2 = m.  It's negative because as x increases, y decreases

plug that into the point slope formula, with either point.  generally use the most simple point

y-h= m(x-k) where m= -2 and (k,h) = (2,-2)

y+2 = -2(x-2)

simply if you want

Y = -2x +4 -2 = -2x +2

or

2x +y = 2

Step-by-step explanation:

Answer:

Your slope is -1

Your y inter is -3

Step-by-step explanation:

Hope this helps you :)

Jake and Natalya both have jobs that pay by the hour. The amounts they earned based on various numbers of hours worked are shown in the tables. Which of these statements is correct? Immersive Reader

A. If the amount Abby earns can be described by p=11.75h, where p is her pay and h is the number of hours worked, the Abby earns more per hour than Jake and less per hour than Natalya.
B. If the amount Bobby earns can be described by p=10.75h, where p is his pay and h is the number of hours worked, then Bobby earns less per hour than Jake and Natalya.
C. If the amount Deion earns can be described by p=12.25h, where p is his pay and h is the number of hours worked, the Deion earns more per hour than Jake and Natalya.
D. If the amount Frederica earns can be described by p=12.75h, where p is his pay and h is the number of hours worked, then Frederica earns less per hour than Jake and Natalya.

Answers

The answer is B...

Explanation....

Mr. Tanner bought some boxes of markers with 18 markers in each box. He kept 2 markers and gave the rest to his students. Use the equation below to calculate the number of boxes (b) he bought. 18b – 2 = 214

Answers

Answer: 18b-2+2=214 +2

Step-by-step explanation:Add 2 both sides of the equation

Answer:

b = 12; he bought 12 boxes.

Step-by-step explanation:

18b - 2 = 214 (subtract 2 on both sides)

18b = 216 ( divide 18 on both sides to get 'b' alone)

b = 12

Under her cell phone plan, Katherine pays a flat cost of $50 per month and
$5 per gigabyte. She wants to keep her bill at $71 per month. How many
gigabytes of data can she use while staying within her budget?

Answers

Answer: x = 4.2

Step-by-step explanation:

To keep her bill at $71 per month, she needs to consume 4.2 gigabyte in a month.

A linear equation is in the form:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the initial value of y.

Let y represent the amount of money paid for x gigabyte.

Given a flat cost of $50 per month and  $5 per gigabyte, hence m = 5, b = 50. Therefore:

y = 5x + 50

For a bill of $71 per month:

71 = 5x + 50

5x = 21

x = 4.2

To keep her bill at $71 per month, she needs to consume 4.2 gigabyte in a month.

Find out more on linear equation at: https://brainly.com/question/14323743

(−4,3),(−2,1),(0,−1),(2,−3) Write a scenario?​

Answers

Answer:

tergtjmsrhatsfdghb

Step-by-step explanation:

8. Do the representations below define a function? *
y =
x - 2
Yes, it is a function.
No, it is not a function.

Answers

Answer:

Step-by-step explanation:

Yes it is a function. Every x has only 1 y associated with it.

Find each angle measure to the nearest degree please help

Answers

9514 1404 393

Answer:

4°48°

Step-by-step explanation:

The inverse cosine function of your calculator is used to find the angle from the cosine value. (Be sure your calculator is set to 'degrees' mode.)

1) A = arccos(0.9976) ≈ 4°

2) U = arccos(0.6691) ≈ 48°

I need assistance please

Answers

Answer:

23

Step-by-step explanation:

6/3 = x-5/9 simplify the first fraction

2= x-5/9 multiply both of the sides

18 = x-5/9 move it around correctly

-x=-5-18 calculate it

-x=-23 the negatives cancel out

x=23

The answer to this question is 23

use long or synthetic division to find the following quotients
(x^3+2x^2!22x-45)÷(x+5) ​

Answers

Answer:

[tex]\boxed{\textsf{ The quotient is $\sf x^2-3x-7$ and the remainder is (-10).}}[/tex]

Step-by-step explanation:

Here we will be using long division method to find the quotient . Here we need to divide (x³+2x²-22x-45) and (x+5) . So lets divide .

x+5) x³+2x²-22x-45 ( x² -3x -7

x³ + 5x²

- -

______________

- 3x²-22x -45

-3x² -15x

+ +

______________

-7x -45

-7x -35

______________

-10

Quotient = x² -3x -7

Remainder = (-10)

Hence the quotient is -3x -7 and the remainder is (-10) .

9.

Jacks Plumbing charges customers $100 per hour for repair jobs. Al's Plumbing charges according to the equation y = 75x + 50, where x = time in hours and y = cost

dollars

Explain why Ars Plumbing charges less than Jacks Plumbing for a 4-hour repair job.

Does Als Plumbing charge less than Jacks Plumbing for all repair jobs? Explain why or why not.

Answers

Answer:

As given,

Per hour cost of Jack's plumbing = $100

Also,

Al's plumbing charges = 75x + 50 where x = time in hours .

Now,

Al's plumbing cost for 4 hours:

Here , x = 4

⇒75x + 5 = 75(4) + 50 = 300 + 50 = 350

∴ we get

Al's plumbing cost for 4 hours = $350

Now,

As Jack cost for 1 hour = $ 100

⇒ For 4 hour = 4×$100 = $400

∴ we get

Jack's plumbing cost for 4 hours = $400

As we can see that

$ 400 > $350

Jack's plumbing cost for 4 hours  >  Al's plumbing cost for 4 hours

Now,

Al's plumbing charges = 75x + 50 where x = time in hours .

For 1 hour

75x + 50 = 75(1) + 50 = 125

Al's 1 hour cost = $125

whereas Jack Plumbing cost for 1 hour  = $100

∴ we get

$125 > $100

⇒Al's 1 hour cost > Jack's 1 hour cost

Now,

Al's 2 hour cost

75x + 50 = 75(2) + 50 = 150 + 50 = 200

Al's 1 hour cost = $200

whereas Jack Plumbing cost for 2 hour  = $200

∴ we get

$200 =  $100

⇒Al's 2 hour cost = Jack's 2 hour cost

Now,

Al's 3 hour cost

75x + 50 = 75(3) + 50 = 225 + 50 = 275

Al's 1 hour cost = $275

whereas Jack Plumbing cost for 3 hour  = $300

∴ we get

$275 <   $300

⇒Al's 3 hour cost < Jack's 3 hour cost

Als0,

Jack's plumbing cost for 4 hours  >  Al's plumbing cost for 4 hours

∴ we get

We can not say that Als Plumbing charge less than Jacks Plumbing for all repair jobs.

Because the charge is fluctuating ,

For 1 hour , Aly' charge is grater whereas The 2 hour cost of Jack's is higher.

So, the Correct answer is - No, Al's Plumbing charge is not always less than Jacks Plumbing for all repair jobs.

Can someone please help

Answers

Answer:

(-4)^10

Step-by-step explanation:

When doing this sort of problem, we multiply the exponents.

This is the power rule.

Which quadrants are (-4,5) in

Answers

Answer:

Quadrant 2

Step-by-step explanation:

Take a look at the picture I added it should help you on futures questions like this :)

This circle graph shows the results of a survey that asked people to identify their favorite type of music.
What percent of people chose rock or country as their favorite type of music?

A. 9%

B. 35%

C. 45%

D. 55%

Answers

There is no circle graph
The answer is b 35 percent

Probability tree diagram​

Answers

Answer:

?

Step-by-step explanation:

can you explain a little more

I’m not quite sure what you mean

One bottle contains 250 ml of juice. Soham wants 2 liters of juice. How many bottles should he buy?

Answers

Answer:

8 bottles

Step-by-step explanation:

8 bottles
2000 mL in 2L
2000/250= 8

Here is a picture of the Ferris wheel has a radius of 40 m how far does the writer travel in one complete rotation around the Ferris wheel

Answers

Answer:

I'm getting points

Step-by-step explanation:

so I can ask questionss

Solve each single-step equation. Show your work. -15+n=-9

Answers

Answer:

6

Step-by-step explanation:

-15+6 means it goes minus basically its 15-6(-15+6)=-9

Answer:

n=24

Step-by-step explanation:

First add 15 to the right side equaling 24. Therefore n=24

Derek has a bird that weighs 3 pounds. Use the double line diagram below to help you determine approximately how many kilograms this bird weighs.

2 lines. The first line is labeled Pounds and has 6 marks, equally spaced apart, and every other mark labeled 3, 5, 7, respectively. The second line is labeled Kilograms and has 6 marks, equally spaced apart, and every other mark labeled, 1, 2, 3, respectively.
(2 points)

1.5 kilograms
3 kilograms
5.5 kilograms
6 kilograms

Answers

Answer:

about 1.5 kilograms

Step-by-step explanation:

3 pounds=1.36078 so that is closer to the answer 1.5 kilograms

Answer:

1.5

Step-by-step explanation:

i took the test

PLZZZZ HELP QUICK
Ted and Katie have saved up a total of $94.00. Ted has saved 6 dollars less than 4 times as much as Katie. How much has Katie saved?

Answers

Answer:

22

Step-by-step explanation:

94-6 divided by 4

Answer:

LOOK BELOW IN STEP-BY-STEP

Step-by-step explanation:

First, do $94.00 times 4 which is $376

Then, take away 6 dollars from $376 which is $370

Hope that helped!!!

A car depreciates in value each year. Which of the following is NOT true about the value of the car after t years

Answers

Answer:

The car will be worth more in 20 years than the amount it was purchased for.

Step-by-step explanation:

If you look at the graph you see a downward trend, not an upward. That makes it impossible for it to be worth more Hopefully this helps.

Answer: B (top right)

Step-by-step explanation:

−15(x−4)=−2 the 15 is one fifth pls help

Answers

X=-6
1(x-4) over 5 =-2
Multiply all terms by the denominator to get simplified x-4=-10
Add 4 to each side to get x=-6

Describe the mathematical process for finding the area of a rectangle triangle and circle be sure to included explain the formulas for finding the area if each shape

Answers

Can someone help me on my question please answer hurry
A because b so nine is the cool

arrange in order from least to greatest. -3/5, 7/-10,-5/6
[tex] \frac{ - 3}{5} \frac{7}{ - 10} \frac{ - 5}{6} [/tex]
plzz help!!!
fast!!
it is due in 10 min..
I'll make brailiest whose ans is correct...​

Answers

-3/5 = -0.6
-7/10 = -0.7
-5/6 = -0.8333

It’s easier to put them in decimal form!

Remember that in the negatives, the highest number is the lowest.


From least to greatest;

-5/6, -7/10, and -3/5

Please help :( Find X.
Round to the nearest tenth.

Answers

90^2 = 55^2 + 50^2 - 2(55)(50)cosX
(90^2 - 55^2 - 50^2)/(2(55)(50)) = cosX
X = 62.1°

HELP HELP PLSSSSSSSSSSSSSSSSSSSSSSSS

Answers

Answer:

19

Step-by-step explanation:

31 +9 =40

40 by 2 = 20

9-5=4

4 by 4= 1

20-1= 19

9 for the answer is 1
10 I’m not 100%sure on this but pretty sure it’s 359
Hope this helps!!

Choose the number that correctly completes the ratio table.

Answers

Answer:

its 8:9

Step-by-step explanation:

It would be 8 because you can see that the top row multiplies 16 by two in the exact spot where the missing number is.

On which triangle can the law of cosines be applied once to find an unknown angle measure? Law of cosines: a2 = b2 + c2 – 2bccos(A) Triangle X W Y is shown. Angle X Y W is a right angle. The length of hypotenuse W X is y, the length of X Y is a, and the length of W Y is 9. Triangle W X Y is shown. Sides W X and X Y are congruent. The length of W Y is 7. Triangle W X Y is shown. Angle X Y W is 76 degrees. The length of X Y is 5, the length of W Y is 10, and the length of W X is y. Triangle W X Y is shown. The length of W X is 10, the length of X Y is 8, and the length of W Y is 16.

Answers

Answer:

C) Angle X Y W is 76 degrees. The length of X Y is 5, the length of W Y is 10, and the length of W X is y.

Step-by-step explanation:

On which triangle can the law of cosines be applied once to find an unknown angle measure?

The Law of cosines is given as:

a² = b² + c² - 2bccos(A)

From the options given above, the correct option is Option C

C) Angle X Y W is 76 degrees. The length of X Y is 5, the length of W Y is 10, and the length of W X is y.

This is because:

Law of Cosines helps us to find an unknown side of a triangle when we are given 2 known sides and 1 angle.

In the above question, we are given angle 76 degree, and the length of two sides: The length of X Y is 5, the length of W Y is 10

The unknown side is the length of W X which is represented as y.

Hence, Option C is the correct option.

Answer:

D

Step-by-step explanation:

I got it right on my program.

Emilia and Joshua shared some money in the ratio 1:6.
Emilia received £15.
How much did Joshua receive?

Answers

Answer:

15x6

Step-by-step explanation:

do 15x6 and what that is, is the answer

The ratio of boys to girls at a movie is 5:4 . If there are 16 girls ​, how many boys are at the​ movie?

Answers

Answer:

,it's 15. and here's why: if i pick 4,its makes 12 because 3x4=12 and if you put 3 with 5,you get 15 which is the answer.

Step-by-step explanation:

It is 20. How do you get from 4 to 16? You multiply by 4! Thus, times 5 by 4 to get the answer, whilst keeping the ratio.
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