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
forsale [732]
3 years ago
5

The height of a projectile fired upward is given by the formula

Mathematics
1 answer:
natali 33 [55]3 years ago
5 0

Answer:

The projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.

Step-by-step explanation:

The height of a projectile fired upward is given by the formula:

\displaystyle s = v_{0} t - 16t^2

Where <em>s</em> is the height in feet, <em>v</em>₀ is the initial velocity, and <em>t</em> is the time in seconds.

Given a projectile with an initial velocity of 128 ft/s, we want to determine how long it will take the projectile to reach a height of 96 feet.

In other words, given that <em>v</em>₀ = 128, find <em>t</em> such that <em>s</em> = 96.

Substitute:

(96) = (128)t-16t^2

This is a quadratic. First, we can divide both sides by -16:

-6 = -8t+t^2

Isolate the equation:

t^2 - 8t + 6 = 0

The equation isn't factorable, so we can consider using the quadratic formula:

\displaystyle t = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}

In this case, <em>a</em> = 1, <em>b</em> = -8, and <em>c</em> = 6. Substitute:

\displaystyle t = \frac{-(-8)\pm\sqrt{(-8)^2-4(1)(6)}}{2(1)}

Simplify:

\displaystyle t = \frac{8\pm\sqrt{40}}{2} = \frac{8\pm 2\sqrt{10}}{2} = 4\pm \sqrt{10}

Hence, our two solutions are:

\displaystyle t = 4+\sqrt{10} \approx 7.16\text{ or } t= 4-\sqrt{10} \approx 0.84

So, the projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.

You might be interested in
Kate has 21 coins (nickels and dimes) in her purse. How many nickels and dimes does she have if she has $1.50? 3 nickels and 18
Brut [27]
It would be 12 nickels and 9 dimes

4 0
3 years ago
Read 2 more answers
What is 538x46 and how would u show ur work
mylen [45]
Ok listen close. Put 538 on top and 046 on the bottom. Line them up so you don't get confused. don't forget it's multiplication. Start from right to left. Your going to have to cancel out each of the bottom numbers. Cool. Now here's the equation. multiply 8x6. it's 48. put the 8 under the 6 and the 4 small up by the 3 in the 538. That's a remainder. Now it's time for the 3x6 with the remainder of 4. it's 18. now add the remainder to 18.   4+18=22. Put the single 2 next to the other answer just to the left. It should look like blankspacebecauseequationisn'tdone 28. Now Put the remainder (2) small right by the 5 in 538. Next is 5x6 with the remainder. It's 30+remainder of 1= 31 put both those numbers down next to the 28 answer space. It's now 3,128. Now this is where it gets tricky. put a 0 DIRECTLY BELOW the 8 in 3,128. This is for an equation later. Now you worked through the 6 part of 46, now you only have the 4 to work through. Now let's work through 8x4. it's 32. put the 2 right next to the 0 in the answer part. Put the remainder next to the 3 in 538.  Now it's 3x4 +the remainder of 3. It's 12+ 3 + 15. Put the 5next to the 20 in the answer section under 3,128. It should look like blablabla 520. Now let's work out 5x4 With the remainder of 1 from the 15. It's 20 + 1= 21. Put the 21 right next to 520. It should look like 21,520. Now to finish this equation, add the top number 03,128 and the bottom number 21,520. Here if it's easier the equation. 03,128+21,520 which equals 24,748. Hope that helped! 

5 0
3 years ago
diego has 90 songs on his playlist. how many songs are there for each genre ? 40% rock , 10% country , 30% hip hop , the rest is
hjlf

Answer:

Diego playlist has 36 songs in rock genre, 9 songs in Country genre, 27 songs in hip hop genre and 24 songs in electronica genre.

Step-by-step explanation:

Given:

Total Songs on playlist = 90

rock = 40%

country = 10%

hip hop = 30%

rest is electronica.

We need to find the number of songs in each genre.

rock = 40%

So Number of songs in rock genre = \frac{40}{100}\times90 = 36\ songs

country = 10%

So Number of songs in country genre = \frac{10}{100}\times90 = 9\ songs

hip hop = 30%

So Number of songs in hip hop genre = \frac{30}{100}\times90 = 27\ songs.

and rest is electronica genre.

Number of songs in electronica genre can be calculated by Subtracting Number of songs in rock genre and Number of songs in country genre and

Number of songs in hip hop genre from Total number of songs.

framing in equation form we get;

Number of songs in electronica genre = 90-30-9-27 = 24\ songs

Hence Diego playlist has 36 songs in rock genre, 9 songs in Country genre, 27 songs in hip hop genre and 24 songs in electronica genre.

3 0
3 years ago
Read 2 more answers
How do you simplify this expression
ehidna [41]
The picture is blurry
3 0
3 years ago
Using the TI-84 calculator, find the area under the standard normal curve. Round the answers to four decimal places.(a) Find the
madam [21]

Answer:

a) 0.705

b) 0.976

c) 0.01

d) 0.09

Step-by-step explanation:

We have to find the area under the standard normal curve.

a) area under the standard normal curve that lies outside the interval between z= −1.98 and z=0.61.

=P(-1.98

b) area under the standard normal curve to the left of z=1.98

=P(z

c) area under the standard normal curve to the right of z= 2.34

P(z>2.34)\\=1 - P(z

d)  area under the standard normal curve that lies between z= −0.94 and z= −0.63

=P(-0.94

6 0
3 years ago
Other questions:
  • What is the number of square inches in one square foot?
    14·1 answer
  • How can I use fraction circles to find the sum of mixed numbers
    7·1 answer
  • Which graph shows the solution to the following inequality?<br>4d- 6 &lt; 18 <br>PLEASE HELP​
    11·2 answers
  • SALE
    15·1 answer
  • Determine if the two triangles are congruent
    11·1 answer
  • If g(x)=1.5x-3 ,determined if f(x) &gt; g(x) when x = 4​
    9·1 answer
  • How do you solve this? Please help
    5·1 answer
  • Kiran says we should add the constraint 1 is greater than or less than 0
    6·1 answer
  • Please help me. find the value of x. will mark brainliest.
    14·1 answer
  • 1. 0.68 = 0.6 + _____ =_____ x 0.1 +8 x ____. <br><br>2. 0.031 = _____ x 1/100 + _____ × 1/1000​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!