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
eimsori [14]
3 years ago
13

Every year in Delaware there is a contest where people create cannons and catapults designed to launch pumpkins as far in the ai

r as possible. the equation y=12+105x-16x^2 can be used to represent the height,y, of a launched pumpkin, where x is the time in seconds that the pumpkin has been in the air. What is the maximum height that the pumpkin reaches? How many seconds have passed when the pumpkin hits the ground? (Hint if the pumpkin hits the ground, its height is 0 feet.)
A: The pumpkin's maximum height is 184.27 feet and it hits the ground after 3.28 seconds.
B: The pumpkin's maximum height is 3.28 feet and it hits the ground after 6.67 seconds.
C: The pumpkin's maximum height is 184.27 feet and it hits the ground after 6.67 seconds
D: The pumpkin's maximum height is 3.28 feet and it hits the ground after 184.27 seconds

Mathematics
2 answers:
pishuonlain [190]3 years ago
6 0

Answer:  C. The pumpkin's maximum height is 184.27 feet and it hits the ground after 6.67 seconds

Step-by-step explanation:

Since, the given function that shows the height,

f(x) = 12 + 105 x - 16x^2  ------- (1)

Where x is the time in seconds.

Since, the given function is a parabola,

Therefore the maximum height of the parabola is found at the vertex.

And, the vertex of the parabola = \frac{-2b}{a}

Where a is the coefficient of x^2 and b is the coefficient of x.

Thus, the vertex of the given parabola = \frac{-2\times 105}{-16}=3.281

Therefore, the maximum height of the pumpkin = f(3.281)= 12 + 105\times 3.281 - 16\times (3.281)^2 = 184.266 feet ≈ 184.27 feet

Now, the pumpkin hits the ground when f(x)= 0,

⇒ 12 + 105 x - 16x^2=0

⇒ x = 6.675 seconds ≈ 6.67 seconds

Thus, Option C is correct.

Alexeev081 [22]3 years ago
3 0
My numbers aren't exactly the same due to rounding but you can still see the answer.

You might be interested in
What is the slope of the line passing through the points (-1,7) and (4,-1)?
Luden [163]
The answer is A) -8/5
5 0
3 years ago
Which number line represents the solution set for the inequality –4(x 3) ≤ –2 – 2x?
Anna71 [15]

The solution to the inequality expression is x ≥ - 5

<h3>Inequality expressions</h3>

Inequality are expressions not separated by an equal sign. Given the inequality;

–4(x + 3) ≤ –2 – 2x

Expand

-4x - 12  ≤ -2 - 2x

Collect the like terms

-4x + 2x  ≤ -2 + 12

-2x  ≤  10

Divide both sides by -2

-2x/-2  ≤ 10/-2
x ≥ - 5

Hence the solution to the inequality expression is x ≥ - 5

learn more on inequality here: brainly.com/question/24372553

#SPJ1

3 0
2 years ago
Three boxes are stacked one on top of each other one box is 2 feet 11 inches tall one is 3 feet 5 inches tall and one is 4 feet
Natasha_Volkova [10]

Answer:

<u>11 feet 2 inches</u>

Step-by-step explanation:

ill add the inches first

11+5+10= 26

26inches= 2ft 2inches

now I add the feet

2+3+4+2=11 feet

<u>11 feet 2 inches</u>

7 0
2 years ago
What is the anwser to this equation? 36=15+7x
deff fn [24]

Answer:

x = 3

Step-by-step explanation:

  1. Subtract 15 from each side, so it now looks like this: 21 = 7x
  2. Divide each side by 7 to cancel out the 7 next to x. It should now look like this: 3 = x

I hope this helps!

7 0
3 years ago
Read 2 more answers
If joe has12 checkers and 5/6 of them are red how many are red
natta225 [31]

Given:

The number of checkers is 12.

The number of red is 5/6 times of 12.

Multiply 5/6 and 12 to find the number of red.

\text{The number of red =}\frac{5}{6}\times12

\text{The number of red =}5\times2

\text{The number of red =}10

Hence there are 10 red in checkers.

7 0
1 year ago
Read 2 more answers
Other questions:
  • A line l with slope −45 passes through the point (-10, 4). Is the point (-5, 8) on line l?
    13·1 answer
  • Complete the steps to find 3.18x10
    14·2 answers
  • Eleni withdrew $45.00 from her savings account. she then used her debit card to buy groceries for $30.15. what was the total amo
    15·2 answers
  • Amber spent 1,793.34 on a TV after an 18% discount and on an 8% tax. What was the original price of the TV?
    6·1 answer
  • I really need help please
    15·1 answer
  • What is 1/12 - 1/16 answer to
    10·1 answer
  • Pleaseeeee answerrrrrr
    8·1 answer
  • Mean of Frequency Tables
    11·1 answer
  • A taxi ride costs $4, plus an additional<br> $3 per mile.<br> What's the equation? (mx+b)
    12·1 answer
  • 3/5x2/3 thanks for the help
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!