Oct 16, 10:30:54 AM
A rocket is shot into the air. The function f (x) = -16x2 + 64x + 8 gives the
height of the rocket (in feet) as a function of the rockets horizontal distance from
where it was initially shot.
a. What was the initial height of the rocket when it was shot?
b. What is the maximum height the rocket reaches in the air?
a. The initial height of the rocket was
feet.
b. The maximum height the rocket reaches is
feet.

Answers

Answer 1

Answer:

A) 8 feet.

B) 72 feet

Step-by-step explanation:

We have the function [tex]f(x)=-16x^2+64x+8[/tex] which gives the height of the rocket (in feet) as a function of the rocket's horizontal distance.

Part A)

We want to find the initial height of the rocket when it was shot.

At the initial height, the rocket has not moved anywhere. So, the horizontal distance will be 0.

Therefore, to find the initial height, we will substitute 0 into our function. This yields:

[tex]f(0)=-16(0)^2+64(0)+8[/tex]

Evaluate:

[tex]f(0)=8[/tex]

Therefore, the initial height was 8 feet.

Part B)

Notice that our function is a quadratic.

Therefore, the maximum height will be given by the vertex of our quadratic.

To find the vertex, we use:

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

Let's label our coefficients. We have [tex]-16x^2+64x+8[/tex]

Therefore, a=-16, b=64, and c=8.

Substitute them into the vertex formula to find the x-coordinate:

[tex]x=-\frac{64}{2(-16)}\\\Rightarrow x=64/32=2[/tex]

Now, to find the maximum height, substitute 2 back into our function f(x):

[tex]f(2)=-16(2)^2+64(2)+8[/tex]

Evaluate:

[tex]f(2)=-16(4)+64(2)+8\\\Rightarrow f(2)=-64+128+8\\\Rightarrow f(2)=72\text{ feet}[/tex]

Therefore, the rocket reaches a maximum height of 72 feet.


Related Questions

whats 62.7×2.45......?

Answers

Answer:

153.615

Step-by-step explanation:

62.7 × 2.45=153.615

miles say that, when a is any integer greater than 0, the value of a^-3 is always less than -a^3 because the exponent in a^-3 is less than the exponent in -a^3. is miles reasoning correct?​

Answers

Yes, Miles is correct.

What is the product of-3 and-13? Enter your answer as a mixed number, in simplified fom, in the box​

Answers

Answer:

39

Step-by-step explanation:

-3x(-13) = 39.

If this question was asking for something different I apologize.

PLEASE ANSWER, I WILL MARK BRAINLYEST. IF YOU PUT AN ABSURD ANSWER I WILL REPORT. 50+ POINTS

Answers

Answer:

The umbrella will fit in, but there will be a lot of extra room.

Step-by-step explanation:

Remember the Pythagorean theorem:

x^(2) + y^(2) = n^(2)

where "x" and "y" are the legs of the right triangle and "n" is the hypotenuse

In this problem it is given that the sides (legs) are:

38in, and 24in

and diagonally across is 29in

so the hypotenuse is 29in

therefore we can form the equation:

38^(2) + 24^(2) = 29^(2)

without solving it is clear that

38^(2) + 24^(2) > 29^(2)

because 38 is a leg, but it is greater than 29, which means that 38 - 24 - 29 is not a Pythagorean triple,

but because 38 > 29, then the 29 in umbrella will fit into the suitcase, but it will not be a snug fit, there will be a lot of extra room

Answer:

see below

Step-by-step explanation:

The umbrella should fit

The umbrella is the diagonal in a right triangle so we can use the Pythagorean theorem

a^2+b^2 = c^2

18^2 + 24^2 = c^2

324 + 576 = c^2

900 = c^2

Take the square root of each side

sqrt(900) = sqrt(c^2)

30 =c

As long as the umbrella is less than 30 inches, it should fit

The umbrella is 29 inches so it should fit

Claire wants to determine how her math score 690 on a standardized college entrance exam compared to her mother score 680 what she took the exam 20 years earlier the year Clair took the exam the mean math score was 510 with a standard deviation of 110 points on Claires mother took the exam the mean math score was 490 with a standard deviation of 100 points who has the better relative performance

Answers

Answer:

Claires mother did better because her z score was greater than Claires

Step-by-step explanation:

I j took the quiz

Claire's mother did better because her z-score was greater than that of Claires.

What is Z -score?

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

As per the given information, the solution would be as

Here is Claire's data:

ц₁ = 510

σ₁ = 110

X₁ = 690

⇒ z-score = (X₁-ц₁ )/σ₁

Substitute the values,

⇒ z-score = (690 - 510)/110

⇒ z-score = 180/110

⇒ z-score = 1.636

Here is Claire's mother's data:

ц = 490

σ₂ = 100

X₂ = 680

⇒ z-score = (X₂-ц )/σ₂

Substitute the values,

⇒ z-score = (680 - 490)/100

⇒ z-score = 190/100

⇒ z-score = 1.9

So Claire's mother's z-score > Claire's z-score

Therefore, Claire's mother did better because her z-score was greater than that of Claires.

Learn more about the z-score here:

brainly.com/question/13793746

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I don't understand with this question, can you help me with this pls?

Answers

Answer:

By moving the decimal at the end of the number to the correct amount of places for x 10 you move it once to the right for x 100 you move it right twice.

Step-by-step explanation:

Pattie's Produce charges $2.29 for a package of strawberries. On average, Pattie's Produce sells 95 packages of strawberries daily. They estimate that for each 20-cent increase in the cost of a package of strawberries, 9 less packages will be sold each day. Let x represent the number of 20-cent increases in the cost of a package of strawberries. Which inequality represents the values of x that would allow Pattie's Produce to have a daily revenue of at least $255 from selling the packages of strawberries? A. B. -1.872 – 1.615 + 217.55 > 255 -1.812 + 21.61r + 217.55 > 255 -1.8r2 – 21.611 + 217.55 < 255 C. D. -1.812 + 1.61x + 217.55 < 255​

Answers

Answer:

A. -1.8x² – 1.61x + 217.55 > 255

Step-by-step explanation:

Since Pattie's Produce charges $2.29 for a package of strawberries and 95 packages can be produced daily. The money gotten daily = $2.29 × 95 packages = $217 Since 20 cent increase leads to 9 less package.

The number of 20-cent increases in the cost of a package of strawberries can be gotten from:

(2.29 + 0.2x)(95 - 9x) > 255

217.55 - 20.61x + 19x - 1.8x² > 255

-1.8x² - 1.61x + 217.55 > 255

Answer:

A. -1.8x² – 1.61x + 217.55 > 255

Step-by-step explanation:

EDMENTUM

10/3 = x/ (-5/2) what does x equal

Answers

The answer to the equation is [tex]x=-\frac{25}{3}[/tex]

First, you must cross multiply the fractions.

[tex]10*-\frac{5}{2} =x*3[/tex]

[tex]-25=3x[/tex]

Then, you must flip the equation.

[tex]3x=-25[/tex]

Finally, divide 3 on each side

[tex]\frac{3x}{3}=\frac{-25}{3}[/tex]

[tex]x=-\frac{25}{3}[/tex]

What is the perimeter of the building foundation uncovered by the archaeologists?

Answers

Answer:

Wall of Jericho

Step-by-step explanation:

The Wall of Jericho was a Pre-Pottery Neolithic A (PPNA) defensive or flood protection wall suggested to date to approximately 8000 BC.[1] If interpreted as an "urban fortification", the Wall of Jericho is the oldest city wall discovered by archaeologists anywhere in the world.[2] It is built of undressed stones and is located at the archaeological mound known as Tell es-Sultan, in the city of Jericho on the West Bank.

The topic of this article is the unique Neolithic-age stone wall, the earliest one of its kind. Other walls, such as contemporary house walls, or later, Bronze and Iron Age city walls, are only mentioned for the sake of context.

6. The store paid $2.50 for a book and sold it for $5.25. What is the profit as a percent?

Answers

7.75 I hope this helps

Which of these steps will eliminate a variable in this system? 4x-9y=8 2x+3y=24

Answers

For eliminate a variables we need addition method or elimination method.

Define the term Variable?

In an equation or formula, a variable is a symbol or letter that stands in for an unknowable or varying quantity or value.

We can multiply the second equation by -2, so that the coefficient of x in both equations will be the same but with opposite signs:

⇒ 4x - 9y = 8

⇒ -4x - 6y = -48

Add the two equations together: ⇒ -15y = -40

⇒ y = 8/3

Substitute this value of y back into either equation to solve for x.

⇒ 4x - 9(8/3) = 8

⇒ 4x - 24 = 8

⇒ x = 8

Therefore, the steps to eliminate a variable in this system using the addition method are to multiply the second equation by -2, add the two equations together to eliminate the x variable, solve for y, and then substitute that value back into either equation to solve for x.

To know more about elimination method, visit:

https://brainly.com/question/25427192

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Find x and y. Give reasons to justify your solution. AB, CD, EF, and GH are straight lines.

Answers

Answer:

X= 32 Y= 35

Step-by-step explanation:

We know FOB is parralel to AOE meaning x= 32

also, COH = 90 so GOD is also 90.

a straight angle is 180, so

23+90+x or 32= 145,

180-145=35,

y=35

Answer:

X=32

Y=35

Step-by-step explanation:

We know x is 32 because FOB is parrallel to AOE.

We also know that DOG is 90 because COH is 90, and parallel to DOG

So, we can do:

90 + 23 + 32 =145

180-145=35, which is Y

Question 6 of 10
What is the effect on the graph of f(x) = 1 when it is transformed to
g(x) = } - 7?
A. The graph of f(x) is shifted 7 units to the right.
B. The graph of f(x) is shifted 7 units down.
C. The graph of f(x) is shifted 7 units to the left.
O D. The graph of f(x) is shifted 7 units up.
SIR

Answers

Answer:

D I'm pretty sure

Step-by-step explanation:

Answer:

Its B. i just did this question.

Step-by-step explanation:

A normal population has mean =μ7 and standard deviation =σ5. (a) What proportion of the population is less than 18?

Answers

Answer:

P(x< 18) = 0.986

Step-by-step explanation:

Step 1: find the z-score using the formula, z = (x - µ)/σ

Where,

x = randomly chosen values = 18

µ = mean = 7

σ = standard deviation = 5

Proportion of the population that is less than 18 = P(x < 18)

Plug in the values into z = (x - µ)/σ, to get z-score.

z = (18 - 7)/5

z = 11/5 = 2.2

Step 2: Find P(x< 18) = P (z<2.2) using z-table.

The probability that corresponds with z-score calculated is 0.986.

Therefore,

P(x< 18) = 0.986

HELP EASY ASAP MULTIPLE CHOICE

Answers

Answer:

It's the first one 18/3 =6

Step-by-step explanation:

This is the only answer that has all integers or whole numbers. Hope this helps!

Answer:

Its the fisrt one cause its the only one with a whole number.

Step-by-step explanation:

I need help !!!!!!!

Answers

Solution (5) :

Given , KM = 22

Then JL =

This trapezoid is an isosceles trapezoid which means its diagonals will be equal . So ,

KM = JL ( the diagonals in an isosceles trapezoid are congruent )

22 = JL

JL = 22

Therefore , JL = 22 .

Solution (6) :

Given , DF = 8.7

Then , EG =

Since this trapezoid is an isosceles trapezoid , its diagonals will be equal . So ,

DF = EG ( the diagonals in an isosceles trapezoid are congruent )

8.7 = EG

EG = 8.7

Therefore , EG = 8.7 .

Sofia is creating a budget to save $120 for a week of soccer camp. She earns money by working as a mother's helper on Saturday mornings and Wednesday afternoons. She earns $20 each time she works. She wants to save $7.50 a week for the camp. Her mother wants her to save $5 a week for college. She is planning on spending $5 a week for snacks and $5 a week for entertainment.

Answers

Answer:

18 weeks

Step-by-step explanation:im gay

Please help me with all the answers please say like 1: the answer 2: the answer like that thank you so much

Answers

1: 8200,82000,820000 yen
2:12
3:8
4:6
5:4 months

65% of what is 39? ​

Answers

Answer:

The answer is 25.35

Step-by-step explanation:

Hope this helps:)

Answer:

60

Step-by-step explanation:

65 % of 60 = 39

Write an equation in point-slope form for the line that is parallel to y = 3/4x -
3 and passes through point (4,3).

Answers

Answer:

The point-slope form of the equation of the parallel line is y - 3 =  [tex]\frac{3}{4}[/tex] (x - 4)

Step-by-step explanation:

Parallel lines have the same slopes and different y-intercepts

The slope-intercept form of the linear equation is y = m x + b, where

m is the slopeb is the y-intercept

The point-slope form is of the linear equation is y - y1 = m(x - x1), where

m is the slope(x1, y1) are the coordinates of a point lies on the line

∵ The equation of the given line is y = [tex]\frac{3}{4}[/tex] x - 3

→ Compare it with the first form of the equation above

∴ m =  [tex]\frac{3}{4}[/tex]

∴ The slope of it is  [tex]\frac{3}{4}[/tex]

∵ Parallel lines have the same slopes

∴ The slope of the parallel line is  [tex]\frac{3}{4}[/tex]

∵ The point-slope form is y - y1 = m(x - x1)

→ Substitute the value of the slope in the form of the equation above

∴ y - y1 =  [tex]\frac{3}{4}[/tex] (x - x1)

∵ The line passes through the point (4, 3)

∴ x1 = 4 and y1 = 3

→ Substitute them in the equation above

∴ y - 3 =  [tex]\frac{3}{4}[/tex] (x - 4)

The point-slope form of the equation of the parallel line is

    y - 3 =  [tex]\frac{3}{4}[/tex] (x - 4)

The population of China is approximately 1.381x10^9, and the population of the US is approximately 3.23x10^8. About how many people live in both countries combined? Answer in scientific notation

Answers

Answer:

1.704 x 10⁹ people

Step-by-step explanation:

    Population of China = 1.381 x 10⁹

    Population of US = 3.23 x 10⁸

Problem:

Number of people in both countries combined = ?

Solution

   To solve this problem, simply add them together;

Let us make the exponents the same for easy addition;

      Population of China = 1.381 x 10⁹ = 13.81 x 10⁸

      Poplation of US =  3.23 x 10⁸

Adding both:

                   (13.81 x 10⁸)  + (3.23 x 10⁸)

             ⇒ (13.81 + 3.23) x 10⁸

             ⇒ 17.04 x 10⁸

             ⇒ 1.704 x 10⁹

   

diride 660cm in the ratio of 5:6​

Answers

Answer:

Thus, the measure 660 cm is divided into 300 + 360 in the ratio of 5:6

Step-by-step explanation:

Equations

We are required to divide 660 cm in the ratio 5:6, or 5/6.

Let's call:

x = first part of 660

660 - x = second part of 660

The ratio between them is 5/6.

[tex]\displaystyle \frac{x}{660-x}=\frac{5}{6}[/tex]

The above equation will result in x as the smaller part of 660.

Multiply by (660-x)*6 to eliminate denominators:

[tex]\displaystyle (660-x)*6\cdot\frac{x}{660-x}=(660-x)*6\cdot\frac{5}{6}[/tex]

Operating:

[tex]6x=(660-x)*5[/tex]

[tex]6x=3300-5x[/tex]

Simplifying:

[tex]6x+5x=3300[/tex]

[tex]11x=3300[/tex]

Solving:

[tex]\displaystyle x=\frac{3300}{11}=300[/tex]

The other part is 660 - 300 = 360

Thus, the measure 660 cm is divided into 300 + 360 in the ratio of 5:6

Tell whether the sum is positive, negative, or zero without adding them.
-8 + 20

Answers

Answer:

The sum is positive.

Step-by-step explanation:

The 20 is a far greater value than -8, so no matter what, when you add them the sum will be positive. Though this would not be the same were the -8 greater than -20.

Hope this helps!

With the money she had saved by working, Jennifer wanted ​

Answers

Answer:a car

Step-by-step explanation:

Cliff needs 6 meters of wood for a building project. He already has 3
meters of wood.
Approximately how many feet of wood does Cliff need? (One meter
is approximately 3.3 feet.)
1 foot
3 feet
6 feet
10 feet

Answers

letter B 3 feet

Step-by-step explanation:

he needs three more to get 6 meters of wood

10, because he needs 3 more meters and 3 meters = 9.9 feet

Assuming part a is correct, how do you do b and c?

Answers

Step-by-step explanation:

B. Yes, we are 99% confident that the population mean is within the interval.

C. Yes, 225 is below the interval minimum, so it is reasonable to conclude the average cholesterol level is greater than 225 mg/dl.

D. No.  Increasing the sample size would decrease the margin of error, so the ends of the interval would move closer to the sample mean of 251.9.  So the interval minimum would still be higher than 225.

16/25 divided by 15/8​

Answers

Answer:

128/375

Step-by-step explanation:

16/25 divided by 15/8​

16/25 X 8/15 = 128/375

A study conducted in year 2002 found that the mean number of children under 18 per household in a certain community was 1.7. A statistician is trying to determine whether this number has changed in the last 6 years. She declares the null and alternative hypotheses to be: Null: The mean number of children per household in 2002 is equal to 1.7; Alternative: The mean number of children per household in 2002 is not equal to 1.7. Which of the following statements is true about this test?

a. This is a step-tailed test.
b. This is a left-tailed test.
c. This is a two-tailed test.
d. This is a right-tailed test.

Answers

Answer:

c. This is a two-tailed test.

Step-by-step explanation:

When the rejection region is divided between the two tails of the sampling distribution of the test statistic the test is referred to as two tailed or two sided test. In this case the alternative is set up as

Ha : u≠ 1.7

meaning that values both larger and smaller than u are to be included.

When the alternative hypothesis has the "not equal to sign"  it gives the two tailed test.

2) If U is between T and B, find the value of x and the lengths of the segments Label the line show all work
to answer the questions. (4 points)
T
U
B
TU = 2x, UB = 3x, TB = 20
X =
I
TU=
UB=

Number 2

Answers

You want to use the segment addition postulate to help you solve this. That would be TU+UB=TB.

TU = 2x
UB = 3x
TB = 20

2x+3x=20

Solve that equation, you should get:

5x=20

Then divide by 5 on each side to get x.

x = 4

Then you want to plug x into each equation!

TU = 2x, so 2 • 4 = 8.

TU = 8

UB = 3x, so 3 • 4 is 12.

UB = 12


A line with slope -3 passes through the points (5,2) and (9,y). Find y. (and yes I know this is a repost but the other one was wrong its not y=5)

Answers

9514 1404 393

Answer:

  y = -10

Step-by-step explanation:

Using the point-slope form of the equation for a line, we can write the equation as ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y -2 = -3(x -5)

Using the values for the other point, this becomes ...

  y -2 = -3(9 -5)

  y = -3(4) +2

  y = -10

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