A model rocket is launched from the ground with an initial velocity of 40 feet per second. The height of an object h, in feet, after t seconds, with initial velocity v0v0 and initial height h0h0 is given by h(t)=−16t2+v0t+h0h(t)=−16t2+v0t+h0 .

What is the approximate maximum height the rocket reaches?

Enter your answer in the box.

ft

Answers

Answer 1

The rocket reaches a maximum height of 25 feet.

We substitute the velocity given into the equation:
h(t) = -16t² + 40t + h₀

We also use 0 for h₀, as the rocket is launched from the ground:
h(t) = -16t² + 40t + 0

To find the maximum, we find the coordinates of the vertex. To do this, we first find the axis of symmetry:

-b/2a = -40/(2*-16) = -40/-32 = 1.25

This is the x-coordinate of the vertex, which represents the amount of time in seconds. We substitute this back into our function:
h(1.25) = -16(1.25²) + 40(1.25) = 25

Answer 2

The approximate maximum height that the rocket reaches is 25 feet.

What is a function?

Function is a type of relation, or rule, that maps one input to specific single output. Given two function f(x) and g(x) can be written as f(X) + g(X). It is the sum of two functions similar to the addition of any two polynomial functions

+ x -7.

We are given that;

Initial velocity of the rocket= 40 feet per second.

The height of the rocket after t seconds is given by the formula:

h(t) = -16t^2 + v0t + h0

where v0 is the initial velocity (in feet per second) and h0 is the initial height (in feet).

Since the rocket is launched from the ground, its initial height is h0 = 0. Substituting this and v0 = 40 into the formula, we get:

h(t) = -16t^2 + 40t

To find the approximate maximum height that the rocket reaches, we need to find the vertex of the parabolic function h(t) = -16t^2 + 40t. The vertex occurs at the value of t that maximizes the height, which is given by:

t = -b/2a

where a = -16 and b = 40 are the coefficients of the quadratic function. Substituting these values into the formula, we get:

t = -40/(2*(-16)) = 1.25

Therefore, the rocket reaches its maximum height after approximately 1.25 seconds. To find the maximum height, we can substitute this value of t into the formula for h(t):

h(1.25) = -16(1.25)^2 + 40(1.25) ≈ 25 feet

Therefore, by the given function answer will be 25 feet.

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Related Questions

The diagram shows the dimensions of the pool cover for a gotel pool.The numbers are 10ft 20ft 45 ft 8 ft 8 ft 8ft What is the area of the pool cover

Answers

Answer:

684

Step-by-step explanation:

see photo for step by step explanation.

The area of the pool is the amount of space on it.

The area of the pool is 684 square feet

The dimensions of the pool are:

10ft by 20ft, 8ft by 20ft and 27ft by 12ft

The area of the pool is then calculated as:

A = 10 * 20 + 8 * 20 + 27 * 12

Evaluate the products

A = 200 + 160 + 324

Evaluate the sums

A = 684

Hence, the area of the pool is 684 square feet

Answers

The answer to this is going to be 36. Hope this helps.

Answer

The Answer to your question in 6

Step-by-step explanation:

The formula to find the area is

r^2 * pi = area

we know that the area is 113.04 and pi = 3.14

x^2 * 3.14 = 113.04

divide both sides by 3.14

x^2 = 36

now for the final step we need to find the root of both sides

√x^2 = √36

x = 6

so the radius is 6.

The probability of reaching into a drawer without looking and selecting a black sock is 5/6. If there are a total of 24 socks in the drawer, how many socks in the draw are black? Please help me :c

Answers

Final answer:

The probability of selecting a black sock is 5/6 and there are 24 socks in total. By setting up and solving a simple equation, we find that there are 20 black socks in the drawer.

Explanation:

This question is about the concept of probability in mathematics. The probability of an event occurring is calculated by the number of desired outcomes divided by the total number of possible outcomes. In this case, we are given that the probability of reaching into a drawer without looking and magically pulling out a black sock is 5/6. With a total of 24 socks in the drawer, to figure out how many socks are black, we can set up a simple equation where x represents the number of black socks. Thus, x/24 = 5/6. Solving this equation, we get x = (5/6) * 24, which simplifies to x = 20. So, there are 20 black socks in the drawer. That's indeed a lot of black socks!

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a geometric sequence has an initial value of 25 and a common ratio of 1.8. Write a function to represent this sequence . Find.the 23rd term.

Answers

Use the formula

a_n = a_1•r^(n-1)

a_23 = 25•(1.8)^(23 - 1)

Can you finish?

23rd term of the given geometrical sequence is [tex]a_{23} = 25(1.8)^{22}[/tex].

Function to represent sequence is [tex]25,25(1.8), 25(1.8)^{2} , 25 (1.8)^{3} , ....... ,25(1.8)^{n}[/tex]

What is geometric sequence?

" Geometric sequence is defined as the sequence whose ratio of the consecutive terms is always constant."

Formula used

nth term of the geometric sequence

[tex]a_{n} = a r^{n-1}[/tex]

a = first term

r = common ratio

[tex]a_{n}[/tex] = nth term

According to the question,

First term of the geometric sequence 'a' = 25

Common ratio of the geometric sequence 'r' = 1.8

Substitute the value in the formula to get 23rd term,

[tex]a_{23} = 25(1.8)^{23-1}[/tex]

⇒[tex]a_{23} = 25(1.8)^{22}[/tex]

Function to represent this sequence

[tex]a, a(r),a(r)^{2} , a (r)^{3} , ....... ,a(r)^{n}[/tex]

= [tex]25,25(1.8), 25(1.8)^{2} , 25 (1.8)^{3} , ....... ,25(1.8)^{n}[/tex]

Hence, 23rd term of the given geometrical sequence is [tex]a_{23} = 25(1.8)^{22}[/tex].

Function to represent sequence is [tex]25,25(1.8), 25(1.8)^{2} , 25 (1.8)^{3} , ....... ,25(1.8)^{n}[/tex]

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Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p dollars, the revenue R in dollars is
R(p)= -4p^2+4000p

What unit price should be established for the dryer to maximize revenue?

What is the maximum revenue?

Answers

Answer: The maximum revenue is $1,000,000.

The function that is given is a quadratic equation and the graph would be an upside down parabola.

Therefore, the maximum revenue would be at the vertex of the parabola.

To find the vertex, we can use the expression -b/2a to find the x-value.

It would be -4000/2(-4) = 500

Now, input 500 for p and you will get a revenue of 1,000,000.

Answer:

p=$500 is the unit price to get maximum revenue

Maximum revenue = $1,000,000

Step-by-step explanation:

the revenue R in dollars is:

[tex]R(p)= -4p^2+4000p[/tex]

To find out the unit price to get maximum revenue we find out the vertex

In the given quadratic equation a=-4 and b= 4000

Formula to find out the x coordinate of vertex is

[tex]x=\frac{-b}{2a}[/tex], plug in the values

[tex]x=\frac{-4000}{2(-4)}[/tex]

x=500

So p=$500 is the unit price to get maximum revenue

Now we find the maximum revenue . Plug in 500 for p in the given equation

[tex]R(p)= -4p^2+4000p[/tex]

[tex]R(500)= -4(500)^2+4000(500)[/tex]

R(500)=1000000

Maximum revenue = $1,000,000

PLEASE HELP NOWWWWWWWWWWW
A quadrilateral is graphed on the coordinate plane. One of its vertices is translated 5 units to the right. Which of the following options best represents the translation?
x + 5
x - 5
y + 5
y - 5

Answers

y-5 hope this helps

Answer:

The correct answer is: A

Step-by-step explanation:

x+5

I hope this helps!

Plz mark Brainliest I am trying to rank up!

Have a nice day!

Write the ordered pairs that represent the location of Sam and the theater

Answers

Final answer:

The question seems to require using ordered pairs to locate Sam and the theater, but lacks the specific coordinates or context needed for a precise answer. Ordered pairs are essential in geometry for representing positions.

Explanation:

The question seems to pertain to locating positions or objects using ordered pairs, which falls under the domain of algebra and geometry in mathematics. An ordered pair (x, y) is used to define the positions on a plane, with 'x' representing the horizontal component and 'y' representing the vertical component.

Unfortunately, the question lacks specific information about the coordinates of Sam and the theater, making it impossible to provide exact ordered pairs without additional context. In scenarios involving maps or spatial planning such as finding locations in a city or arranging objects with a spatial relation to each other, ordered pairs serve as a crucial means of representation.

Exercises involving ordered pairs deepen understanding of coordinate systems, which are fundamental in geometry and crucial for various applications in science and engineering.

Maria says her pencil is 1.7 meters long is this measurement reasonable

Answers

no 1.7 meters is roughly 5 feet 8 inches

Qual é o perímetro de um quadrado de 3,8 cm de lado ?E sua área?

Answers

I don't know what language your speaking, but I do know it's a Latin language. So I understand a bit since I speak Spanish (another Latin language)

Para encontrar el perímetro tienes que anadir 3.8, 4 veces o mulltiplicar por 4
3.8 + 3.8 + 3.8 + 3.8 = 15.2
3.8 x 4 = 15.2
15.2 es tu respuesta

Para encontrar el area multiplica 3.8 por 3.8
3.8 x 3.8 = 14.44
14.44 es tu area

Solve the equation and show all work please show steps!!
m/9 - 17=21

Answers

Okay. The question is m/9 - 17 = 21. First off, we will add 17 to both sides. -17 + 17 cancels out. 21 + 17 is 38. That leaves m/9 = 38. Multiply each side by 9 to isolate the m, because m is the numerator and 9 is the denominator. m/9 * 9/1 cancels out. 38 * 9 is 342. Let's check this. 342/9 is 38. 38 - 17 is 21. 21 = 21. There. x = 342.

m/9 - 17=21
------------
Simplify
1/9m - 17 = 21
----------------
Add 17 to each side
1/9m-17+17=21+17
1/9m = 38
------------------------
Multiply each side by 9
9 * (1/9m) = 38 * 9
m = 342 is your answer

1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown:

(a) Suppose a car is traveling east on 4th Street and turns onto King Avenue heading northeast. What is the measure of the angle created by the car's turning? Explain your answer.
(b) Suppose a car is traveling southwest on King Avenue and turns left onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.
(c) Suppose a car is traveling northeast on King Avenue and turns right onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.

Answers

Q1)
As shown in the diagram attached, the angle made between 4th street and king avenue if car is traveling from the west side is 75°.
when the car is travelling from the east side and is supposed to take a turn towards north east lets call the angle it makes with the turn as x.
4th street is a straight road, therefore straight line
and sum of angles of a straight line is 180°.x and 75 are supplementary angles.
Therefore x + 75° = 180°
x = 105°
therefore the angle it makes in the turn is 105°

Q2)
When the car is travelling south west and turns left towards 3rd street, the angle it makes is termed as y. when 2 parallel lines are cut by a transversal, x° and y° are corresponding angles.
This means that the angle at which transversal cuts 3rd street and 4th street to the left are both equal. these are called corresponding angles.
this means that x = y
as derived in the previous question, x = 105°,
hence, y = 105°.

Q3)
When the car is travelling north east and turns right onto 3rd street, lets name the angle it makes with the turn as z.
angles y and z are called vertically opposite angles. When 2 straight lines cut each other, the opposite angles formed are equal to each other.
Therefore y = z.
as derived in the previous question y = 105°.
since y = z
hence, z = 105°

Answer:

the guy is right except number 2

Step-by-step explanation:

if the car turns left that means it went west and since 4th and 3rd street are parallel and King Ave. is a transparent then street 4 and 3 have the same angles. y is 75 and a vertical that means the car makes a 75 degrees angles .

sorry for the bad explanation

Work the answer out n I’ll give xtra points

Answers

126/3 = 42 . . . . . matches selection B

_____
The sheet of 100 is 9+1 = 3 groups of 3 sticks with 1 left over.
The 2 sticks with the one left over are 3 groups of 1.
The 6 singles are 3 groups of 2.

Altogether, you have 3 groups of (3 sticks +1 stick +2 singles).

Solve the following equation: x^3+3x^2-10x=0

Answers

x³ + 3x² - 10x = 0
The GCM of those three terms is x. So group them by x.

x(x² + 3x - 10) = 0
factor x² + 3x - 10
x(x - 2)(x + 5) = 0

x = 0 , x = 2 , x = -5

The table shows the results of rolling a number cube, with sides labeled 1 through 6, several times. What is the experimental probability of rolling a 1 or a 5? Enter your answer as a fraction in simplest form, in the box.

Answers

i'm pretty sure that the answer is 1/6.

It's got to be 1/6. A number cube, or any cube at that has 6 sides

A square has side lengths of 7 inches. Find the length of the square’s diagonal.

Answers

Since the side lengths of the square is seven inches, the legs of the triangle to find the diagonal will be 7 inches as well. Since we have the two legs to find the hypotenuse which is equal to the square’s diagonal, we can find the diagonal by squaring the two legs and adding them together, then finding the square root of the answer.
7•7=49
7•7=49
49+49= 98
Now let’s find the square root of 98. I usually go to the hundredths place since I know 98 doesn’t have a perfect square.
9.9•9.9= 98.01 (the hundredths place rounded to that)
So the length of the square’s diagonal is about 9.9 inches.

Final answer:

The length of the square's diagonal with side lengths of 7 inches is found using the Pythagorean theorem, leading to a diagonal of approximately 9.899 inches.

Explanation:

To find the length of the square's diagonal when the side lengths are 7 inches, we can use the Pythagorean theorem. The diagonal of a square creates two right triangles, with the diagonal being the hypotenuse. You can think of this as half of the square divided along the diagonal. Each of these triangles has two legs that are each equal to the side of the square and a hypotenuse which is the diagonal we want to find.

The formula for the Pythagorean theorem is a² + b² = c², where a and b are the legs of the right triangle, and c is the hypotenuse. Since the legs are both 7 inches (the side length of the square), we have:

7² + 7² = c²
49 + 49 = c²
98 = c²

This simplifies to:

c = √98
c ≈ 9.899 inches (rounded to three decimal places)

Therefore, the diagonal of the square is approximately 9.899 inches long.

10 POINTS AND BRAINLIEST
Which set of numbers is finite?

Even numbers between 1 and 89

Real numbers greater than 1

Rational numbers between 1 and 2

Whole numbers with tens digits at zero

Answers

Rational numbers between 1 and 2 because the rest go on and on

All of them go on and on except for the first one (Even numbers between 1 and 89) because even numbers are whole numbers and there is a limit to them in between 1 and 89.

Answer: #1

The area of the square is 81 square centimeters. Which of the following is closest to the circumference , in centimeters, of the circle inscribed in the square?
A. 14.13
B. 28.26
C. 63.59
D. 127.17

Answers

Answer: 28.26

Step-by-step explanation: I think it's 28.26, I tried

Answer:

Step-by-step explanation:

Which statement is true?
All rectangles are parallelograms.
All rectangles are squares.
Some triangles are quadrilaterals.
Every rhombus is a square.

Answers

Answer:

Step-by-step explanation:

All rectangles are parallelograms and all their sides are parallel.

A tree 63 ft high casts a 38 ft shadow. How tall is a tree that casts a 52 ft shadow at the same time of the day? (to the nearest tenth

Answers

52/38 = 1.368

1.368 x 63 = 86.21

tree is 86.2 feet high

Convert fraction with numerator 7 and denominator 8 to a decimal.

0.375

0.875

0.925

0.965

Answers

[tex] \frac{7}{8}=7:8=\bold{0.875} [/tex]

Answer:

Step-by-step explanation:

Community center has an L shaped swimming pool that is 10 feet deep. What is the volume of the pool

1200

1040

640

880

Answers

Answer:

B. 1,040 cubic feet

Step-by-step explanation:

I just took a test with this question and this was the right answer

~Please mark me as brainliest : )

Answer:

I hope this helps

Step-by-step explanation:

a2-20-3b= quick answer please using pemdas

Answers

Pretty sure the answer is -ab-20

Which line segment is a radius of circle F?

ED¯¯¯¯¯

AC¯¯¯¯¯

DC¯¯¯¯¯

FE¯¯¯¯¯

Answers

The answer would be FE...

Write to explain how to do bd an equivalent fracrion for the fraction 3/9

Answers

To make an equivalent fraction, we multiple or divide both the numerator and the denominator by the same factor.

[tex] \dfrac{3}{9} = \dfrac{3 \div 3}{9 \div 3} = \dfrac{1}{3} [/tex]

[tex]\text {Answer = } \dfrac{1}{3} [/tex]

Answer:

1/3

Step-by-step explanation:

How many triangles exist with the given angle measures? 32 degrees, 51 degrees, 97 degrees

A. Exactly one unique triangle exists with the given angle measures.
B. More than one unique triangle exists with the given angle measures.
C. No triangle exists with the given angle measures.
D. A triangle can be drawn with more than one acute angle.

Answers

Answer: The correct answer is B.

The first thing to check is the sum of the angles. 32 + 51 + 97 = 180. Therefore, the sides equal 180 and we can have a triangle because all triangles have exactly 180 degrees.

Second, the number of triangles with these measures is endless. Imagine taking the initial triangle and doubling the size. The angles don't change but the triangle does. We could keep doubling the size forever.

Answer:

Step-by-step explanation:

Michael surveyed 40 of his friends to determine their favorite season. His data shows that 70% said summer, 10% said winter, 5% said fall, and the rest said spring. What circle graph best represents Michael's data?

Answers

The answer is D.) because 70% was summer which, of course, would be the biggest piece of the pie and would be more than Half of it.

Answer:

Correct answer is D the last on in the pic

For a single roll of two dice, are rolling a sum of 6 and rolling doubles mutually exclusive events?

Answers

Answer: They are not mutually exclusive events.

Step-by-step explanation:

Let A be the event of getting a sum of 6 on dice.

Let B be the events of getting doubles .

A={ (1,5), (2,4), (3,3), (4,2), (5,1) }

B = { (1,1) , (2,2), (3,3), (4,4), (5,5), (6,6) }

Since we know that Mutaullty exclusive events are those when there is no common event between two events.

i.e. there is empty set of intersection.

But we can see that there is one element which is common i.e. (3,3).

So, n(A∩B) = 1 ≠ ∅

Hence, they are not mutually exclusive events.

Answer:

They are not mutually exclusive events.

Step-by-step explanation:

help ASAP, please
Four more than three times a number, is less than 30. Which of the following is not a solution?

A.6
B.12
c.8
D.7

Answers

i think it is 6 i hope i help please dont report bec i am sorry if ii get it wrong

Answer:

THE ANSWER IS B OR 12

Step-by-step explanation:

what is the volume of this container?

Answers

V = 3*3*4 - 1*3*2 = 36 - 6 = 30 ft³

look at the pictureeeeee

Answers

1.8k - 5 + 3.5 + 6.1k + k + 1.5

add 1.8k , 6.1k , and k
8.9k

add -5 + 3.5 + 1.5
0

so the answer would be 8.9k

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For a school group, a skating rink charges a flat fee of $50 for skates for the students to use the skating rink.For 40 Students the skating rink charges 180.For 75 students, the skating rink charges 293.75Which question represents the amount the skating rink charges for x students?A)y=3.25x+35B)y=3.25x+ 50C)y=4.50x+ 35D) y=4.50x+ 50 Triangle ABC was dilated and translated to form similar triangle A'B'C'. What is the scale factor of the dilation?A. 1/5B. 2/5C. 5/2D. 5/1 If a parabola has its vertex at (4, -2). One of its zeros is 1. What is the other zero? Jake needs to put gas in the delivery van. Regular gasoline is $3.20 per gallon. He only had a $ 20 bill on him. How many gallons can he buy What is the greatest value of the data represented by the box plot?Enter your answer in the box. PLZZZZ HELP ME!!!! U WILL GET 30 POINTS!!!!After a juvenile has been taken into custody, which of these is the next step in the judicial process that must be taken? A. adjudicatory hearing B. probable cause hearing C. a verdict must be rendered D. he/she must be released to the parent/guardian find the approximate surface area of a bowling ball with a raius of 5 inches A scientist is testing the effectiveness of Drug X on cancer. She gives a small amount of the drug to mice that have cancer. She gives each mouse a different amount from 1 to 10 grams, and then measures the size of the tumor in each mouse before the drugs and two weeks after the drugs. She gives one of the mice sugar instead of Drug X. What is her control in this experiment? Natasha wants to treat her friends to the movies. The tickets cost $11 each and she also wants to spend $21 worth of popcorn and candy for her friends to share. She can spend under $131. Write an inequality to represent how many people she can treat to the movies Convert -1.2 repeating as a mixed number Can you please answer this? If a pilot is converting standard time to UTC time and is given the time 1730 UTC, what would EST be? How could you beat restate this question to encourage yourself to ask questions rather than simply collect information Help please been stuck on this for a week. What two nations gained land that had been part of germany? Which function has a domain of all real numbers except x=/2 n? A.y=secx B.y=cosx C.y=1/sinx D.y=cotx, Which of the following best describes the music of the Rococo period? A.Heavily contrapuntal lines B.Lush, flowing melodies C.Light and graceful tunes D.Dramatic statements A scientist studied four pieces of fossil evidence that show the evolution of the modern-day man. These date back to 2 million years, 1 million years, 0.5 million years, and 0.25 million years ago. Which fossil is the least similar to the modern-day man? 7. Why is it difficult to create accurate maps of Earth? (1 point) It is impossible to accurately depict the actual size of objects on Earth's surface. There is an inherent difficulty in depicting any three-dimensional object in a two-dimensional format. Maps always exaggerate the relative size and importance of European countries. The surface of Earth is constantly changing.8. In what way is geography an integrative science? (1 point) Geography is an integrative science because it examines Earth in both physical and human terms. Geography is, Why does Friar Lawrence agree to marry Romeo and Juliet? He thinks it will bring the two fighting families together. He has always had a soft spot for young love. He wants to help Romeo get over Rosaline. He is tricked by Romeo; he doesn't know the marriage is a secret.