Hurry. A catapult launches a pumpkin with an upward velocity of 150 ft./s.
The height of the pumpkin, h, in feet after t seconds is given by the
function h = -16t2 + 150t + 20. How long does it take the
pumpkin to reach its maximum height? What is the pumpkin's
maximum height? Round to the nearest hundredth, if necessary.

Answers

Answer 1

Answer:

Time taken to reach maximum height=4.69 seconds

Maximum Height=371.56feet

Step-by-step explanation:

Given the height function of the pumpkin:

[Tex]h = -16t^2 + 150t + 20[/tex]

The pumpkin reaches it's maximum height at its axis of symmetry.

Therefore, we determine its equation of symmetry.

The equation of symmetry:

[Tex]t=-\frac{b}{2a}[/tex]

a=-16, b=150.

Therefore:

[Tex]t=-\frac{150}{2*-16}=4.6875[/tex]

The pumpkin reaches maximum height after 4.6875 seconds.

At t=4.6875

[Tex]h = -16(4.6875)^2 + 150(4.6875)+ 20\\=371.5625\approx 371.56 \:feet[/tex]

The pumpkin's maximum height is 371.56 feet.


Related Questions

Making late payments helps maintain a positive credit history(True or false?

Answers

Answer:

no

Step-by-step explanation:

Answer: false

Step-by-step explanation:

Use elimination to solve the system of equation
4x+y=-2
3x+2y=6







Answers

Answer: x= -2,y=6

Step-by-step explanation:

4x+y= -2......equation 1

3x+2y=6.....equ2

Y= -2-4x........equation 3

Substitute equation 3 into 2

3x+2(-2-4x)=6

Open the bracket

3x+(-4-8x)=6

3x-4-8x=6

3x-8x=6+4

-5x=10

X= 10/-5

X= -2

Substitute for x in equation 1

4x+y= -2

4(-2)+y= -2

-8+y= -2

Y= -2+8

Y=6

Therefore, x= -2 & y=6

A scientist needs 120 ML of a 20% acid solution for an experiment. The lab has available at 10% solution and a 25% solution. How many milliliters of the 10% solution and how many milliliters of a 25% solution should the scientist mix to make the 20% solution?

Answers

Answer:

40 milliliters of the 10% solution and 80 milliliters of the 25% solution the scientist should mix to make the 20% solution.

Step-by-step explanation:

Given:

A scientist needs 120 ML of a 20% acid solution for an experiment. The lab has available at 10% solution and a 25% solution.

Now, to find the milliliters of 10% solution and 25% solution to make 20% solution:

Let the 10% solution be [tex]x.[/tex]

And let the 25% solution be [tex]y.[/tex]

So, total milliliters of solution are:

[tex]x+y=120\\\\x=120-y\ \ \ \ .....(1)[/tex]

Now, to get the milliliters of 10% solution and 25% solution to make 20% solution we solve the equation:

[tex]10\%\ of\ x+25\%\ of\ y=20\%\ of\ 120\\\\\frac{10}{100} \times x+\frac{25}{100} \times y=\frac{20}{100} \times 120\\\\0.10x+0.25y=24[/tex]

Substituting the value of [tex]x[/tex] from equation (1) we get:

[tex]0.10(120-y)+0.25y=24\\\\12-0.10y+0.25y=24\\\\12+0.15y=24[/tex]

Subtracting both sides by 12 we get:

[tex]0.15y=12[/tex]

Dividing both sides by 0.15 we get:

[tex]y=80.[/tex]

Thus, the 25% solution is 80 ml.

Now, substituting the value of [tex]y[/tex] in equation (1) we get:

[tex]x=120-y\\\\x=120-80\\\\x=40\ ml.[/tex]

Hence, the 10% solution is 40 ml.

Therefore, 40 milliliters of the 10% solution and 80 milliliters of the 25% solution the scientist should mix to make the 20% solution.

will give brainiest if answered first plz helppp!!!!

Answers

Answer:

The answer is b

Step-by-step explanation:

The answer is B.

Since I cant post it until I have 20 letters, lets start a conversation.

Hello. How is your day/night going so far?

Whats the midpoint of (3,-8) and (5,-2.5)

Answers

(4, -5.25) ................

Find the area of the shape shown below, 7.5, 2.5, 2.5

Answers

A= 12.5 this is correct for the equation
The answer is 12.5 yw gl

Question 1(Multiple Choice Worth 3 points)
(08.05)Theresa earned scores of 88 points, 84 points, 88 points, and 91 points on four tests. What is the lowest score she can get on the fifth test and still finish with an average score of 90 points?

96 points
97 points
98 points
99 points

Answers

Answer: D) 99 Points

Step-by-step explanation: Theresa earned scores of 88 points, 84 points, 88 points, and 91 points on four tests

Therefore the totals points are 351

351 is her total score for 4 tests, if she gets an average score of 90 on her fifth test then all we have to do is:

5 x 90 = 450 (The 5 being her fifth test)

450-351 = 99

Option D

What is the sum of the first 20 terms of a finite geometric series where a1 =3 and r = 3/2

Answers

Answer: The answer should be 6

Step-by-step explanation:

I have $45. I want to go to the store and buy some cheez-its. They are $2.75 a box. How many boxes can I get? Do I have any money left over? How much?

Answers

Answer:

You can by 16 boxes of cheez-its. You have 1 dollar left over.

Step-by-step explanation:

Divide 45 by 2.75 and you get 16.36, then multiply 2.75 by 16 to get 44.

So, you can pay 44 dollars for 16 boxes of cheez-its.

Hope this helps!!

Please mark Brainliest!

Answer:

16 boxes with 1 dollar leftover

Step-by-step explanation:

45 / 2.75 = 16.3636...

An item is regularly priced at $85. It is now priced at a discount of 60% off the regular price. What is the price now?

Answers

Answer:

34$

Step-by-step explanation:

plz make brainliest

Can someone help with this? My daughter needs help with these.

Answers

Answer:

the missing side length for the shape with a perimeter of 43 m. is  12

Step-by-step explanation:

the missing side length for the shape with a perimeter of  62 ft is 16

the missing side length for the shape with a perimeter of  33 cm is 5

the missing side length for the shape with a perimeter of  68 in is 24

1=1/8+x+2/8
Pls help and hurry

Answers

Answer:

x = 5/8 plz give branliest

Step-by-step explanation:

Using the equation,[tex]1 = \frac{1}{8} + x + \frac{2}{8}[/tex]

simplify 1 = x + [tex]\frac{3}{8}[/tex]

1 - [tex]\frac{3}{8}[/tex] = x

[tex]\frac{5}{8}[/tex] = x

Answer:

x = 5/8 or 0.625

Step-by-step explanation:

Rewrite the equation as 18+x+28=118+x+28=1.

18+x+28=118+x+28=1

Simplify 18+x+2818+x+28.

Tap for more steps...

x+38=1x+38=1

Move all terms not containing xx to the right side of the equation.

Tap for more steps...

x=58x=58

The result can be shown in multiple forms.

Exact Form:

x=58x=58

Decimal Form:

x=0.625

The graph shows f(x) = |x – h| + k. What is the value of h?

Answers

Answer:h=1

Step-by-step explanation:

A

Step-by-step explanation:

edge2021 Algebra

Please answer and tell me how you did it. Unfortunately, I would give more points but there's still more questions I need.

Answers

Answer:

y=3x

Step-by-step explanation:

if you look 3*3=9   5*3=15 8*3=24 and 10*3=30 so they are taking x*3

Answer:

Y=3x

Step-by-step explanation:

The way a function table works is how x has something done to it to equal y. So if x =4, and y=16

You could formulate the equation y= 4x.

So if we look at the patterns

3 to 9

5 to 15

8 to 24

10 to 30

Y is equal to x times 3.

3(x)·3=9(y)

3(x)=y

3x=y

The equation would be 3x=y

In ΔDEF, d = 92 cm, e = 42 cm and ∠F=141°. Find the length of f, to the nearest centimeter.

Answers

Answer:

f=127 cm

Step-by-step explanation:

Law of Cosine:

x squared=92 squared+42 squared-2(92)(42)(cos 141)

x squared =8464+1764-7728(cos 141)

x=127 cm

Which expression is equivalent to StartRoot StartFraction 128 x Superscript 5 Baseline y Superscript 6 Baseline Over 2 x Superscript 7 Baseline y Superscript 5 Baseline EndFraction EndRoot? Assume x Greater-than 0 and y > 0. Plz help

Answers

Answer:

D

Step-by-step explanation:

I did the work its D on edge.

Final answer:

To simplify the given expression, we first simplify the fraction within the square root, performing the division of similar bases by subtracting exponents. Then, we take the square root of 64 to get 8 and obtain the final simplified expression: 8/x^2y.

Explanation:

To solve the specific expression, equivalent to StartRoot StartFraction 128 x Superscript 5 Baseline y Superscript 6 Baseline Over 2 x Superscript 7 Baseline y Superscript 5 Baseline EndFraction EndRoot, we will start by simplification inside the square root bracket. Perform the division with the fractions first. As a general rule, when dividing powers with the same base, we subtract the powers.

We'll start by simplifying 128/2, which is 64. For x Superscript 5 Baseline / x Superscript 7 Baseline, subtract the exponents, which gives us x to the power of -2 (since 5-7 is -2). For y Superscript 6 Baseline / y Superscript 5 Baseline, we also subtract the exponents, which results in y to the power of 1, or simply y.

Hence, the simplified version of the fraction inside the square root is 64x^-2y. Finally, since the square root of 64 is 8, and the square root of any variable raised to the negative power is the reciprocal of the variable, our final simplified expression is 8/x^2y.

Learn more about Mathematical Simplification here:

https://brainly.com/question/33857870

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Here is how Lydia found the product 4/5 x 10. Use the model given to show that Lydia’s answer is correct.

Answers

-[tex]\frac{10}{1}[/tex]Answer:

lydia's answer is correct.

Step-by-step explanation

 4/5 X 10=8 because

[tex]\frac{4}{5}[/tex]  X [tex]\frac{10}{1}[/tex]  -->we do the denominator first so 5 x 1 = 5 so now it's

[tex]\frac{4}{5}[/tex] [tex]\frac{10}{5}[/tex] so 4 X 10= 2 x 5(we replace 10 with that ) over 5  and the you will be left with 4 x 2 over 5  that is because 5 and 5 canceled out so

now  you're left with this 4 x 2 = 8 so 8 is you final answer without the fraction :) hope this helps

                                                                                         

cross products question, 3/5 over x multiplied by 12 over 20
what is x

Answers

Answer:

9/25x

Step-by-step explanation:

3/5/x ×12/20

3/5×1/x ×12/20

36/100x

Divide both by 4

9/25x

The exact value of x cannot be determined because we don't know what the equation is equated to

So we will have to leave the answer as 9/25x

5. In the figure, BE||CD. Solve for x. Show your work.

Answers

Answer:

x = 15

Step-by-step explanation:

There are theorems regarding Property of Similar polygons.

Corresponding sides are in proportion.

triangle ABE is similar to triangle ACD

so

AB:BC = AE: ED

x:10 = 9:6

(x/10) = (9/6)

x = 10*9/6 = 5*3 = 15

Find the slope of the line that goes through the points
(12,-14) and (3,-12)
Slope, m=

Answers

Answer:

-2/9

Step-by-step explanation:

The slope is found by

m= (y2-y1)/(x2-x1)

   = (-12- -14)/(3-12)

    =(-12+14)/(3-12)

    =2/-9

   = -2/9

A chorus has twelve music stands for thirty singers. What is an equivalent ratio of music stands to singers?

Answers

Answer:

2:5

Step-by-step explanation:

12:30 would be 40% then simplify by dividing each number by 6.

Answer:

2.5

Step-by-step explanation:

A storage tank is 20% filled with water. The storage tank holds, 1,160 gallons of water. How many gallons of water are needed to fill the storage tank to the top?

Answers

20% is 1/5
So if you multiply 1,160 by 5 you get 5,800.

So 1,160 is 20% of 5,800

Your answer is (5,800)

Plz mark brainliest

The storage tank requires an additional 4,640 gallons of water to be filled to the top, calculated by finding the total tank capacity using the 20% already filled and subtracting the current water volume.

The student asks about the amount of water needed to fill a storage tank to the top given that the tank is already 20% full with 1,160 gallons of water. To find out how much more water is required, we first need to establish the total capacity of the tank.

Since 1,160 gallons represent 20% of the tank's capacity, we can calculate the full capacity by dividing the amount of water currently in the tank by 0.2. After finding that number, we need to subtract 1,160 from the total capacity to find the amount of water needed to fill the tank.

Calculation:

1. Calculate the full capacity of the tank:
Total capacity = 1,160 gallons / 0.20 = 5,800 gallons.

2. Calculate the gallons of water needed to fill the tank:
Gallons needed = Total capacity - Current amount of water
Gallons needed = 5,800 gallons - 1,160 gallons = 4,640 gallons.

Therefore, 4,640 gallons of water are needed to fill the storage tank to the top.

HELPPPPPPPPPPPPPPPPPPPPP 29PTS AND BRAINLIEST A box at the post office has dimensions as shown below. A rectangular prism with a length of 12 inches, width of 8 inches, and height of 16 inches. What is the volume of the box? A.1,304 B.1,536 C.1,636 D.2,304

Answers

Answer:

b)1536

Step-by-step explanation:

We find the volume of a rectangular prism by using the formula Bh

or l x w x h

8x12x16=1536

brainliest plz i need one more

Answer:

B.1,536

Explanation:

length x width x height = v

12 x 8 x height = 96 x height

12 x 8 x 16 = 1536 or v

What expression represents the value of v?
1.) v = [tex]\sqrt{zy}[/tex]
2.) v = [tex]\sqrt{wz}[/tex]
3.) v = [tex]\sqrt{w(w+z)}[/tex]
4.) v = [tex]\sqrt{z(w+z)}[/tex]

I know for a fact that 1 is not the answer. See the attached image for the triangle in question.

Answers

The expression represent the value of v is :[tex]v=\sqrt{z(w+z)}[/tex]

The correct option is D

We have the attachment.

As shown, when deconstructing the largest right triangle, we got two similar triangles.

The corresponding sides of similar are proportional. Therefore, we can write the following proportion:

v/ w+ z = z/v

By Cross - multiply, we get:

z(w + z) = [tex]v^2[/tex]

And taking the square root of both sides, we get:

[tex]v=\sqrt{z(w+z)}[/tex]

So, The correct option is D

Learn more about Triangle at:

https://brainly.com/question/2773823

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Nadia says the hypotenuse of the right triangle has a length of 73 because the Pythagorean theorem states that (28+45)squared equals to 73squared. Which describes her solution?

Answers

Answer: Her solution is incorrect. The hypotenuse is 53 units

Step-by-step explanation: The error occurred when she quoted the Pythagorean theorem. She added up both sides and squared them and made the answer equal to the square of the hypotenuse. She was supposed to have squared them first, before adding up.

The Pythagorean (or Pythagoras) theorem states that the sum of the squares of two sides of a right angled triangle equals the square of the hypotenuse of the triangle. That is, in triangle ABC, if the hypotenuse is given as line AC, the Pythagoras theorem states that

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse and AB and BC are the other two sides.

In Nadia’s solution, if the hypotenuse is given as 73, and the other two sides are 28 and 45, then the Pythagorean theorem properly expressed would be as follows;

73^2 = 28^2 + 45^2

5329 = 784 + 2025

5329 ≠ 2809

As we have determined, writing out the expression as

73^2 = (28 + 45)^2 is very incorrect as this is not the Pythagorean theorem and of course, the triangle cannot have 73 as its hypotenuse as we have determined by properly writing out the Pythagorean theorem.

The correct solution is as follows;

AC^2 = AB^2 + BC^2

AC^2 = 28^2 + 45^2

AC^2 = 784 + 2025

AC^2 = 2809

Add the square root sign to both sides of the equation

AC = 53

Therefore, the hypotenuse is 53 units

It would be C, because when you find the length using th pythagreon theorem... you can begin to see the relationship through all of the figures and side lengths... Make sense?

F(x) = 5x -3 solve for f(5)

Answers

Answer:

22

Step-by-step explanation:

f(x)=5x-3

f(x)=5(5)-3

f(x)=25-3

f(x)=22

Answer:

[tex]f(5)=22[/tex]

Step-by-step explanation:

since the function is f(x), then you would plug in the 5 since that is x value that is being given then it would be [tex]f(5)=5(5)-3[/tex]. from there multiply 5 and 5 to get 25 then subtract 3 to get 22.

ON THE SMARTBOARD, THE
MATH TEACHER DREW A
RECTANGLE WITH A PERIMETER
The
OF 406 cm. THE LENGTH OF THE
RECTANGLE IS 7cm LONGER
THAN THE WIDTH. FIND THE
DIMENSIONS OF THE RECTANGLE.

Answers

The length of rectangle is 105 cm and width is 98 cm.

Step-by-step explanation:

Given,

Perimeter of rectangle = 406 cm

Let,

w be the width of rectangle

Length of rectangle = w+7

We know that

Perimeter of rectangle = 2(Length + Width)

[tex]406 = 2(w+7+w)\\406 = 2(2w+7)\\406 = 4w+14\\406-14 = 4w\\392=4w\\4w=392[/tex]

Dividing both sides by 4

[tex]\frac{4w}{4}=\frac{392}{4}\\w=98[/tex]

Width of rectangle = 98 cm

Length of rectangle = 98+7 = 105 cm

The length of rectangle is 105 cm and width is 98 cm.

The expanded form 700,000 + 10,000 + 3,000 + 9 represents the whole number

Answers

Answer:

713,009

Step-by-step explanation:

A construction manager weighs a bundle of 9 identical bricks and a 7 pound concrete block. The bundle weighs 30 pounds.

Answers

Answer:

30 = 9x + 7

Step-by-step explanation:

The total weight of the bundle = 30 pounds

The weight of the bricks = x pounds

But he carried 9 bricks = 9x pounds

He also carried additional 7 pounds of concrete block.

An equation to show the total weight he carried is

30 pounds = (9x + 7) pounds

Since 9x represents the total weight of the bricks he carried

7 represents the weight of the concrete block

And 30 pounds represents the total weight of everything he carried.

Ella ate half of her gummy bears before adding thirteen more to the bowl.if she now has 25 gummy bears.how many did she start with??

Answers

she ate half before adding 13 so half was 12 which means she started with 24 bear gummies

12+13=24
she started with 12 gummy bears and then added 13 which equals 25
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Tap on the photo to viewAnswer only the first question and you have to write it in 3 sentences and about 3 characters.Do ASAP!Extra Points!Will mark Brainiest! Which of the following best describes the cause of the Cultural Revolution?Group of answer choices:A) Lack of idealism and the compromising of communist ideologyB) The strong influence and inflexibility of communist ideologyC) The replacement of communist ideology with an inferior ideologyD) A wavering commitment to communist ideology on the part of young radicals Jack is a crook with an honest face. People easily trust him. Jack works a scam in which he convinces the elderly to invest their life savings in a false company based on false annual reports of highly lucrative returns. He insists that the investment must be in cash to facilitate timely return on investment. Jack is guilty of a crime involving what Match each vocabulary word with its definition. What was unprecedented about the allied strikes on Hiroshima and Nagasaki The following table shows the speeds at which Jeff does 444 activities. For example, biking has a rate of 191919 miles in 222 hours. A healthy radish plant growing in a greenhouse is covered with a screen box that blocks sunlight. After 10 days, the mass of the plants has ___________ because the rate of cellular respiration is _________ the rate of photosynthesis. Select the correct statement concering the "designer amphetamines." A. Use of MDA dulls the sense of touchB. MDA use typically causes LSD-like visuals and auditory hallucinationsC. Compared to MDA, MDMA has more psychedelic and less stimulant activityD. MDA is also known as "ecstasy" HELPPPPPPPPPPPPPPPPPPPP What big change occurred in the Electoral College during this era? How did the structure of the Articles of Confederation support states' rights?States made all the decisions for the country and were not bound to the national governmentStates had power over their own governments with little or no input from the national governmentThe national government respected state governments, but the rule of the national goverment was supremeThe national government determined how the country acted in all matters with no input from the states What does the Cyclops do as Odysseus and his men sail away?*-drops to his stomach and throws a tantrum-searches for any remaining men in his cave-calls for the other Cyclopes to board ships and chase after them-prays to his father, Poseidon to curse Odysseus (1) 3. Suppose Kaitlyn wants to make the statement that 25% of the 24 studentsshe sampled raised over a certain amount for the charity. What is thatamount? Explain. I believe one of the answers is D, but i cant find any other ones. Can someone check my work and make sure i am correct? thank you! What is the first stage in creating a new public policy?OA. The executive branch creates a proposal.OB. The legislative branch debates and fine-tunes an idea.OC. A state official petitions the federal government.D. The Supreme Court identifies a need to change a law. Convert the angle 0 = 345 to radians. 1. 6/5/2/5A)2 4/5B) 3C)1 2/5D) 12/25 A coyote can alter its diet to match seasonal abundance of plants, fruits, or small animals, and would therefore be considered ________. A coyote can alter its diet to match seasonal abundance of plants, fruits, or small animals, and would therefore be considered ________. density independent and resource-neutral a generalist a specialist, able to specialize on whatever is available at the time an endemic an organism with a type II survivorship curve Let's return to our friend the sphere, with surface charge density (, f) = 0sincos2f . Find the net polarization of this sphere, assuming the charge density is bound charge. You can assume the sphere is not rotating (f is azimuthal angle). What is the electric potential a large distance from the sphere? Price supports (such as those placed on agricultural goods) Select one: a. are designed to benefit suppliers. b. hurt demanders because they face artificially higher prices. c. create surpluses that have to be purchased by government agencies. d. impose a higher tax burden on society in order to finance government purchases. e. generate all of the above consequences. According to the reaction below, what mass of oxygen gas is required to produce 22 g of carbon dioxide?C(s) + O2(g) --> CO2(g)A.) 16 gB.) 4.0 gC.) 8.0 gD.) 32 gE.) 12 g