3. A water balloon was thrown
from a window. The height
of the water balloon over
time can be modeled by the
function y= 16x2 + 160x + 50.
What was the maximum
height of the water balloon
after it was thrown?


Answers

Answer 1

Note: It the given equation the coefficient of [tex]x^2[/tex] must be -16 instead of 16.

Given:

Consider the height  of the water balloon over  time can be modeled by the  function

[tex]y=-16x^2+160x+50[/tex]

To find:

The maximum height of the water balloon  after it was thrown.

Solution:

We have,

[tex]y=-16x^2+160x+50[/tex]

Here, leading coefficient is negative. So, it is a downward parabola and vertex of a downward parabola, is the point of maxima.

If a parabola is [tex]f(x)=ax^2+bx+c[/tex], then

[tex]Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]

Here, [tex]a=-16,b=160,c=50[/tex]. So,

[tex]-\dfrac{b}{2a}=-\dfrac{160}{2(-16)}[/tex]

[tex]-\dfrac{b}{2a}=-\dfrac{160}{-32}[/tex]

[tex]-\dfrac{b}{2a}=5[/tex]

Now, put x=5 in the given equation.

[tex]y=-16(5)^2+160(5)+50[/tex]

[tex]y=-16(25)+800+50[/tex]

[tex]y=-400+850[/tex]

[tex]y=450[/tex]

The vertex of the given parabolic equation is (5,450).

Therefore, the maximum height of the balloon is 450 units after 5 units of time.


Related Questions

Another function I hate these things :C can someone help!

Answers

Answer:

No, this is not a function.

Step-by-step explanation:

This is not a function because not every input goes to exactly one output. In this example, 2 is listed twice. 2 goes to both 4 and 8. Because of this, it is not a function.

1. Ice Tea
A - $3 for 4 refills
B- $4 for 3 refills
Which is the better buy
Can you fill in the two boxes for me?

Answers

Answer:

A

Step-by-step explanation:

A- 3/4=0.75 per refill

B- 4/3= 1.33 per refill

B- 3$ for 4 refills

Find the length of YZ

Answers

Answer:

[tex]YZ = 19cm[/tex]

Step-by-step explanation:

To figure out what line YZ equals, we must first find x. And to do this, let's set up an equation.

Firstly, we know that XY is 8cm, and XZ is 4x+3. So, we know that XY + YZ will equal XZ. Let's set that up:

[tex]8 + 2x+7=4x+3[/tex]

Combine like terms.

[tex]2x+15=4x+3[/tex]

Subtract 2x from both sides.

[tex]15=2x+3[/tex]

Subtract 3 from both sides.

[tex]12=2x[/tex]

Divide both sides by 2.

[tex]6=x[/tex]

Now, we just need to plug 6 into the equation of YZ.

[tex]2(6)+7[/tex]

[tex]12+7[/tex]

[tex]YZ = 19[/tex]

Translate One-third of a number is 14 into an equation

Answers

Answer:

1/3x=14

answer for x is 42

Step-by-step explanation:

x represents the original number and 1/3 of the number equals 14. So 1/3x=14

So therefore 1/3x=14 which x = 42 in case if you were wondering.

Some hotdogs come in packages of eight why would a baker of hot dog buns package seven hot dog to a package

Answers

Answer:

Some hot dogs come in packages of 8.

A baker of hot dog buns package 7 hot dog buns to a package.

So, on every hot dog the baker will earn have a profit of price of one hot dog

Suppose, baker bought 8 packets of packages of 8 hot dogs.

He will have profit of 8 hot dogs

Because if he is selling 8 packets of packages of 7 that means he will earn profit of price of 8 hot dogs.

Step-by-step explanation:

17.
Sean spent $41.20 ordering books from an online
store. The shipping and handling charge was 5%
of the total order. How much did Sean spend on
shipping and handling?
A. $0.42
B.
$0.85
C. $2.06
D. $8.24

Answers

Answer:

the awnser is c

Step-by-step explanation:

first you take 41.20$ and you subtract you're 5%

therefore that gives you 39.14$

subtract 39.14$ from 41.20

and you get a left over of 2.06$

therefore c is you're awnser

A percentage is a number or ratio expressed as a fraction of 100.

The amount spent on shipping and handling charges is $2.06.

What is a percentage?

A percentage is a number or ratio expressed as a fraction of 100.

Example:

50% = 50 / 100 = 1/2

20% = 20 / 100 = 1/5

25% = 25 / 100 = 1 / 4

10% = 10 / 100 = 1 / 10

We have,

Total spending on books = $41.20

Shipping and handling charges = 5% of $41.20

The amount spent on shipping and handling charges:

= 5% of $41.20

= 5/100 x 41.20

= 5/100 x 4120/100

= 5 x 4120 / 10000

= 20600 / 10000

= $2.06

Thus the amount spent on shipping and handling charge is $2.06.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ5

For the piecewise function, find the specified function value
if xs1,
(2x-4, if x > 1
f (x) = (-5,
a) Find f(1) =
(1) b) Find f(5) =
(1)

Answers

Answer:

f(1) = - 5, f(5) = 6

Step-by-step explanation:

(a)

f(1) with x = 1 is in the interval x ≤ 1 , thus

f(1) = - 5

(b)

f(5) with x = 5 is in the interval x > 1 , thus f(x) = 2x - 4 , so

f(5) = 2(5) - 4 = 10 - 4 = 6

WHAT IS THE DOMAIN OF F?
HELP ON MATH PLEASEEE ASAP

Answers

Answer:  The domain is -7 to +7   [-7, 7]

Step-by-step explanation:

The domain is the lowest x-value to the highest x-value.

The ladybug population has been increasing at a rate of 3% every 6 years.
If the population in 1993 was 190 ladybugs, how many ladybugs would
there be in 2019?

Answers

Answer:

there would be 4940 ladybugs in 2019

Step-by-step explanation:

solve the proportion 1/6 ÷3/4​

Answers

Answer:

the answer is 2/9

Step-by-step explanation:

1/6 ÷ 3/4

= 1/6 × 4/3

= 4/18

= 2/9

What is 15.60 to 11.70?

Answers

Answer:

the answer is 133.33

Step-by-step explanation:

hope this helps

Can someone help me with this please?!?!?

Answers

Answer:

with what know question was there

it’s me again lol pls help

Answers

Answer:

C

Step-by-step explanation:

This might look strange, but I would begin by adding 4y to both sides.

12x = 20 + 4y          Subtract 20

12x - 20 = 4y           Divide both sides by 4

12x/4 - 20/4 = 4y/4 Combine

3x - 5 = y

Simplify : 5c + 3 – 12c – 8 show steps

Answers

Answer:

-7c - 5 can also be written  -5 - 7c

Step-by-step explanation:

5c + 3 - 12c - 8

1. subtract 3 and 8

5c - 12c - 5

2. subtract 5c and 12c

-7c - 5

−(1/4w+8)+8=3
the 1/4 is a fraction

Answers

Answer:

w = -12

Step-by-step explanation:

-1/4w - 8 + 8 = 3

-1/4w = 3

w = 3 / -1/4

w = 3*4/-1

w = 12/-1

w = -12

The ratios 5:3 and 10:6 are equivalent ratio

Is the ratio 15:12 equivalent to these?? Explain your reasoning

Answers

The ratio of 15:12 is not equivalent to the other ratios. This is because when you simplify the ratio, you get 3:4 instead of 5:3.

No, the ratio of 15:12 is not equivalent to 5:3 and 10:6 because

- 15:12 = 5:4

- 5:3

- 10:6 = 5:3

Given,

5:3 and 10:6 are equivalent ratios.

We need to see whether these ratios are equivalent to 15:12.

What are proportional ratios?

The ratios which are equal are called proportional ratios.

Example:

1:2 = 5:10 = 6:12 = 7:14

5/10 = 1/2

6/12 = 1/2

7/14 = 1/2

We have,

5:3 and 10:6

- 5/3

- 10/6 = 5/3

We have,

15:12

= 15/12

= 3x5/3x4

= 5/4

We see that 5:3 and 10:6 are not equivalent to 15:!2.

Thus,

No, the ratio of 15:12 is not equivalent to 5:3 and 10:6 because

- 15:12 = 5:4

- 5:3

- 10:6 = 5:3

Learn more about equivalent ratios here:

https://brainly.com/question/13513438

#SPJ2

URGENT PLZ BE QUICK!!

Pauline is buying a shirt that was originally priced at $15. The star has a today - only discount of 25%. What is today’s price for the shirt?

Answers

Answer:

$11.25

Step-by-step explanation:

.25x15=3.75

15-3.75=11.25

plz help. this is for apex if you dont know.

Answers

Answer:

1/4/4/3 is the same as 1/4 x 3/4

Step-by-step explanation:

first fraction-keep

Division sign-flip to multiplacation

Second sign-flip

Find the value of this triangle!

Answers

Answer:

x=35

y=145

z=25

Step-by-step explanation:

(do first)x:

55 + 90 = 145

180-145=35

(do last)y:

25+10=35

180-35=145

(do second)z:

65+90=155

180-155=25

Answer:

x = 35, y = 145, z = 25

Step-by-step explanation:

All triangles' angles have a sum of 180°. Because we know this, we can solve the first triangle easily.

180 = x + 90 + 55

180 = x + 145

35 = x

Angles x and y are what we call suplementary angles. This means they have a sum of 180°.

180 = 35 + y

145 = y

Once again, we know that triangles have a sum of 180°. So the next triangle should now be easy to solve.

180 = 10 + 145 + z

180 = 155 + z

25 = z

What is the domain of the function f(x) = 3x + 4 + 1?
all real numbers
O all real numbers less than or equal to -4
O all real numbers greater than or equal to 1
O all real numbers greater than or equal to -4

Answers

Answer:

c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

No 2 please.Quick. HELP ASAP

Answers

Part A

We have 20 cards, 4 of which are kings (one of each suit). The probability of getting a king on the first draw is 4/20 = 1/5.

Answer: 1/5

===========================================================

Part B

We have 20-4 = 16 cards that aren't a king out of 20 total.

The probability of getting a non-king card is 16/20 = 4/5

After selecting the first card and not putting it back, we have 20-1 = 19 cards left. Four of which are a king, so 4/19 represents the probability of getting a king on this draw.

So (4/5)*(4/19) = 16/95 is the probability of getting a king on the second draw where the first draw is not a king.

Answer: 16/95

===========================================================

Part C

16/20 is the probability of getting no kings on the first draw

15/19 is the probability of getting no kings on the second draw (notice I stepped the values down by 1)

14/18 is the probability of getting no kings on the third draw

Multiplying out the fractions gives

(16/20)*(15/19)*(14/18) = 28/57

I skipped a few steps when multiplying the fractions but you get the idea.

The probability of drawing 3 cards, none of which are a king, is 28/57

Subtract this from 1 to get the complementary probability

1-(28/57) = 57/57 - 28/57 = (57-28)/57 = 29/57

This works because we have two choices: either we get no kings, or we get at least one king. So that's why the two events are complementary and their probabilities add to 1.

Answer: 29/57

Karen earn a commission of $140.00 per course that you sell on the internet. She
sold 112 courses.
What is her commission?

Answers

Answer:

$ 15680

Step-by-step explanation:

From the question given above, we were told that Karen earn a commission of $ 140 per course.

To know her commission for selling 112 courses, we simply do the following:

Karen earn a commission of $ 140 for 1 course.

Therefore, she will ear $ X for 112 courses i.e

$ X = $ 140 × 112 course/ 1 course

$ X = $ 15680

Therefore, Karen commission for selling 112 courses is $ 15680

May you please help me with my geometry. ​

Answers

Answer:

uhm

Step-by-step explanation:

Can someone please help me ASAP

Answers

The answer is 2.2 x 10^5

HELPPPPPPPPPPPPP PLEASEEEEEEEEEEEEEEEEE ITS DUEEEEEEEEEEEEEEEEEEE

Answers

Answer:

Look below.

Step-by-step explanation:

13.)

The lines are neither because the slopes are reciprocals.

14.)

The lines are perpendicular because the slopes are opposite reciprocals.

help pls pointssssssssss​

Answers

Answer:

the second one i believe:)

Step-by-step explanation:

i literally just did this in algebra lol...hope this helps:))

Answer:

A

Step-by-step explanation:

helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

The one on the left

Step-by-step explanation:

i thought about it and its the dot on the left

A line has an x-intercept of 3 and a y-intercept of -6.

The slope-intercept form of its equation is
.

Answers

Y=3x-6
The equation for slope intercept is y=mx+b whereas m is the slope and b is your y intercept
So you plug in what you have been given into that equation. Hope that helps!

Answer:

y = 2 x - 6

the second answer is

y + 6 = 2 (x - 0)

Step-by-step explanation:

Geometry. Unit 1. Lesson 5. (5.2: Make it Right) Use GeoGebra

Answers

Answer:nnjjj

Step-by-step explanation:

Twice a number y is no more than 12.

Answers

5? 5 times 5 is 10, which is less than 12
Other Questions
A sudden increase in the amountof available nutrients can createproblems for an aquaticecosystem. How?A. Large numbers of producers can confuseherbivores.B. Increased nutrients can cause producers tocompete aggressively with one another.C. There is not enough oxygen in theatmosphere to support excessive numbers ofaquatic plants. What symbols do composers use when notes go beyond the staff?A. Cliff Lines B. Many lines C. Ledger Lines HELP! ASAP Referring to the figure, select the letter of the position that the word in quotes should occupy: The plane swooped toward them, "but" the pilot did not wave. a. b. c. d. Which ratios have a unit rate greater than 1? Choose ALL that apply. Which pair of numbers are relatively prime?22 and 3532 and 1621 and 5630 and 85 There are 216 identical plastic chips numbered 1 through 216 in a box. What is the probability of reaching into the box and randomly drawing the chip numbered 170? Express your answer as a simplified fraction or a decimal rounded to four decimal places. Determine the intercepts of the linex- intercept (_,_)y- intercept (_,_) 15. Which of the following shows the correct sequence of what happens to the water molecules in an icecube when it is removed from the freezer?(1 point)1. The molecules gain enough energy to break free from each other.2. The ice begins to melt.3. The molecules vibrate in a fixed position.4. The temperature of the of molecules increases.5. Thermal energy is absorbed from the surroundings.6. The molecules vibrate faster.0 3,1,4,6,5,2O 5,1,4,6,3,2O 3,5,6,1,2,4O 5,3,1,4,6,2 angles a and b are vertical angles. If mA = (5x 24) and m B = (3x + 24),then find the value of x. To mail 10 letters costs $ 4.50 . How much would it cost for 12 letters? Assume the relationship is proportional. What does Eric Schlosser say his book is primarily about in his Introduction toFast Food Nation?A. The amount of money Americans spend on fast food in a yearB. The way fast food has shaped America and what it representsC. The history of fast food and how it came to be successfulD. The number of animals killed each year in the fast-food industry Deshawn's Bikes rents bikes for $11 plus $5 per hour. Maria paid $51 to rent a bike. For how many hours did she rent the bike? Joseph is having a difficult time comparing two characters in a novel for a language arts assignment. Which reading strategy would help him most?1. using metacognition more regularly2. summarizing every chapter3. completing a graphic organizer4. relating the story to his own experiences March 1, 1988 Mr. Philip Bravin Presidential Search Committee Gallaudet University 7th and Florida Avenue, NE Washington, DC 20002 Dear Mr. Bravin: It is my understanding that Gallaudet University* is in the process of selecting a new President. I also understand that you have identified six finalists who are highly qualified for the position, three of whom are deaf. I have a deep interest in disability civil rights. Over the past few years I have worked with many national and local organizations run by and for disabled people, including the National Council on Independent Living, the National Council on the Handicapped, Capitol People First of Sacramento and the Association on Handicapped Student Service Programs in Post-Secondary Education. I have also had many conversations with disabled leaders, including deaf persons, throughout the United States. And my office has served as the focal point for the development of the Administrations disability policy. From this experience, I have become aware of the two basic principles underlying the disability rights movement; the right of disabled people to control their own lives and the right to integration and involvement in society. Gallaudet University has a critical role to play in advancing these principles. It is held in the highest regard by deaf people throughout the United States and the world. It provides an excellent education and a meaningful future for thousands of deaf persons. More importantly, Gallaudet University is a symbol of leadership and opportunity, not only for deaf people, but for all of us. In the last two decades our society has undergone a quiet revolution. The Congress, the Courts and the Administration have strongly supported the right of people with disabilities to hold positions of trust and leadership. Our government has enacted numerous laws to ensure that disabled people are ensured equality of opportunity. Accordingly, as an entity funded by the Federal government, Gallaudet has a responsibility to set an example and thus to appoint a President who is not only highly qualified, but who is also deaf. I hope that the Trustees will keep Gallaudets critical leadership position in mind when they make their decision. Sincerely, George Bush Which of the following best describes the organization of the second paragraph? Which of the following is a valid step in the solution of $2x + 4x + 3 = 0? 2 42x12 = (4x+3 2 42x -VX+31 x 421 VI-3 4271* = -41+316 RETRY Which of these is an opinion (helppp) (1) Whenever you buy a present, you should consider the interests of the receiver. (2)(3) If, on the other hand, you are selecting a gift for your little cousin, you might choose a caboose forhis new electric train set. please help guys, im so lost aaahhhhConsider a geometric sequence with a first term of 4 and a fourth term of -2,916.a. find the common ratio of this sequence.b. find the sum to infinity of this sequence Maggie baked 96 cookies in 4 batches. What is the number of cookies per batch? What is an ORGANELLE And put a sentence that supports it#STAY POSTED IM PUTTING SOME OTHER QUESTIONS UP SOON