Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation 2 h tt = − 16t^2+ 72t+ 100 (where t is time in seconds and h is height in feet) How long will it take the coin to reach the stream?

Answers

Answer 1

Answer:

It will take 5.61 seconds for the coin to reach the stream.

Step-by-step explanation:

The height of the coin, after t seconds, is given by the following equation:

[tex]h(t) = -16t^{2} + 72t + 100[/tex]

How long will it take the coin to reach the stream?

The stream is the ground level.

So the coin reaches the stream when h(t) = 0.

[tex]h(t) = -16t^{2} + 72t + 100[/tex]

[tex]-16t^{2} + 72t + 100 = 0[/tex]

Multiplying by (-1)

[tex]16t^{2} - 72t - 100 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]16t^{2} - 72t - 100 = 0[/tex]

So

[tex]a = 16, b = -72, c = -100[/tex]

[tex]\bigtriangleup = (-72)^{2} - 4*16*(-100) = 11584[/tex]

[tex]t_{1} = \frac{-(-72) + \sqrt{11584}}{2*16} = 5.61[/tex]

[tex]t_{2} = \frac{-(-72) - \sqrt{11584}}{2*16} = -1.11[/tex]

Time is a positive measure, so we take the positive value.

It will take 5.61 seconds for the coin to reach the stream.


Related Questions

Natalie baked 20 cupcakes for a fundraising event at school. On the way to the event she dropped 35% of the cupcakes on the floor. What is the total number of cupcakes that natalie dropped?

Answers

Answer:

The total number of cupcakes that Natalie dropped is 7.

Step-by-step explanation:

This question can be solved using a rule of three.

The amount of cupcakes that she has, which is 20, is 100% = 1. How many cupcakes is 35% = 0.35?

20 cupcakes - 1

x cupcakes - 0.35

x = 20*0.35 = 7

The total number of cupcakes that Natalie dropped is 7.

Find the mode of the data.
41, 38, 37, 34, 37, 43, 37, 39, 41, 37

Answers

Answer:

Step-by-step explanation:

37

Answer: 37

Step-by-step explanation:

To find the mode, or modal value, it is best to put the numbers in order. Then count how many of each number. A number that appears most often is the mode. All you have to do is look for the number that occurs in any of those the lists the most and that number is the mode.

was da answer people?

Answers

Answer:

39 homes

Step-by-step explanation:

The fraction of people having computers is

13/20

Multiply by the number of homes

13/20 * 60

13 * 60/20

13*3

39

39 homes

Answer:

39 Computers

Step-by-step explanation:

i never really understood how everyone does these types of question so i just do them my own way:

60/20 = 3  

13*3 = 39

ʕ•ᴥ•ʔ  (dats a bear)

What is the value of x in the equation below 1/3(12x-24)=18? 2 6 8 10

Answers

Answer:

x = 6

Step-by-step explanation:

solve the equation for x

1/3(12x-24)=18

distribute

(1/3)(12x) - (1/3)(24) = 18

4x - 8 = 18

add 8 to both sides

4x = 24

divide each side by 4

x = 6

hope this helps!

Answer:

6

Step-by-step explanation:

Need help ASAP. WILL MARK BRAINLIEST.

Answers

Answer:

The answer is 9.43 cm.

Step-by-step explanation:

The formula for circumference is πd or 2πr.

The diameter is the radius times 2. 1.5 times 2 is 3.

3 times π is about 9.43.

I hope this helps! :)

the rational number of 2 x -7/4​

Answers

The rational number in this equation is 2

What is the solution to the equation 3(2x + 5) = 3x + 4x?
a
X= 15
b.
X= 5
X=0
dx = 4

Answers

Answer: A

Step-by-step explanation:

Distribute the 3(2x+5) which gives you 6x+15. Than add 3x+4x which gives you 7x. Subtract the 6x giving you 15=x or 15=1x, divide the one to get the x alone and you get A.

A rectangular table has an area of 5/6 of a square meter. The length of a table is 2/3 of a meter. What is the width of the table in meters?

Answers

Answer:

Width is [tex]1 \frac{1}{4} m[/tex] or 1.25m

Step-by-step explanation:

[tex]\frac{5}{6}[/tex] ÷ [tex]\frac{2}{3}[/tex] = 5/6 x 3/2 = 5/4

OUR TEACHER CALLED THIS A PUZZLE IN A PUZZLE I DONTB GET THIS MATH HW BUT DO U?

What are the next two letters in the following series and why?
W A T N T L I T F S _ _
*Hint: Check Puzzle Title

this is what she said
i copy and pasted from my computer

Answers

Answer:

A and W that's awesome puzzle!!

Answer:

its A and W

i had this on my math HW to 2 weeks ago

Step-by-step explanation:

What are the next two letters in the following series and why

what are the beginning letters in all of words

W A T N T L I F S

and so the remaining is and why which is A W

so its supposed to be like this

W A T N T L I F S A W

hope this helped :D

Dependent variable C depends on both independent variable A and independent variable B. Which statement is correct?
The relationship between independent variable A and dependent variable C and the relationship between independent variable
B and dependent variable C can both be analyzed using the same scatterplot.
The relationship between independent variable A and dependent variable C, and the relationship between independent
variable B and dependent variable C can both be analyzed, but they must be analyzed using separate scatterplots.
Only the relationship between independent variable A and dependent variable C can be analyzed using a scatterplot.
Only the relationship between independent variable B and dependent variable C can be analyzed using a scatterplot.
Save and Exit
Next
Submit
Mark this and retum

Answers

Answer:

its the second one

The relationship between independent variable A and dependent variable C, and the relationship between independent  variable B and dependent variable C can both be analyzed, but they must be analyzed using separate scatterplots.

Step-by-step explanation:

Answer:

B) The relationship between independent variable A and dependent variable C, and the relationship between independent variable B and dependent variable C can both be analyzed, but they must be analyzed using separate scatterplots.

Step-by-step explanation:

I just took the test on edge

Divide -x^3-2x^2-2x+4 by x -3

Answers

Answer:

− x 2 − 5 x − 17 − 47 x − 3

Step-by-step explanation:

 Divide using polynomial division.

Polynomial :

An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to integral powers.

Please help. I also will post another question I need help with. Thank you if you help.

Answers

Geometric progression, first term 5, common ratio 3.

Answer: 5, 15, 45, 135

How do I calculate this parent function of a linear function? The parent function of a linear function is y=x. When the parent function is changed to y=x+5, how does the graph transform?

Answers

Step-by-step explanation:

This only moves the linear function up 5 units. So, before the y-intercept and the x-intercept both was (0,0). Now, the y-intercept is (0,5) because the graph was shifted up 5 units.

hope this helps :)

Someone help me please

Answers

Answer:

f(g(3)) =31

Step-by-step explanation:

f(x) = 3x+4

g(x) = x^2

f(g(3) ) =

First find g(3)

g(3) = 3^2 =9

The use 9 in f(x)

f(g(3)) = f(9) = 3*9+4 = 27+4 = 31

Jill has 64 ounces of lemonade. Each day, her brother drinks 16 ounces. Then at the end of each day Jill adds 25% of the remaining total back into the lemonade container. Which recursive formula models the number of ounces of lemonade in the container, an, at the end of the nth day?

Answers

Answer:

what is the nth day?

Step-by-step explanation:

Answer:

A

Step-by-step explanation: an=1.25(an-1-16);a1=64

:)

Part of the population of 5,250 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 11 of them are infected. How many elk are likely to be infected?

Answers

Answer:

1,155 elk are infected.

Step-by-step explanation:

Let's use a ratio:

infected : fine

    11       :   50

  1155     : 5250

Estimate the solution to the system of equations. asap, please!! I will mark for brain list

​7x−y=7

x+2y=6

please have a mixed fraction for both the y and x answers

Answers

Answer:

(1 [tex]\frac{1}{3}[/tex], 2 [tex]\frac{1}{3}[/tex] )

Step-by-step explanation:

Given the 2 equations

7x - y = 7 → (1)

x + 2y = 6 → (2)

Multiplying (1) by 2 and adding to (2) will eliminate the y- term

14x - 2y = 14 → (3)

Add (2) and (3) term by term to eliminate y

15x = 20 ( divide both sides by 15 )

x = [tex]\frac{20}{15}[/tex] = [tex]\frac{4}{3}[/tex] = 1 [tex]\frac{1}{3}[/tex]

Substitute this value of x into either of the 2 equations and solve for y

Substituting in (2)

[tex]\frac{4}{3}[/tex] + 2y = 6

2y = 6 - [tex]\frac{4}{3}[/tex] = [tex]\frac{14}{3}[/tex] ( divide both sides by 2 )

y = [tex]\frac{7}{3}[/tex] = 2 [tex]\frac{1}{3}[/tex]

Find the area of the triangle

Answers

Answer: Area of a triangle = (b*h)/2

Step-by-step explanation:

8*14= 112

112/2=56

The area of the triangle is 56 square units.

Answer:

56

Step-by-step explanation:area of aa triangle is 1/2bh

=1/2*8*14+56 square units

hope this hepls

plz mark me brainliest

Please help, and thanks in advance!

Answers

Answer:

c i believe sorry if its wrong

Step-by-step explanation:

Answer:

3. A.

4. 136

Step-by-step explanation:

3. Find the surface area:

2 * 1  = 2

3 * 2.2 = 6.6

2 * 3 = 6

3 * 1 = 3

2 + 6.6 + 6 + 3 =  17.6

4. Find the surface area:

5 * 7 * 2 = 70

6 * 4 = 24

7 * 6 = 42

70 + 24 + 42 = 136

HELP ASAP DUE NOW GIVEIN BRAINLIST

Answers

The student did not properly distribute the 4 to all terms in the parenthesis:

-8n + 4(1 + 5n) = -6n - 14

First, distribute 4 to ALL terms in the parenthesis:

-8n + 4 + 20n = -6n - 14

Next, isolate the variable, n. Add 6n and subtract 4 from both sides:

-8n + 20n (+6n) + 4 (-4) = -6n (+6n) - 14 (-4)

-8n + 20n + 6n = -14 - 4

Simplify. Combine like terms:

(-8n + 20n) + 6n = -18

12n + 6n = -18

18n = -18

Isolate the variable, n. Divide 18 from both sides:

(18n)/18 = (-18)/18

n = (-18)/18

n = -1

n = -1 is your answer.

~

Answer:

-According to the student's work shown, The student needs to distribute 1 and 5[tex]n[/tex] by 4. So, the mistake was that the student did not distributed the 1 and 5[tex]n[/tex], in which the student only distributed the 1.

-The equation: [tex]8n + 4(1+5n)=-6n-14[/tex]

-Distributed Incorrectly:

[tex]8n + 4+5n=-6n-14[/tex]  (only distributed the 1 by the 4)

-Distributed Correctly:

[tex]8n + 4+20n=-6n-14[/tex]  (distributed both 1 and 5[tex]n[/tex] by the 4)

-The correct calculation:

[tex]8n + 4(1+5n)=-6n-14[/tex]

[tex]8n + 4+20n=-6n-14[/tex]

[tex]12n+4 = -6n -14[/tex]

[tex]12n + 4+ 6n=-6n+6n-14[/tex]

[tex]18n +4 = -14[/tex]

[tex]18n +4 -4 = -14 -4[/tex]

[tex]18n = -18[/tex]

[tex]\frac{18n}{18}= \frac{-18}{18}[/tex]

[tex]n = -1[/tex]

The correct answer is [tex]n = -1[/tex] .

The graph of the function, f(x) = - x2 - 3x + 1, opens and has a, value.

Answers

Answer:

downward, maximum value

Step-by-step explanation:

f(x) = - x^2 - 3x + 1

The negative in front of the x^2 means the graph opens downwards

The y intercept is 1

Because it opens downward it has a maximum value

Answer:

Opens downwards and has a maximum value

Step-by-step explanation:

f(x) = -x² - 3x + 1

a is the coefficient of x², which is -1

Since a < 0, it's a concave down graph which opens downwards. Therefore it has a maximum turning point

Find the volume of a rectangular prism with base length = 8ft , base width =5 ft, and height =2ft

Answers

Answer:

80

Step-by-step explanation:

All you are doing is 8 times 5 times 2 to give you the answer of 80ft.

Your volume is 80
The formula for volume is base x width x height

3. How is the circumference of a circle related to the length of its diameter?

Answers

Step-by-step explanation:

.The circumference is the distance around the circle. The circumference is equal to two times pi times the radius (C = 2*pi*r). Because the diameter is equal to two times the radius, the circumference is equal to the diameter times pi (C = D*pi), where pi is about 3.14… The diameter of a circle is 2 units.

Sausages come in packets of 7. Bread rolls come in packets of 5. Dan wants to buy enough
packs of sausages and rolls so that there are an equal number of sausages and rolls. What is
the minimum number of sausages and rolls he needs to buy?

Answers

Answer:

5 packs of sausages

7 packs of rolls

Step-by-step explanation:

So the least common multiple of 5 and 7

That's 35

Dan needs to buy 5 packs of sausages and 7 packs of rolls.

A bag of marbpes contains 6 blue marbles, 2 yellow marbles, 4 red marbles, and 1 green marbpe. What is the probability of reaching into the bag and selecting a yellow marble

Answers

Answer:

1/6 or 1.6666666

Step-by-step explanation:

12 marbles, 2 yellow

12/2= 6

1/6

ZA=
Round your answer to the nearest hundredth.
С
5
B
7
?
А

Answers

Answer:

∠ A ≈ 35.54°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan A = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{5}{7}[/tex], thus

A = [tex]tan^{-1}[/tex] ([tex]\frac{5}{7}[/tex] ) ≈ 35.54° ( to the nearest hundredth )

Chitra is buying a TV. At A-Mart, the TV is on sale for $199, with 7%
sales tax. At B-Mart the TV is $299, but has a $100 mail-in rebate.
Sales tax of 7% is based on the full price. After the rebate, which is the
better deal?

5 point pls help​

Answers

the best would be the first choice because it's 7 dollars less than the second choice

Margo can purchase tile at a store for $0.89 per tile and rent a tile saw for $45. At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile. How many tiles must she buy for the cost to be the same at both stores?


Margo must buy ____ tiles for the cost to be the same at both stores.

Answers

Answer:

She must buy 90 tiles for the cost to be the same at both stores

Step-by-step explanation:

Let x be the no. of tiles bought for the cost to be the same at both stores

Margo can purchase tile at a store for $0.89 per tile at shop 1

Cost of x tiles =0.89x

She rent a tile saw for $45.

So, total cost at Store 1 = 0.89x+45

At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile.

So, cost of 1 tile = 1.39

Cost of x tiles = 1.39x

ATQ

0.89x+45=1.39x

45=1.39x-0.89x

45=0.5x

[tex]\frac{45}{0.5}=x[/tex]

90=x

Hence She must buy 90 tiles for the cost to be the same at both stores

What is x/6 = 10/15?

Answers

Answer:

x = 4

Step-by-step explanation:

Given

[tex]\frac{x}{6}[/tex] = [tex]\frac{10}{15}[/tex] ( cross- multiply )

15x = 60 ( divide both sides by 15 )

x = 4

Answer:

3

Step-by-step explanation:

Can someone help me? i'll be giving brainliest

Answers

Answer:

x= 55

Step-by-step explanation:

Answer:

the answer id 62

Step-by-step explanation: 62!!!!!!!!!!

Other Questions
Der Kuss kann die Liebe zeigen. CorrectIncorrect You receive the following prescription: Jessie DeCato Age: 3 Weight: 22 lbs Acyclovir oral suspension 20mg/kg four times daily x 5 days a. How much acyclovir should be administered per dose? Hint: There are 2.2 lbs to 1 kg. How many feet would a 27-inch object measure? What is the reciprocal of 3/4?24/33/41/4 lbnone of the above Which two statements accurately express cause-and-effect relationships expressed or implied by the passage?A)The Thames River helped aid refugees in times of trouble.B)The Thames River enabled London to become a great center for trade.C)The Thames River caused other countries to develop their river resources.D)The Thames River inspired some artists to create powerful and effective art.E)The Thames River helped scientists understand the cycle of the tides better. 1. Mi amigo era agresivo pero ahora es simptico.2. Yo vea a mi abuela mucho pero ahora no porque vivimos en pueblos diferentes.3. El hombre vio una chupacabra mientras iba al supermercado!4. La muj siempre vea a su amiga cuando iba al gimnasio.5. Los domingos, su esposo siempre iba a la casa de su hermano. Which statements are true? Select three options. F corresponds to F'. Segment EE' is parallel to segment FF'. The distance from point D' to the origin is the distance of point D to the origin. The measure of E' is the measure of E. DEF Prompt: What are the central arguments in favor of and against immigration? Which of these arguments do you find to be the most convincing? What arguments of your own could you add to the debate?will mark brainly! need a full paragraph! 70 points! What are the most useful bones for determining biological sex, and age of a skeleton? Answer each one individually, they are not necessarily the same bones.(Forensics) 10x+4y=25x2y=2Choose all answers that apply:Choose all answers that apply:(Choice A)AMultiply the bottom equation by 2, then subtract the bottom equation from the top equation.(Choice B)BMultiply the top equation by 1/2, then add the equations. (choice C)Add the equations. HELPP MEE FASTT I HAVE LESS THAN 10 MINFarrah borrowed $155 from her brother. She has already paid back $15. She plans to pay back $35 each month until the debt is paid off. Which describes the number of months it will take to pay off the debt? Select three options.x + 15 + 35 = 15535 x + 15 = 15535 x = 155 minus 15It will take 8 months to pay off the debt.It will take 4 months to pay off the debt. PLSSS HELP ILL GIVE BRAINLIEST AND 30 PTS AND IF U ANSWER MY OTHER QUESTIONS ILL GIVE 99 PTS + BRAINLIEST Write an equation of the line passing through the point A(2, 0) that is parallel to the line y = 3x5 Helppppppp!!!!!!!!!! Simon needs to learn a number of new vocabulary words to help write an essay for his literature class. Which online note-taking tool would be the most helpful? What is the difference between a haploid species and a diploid species? Find the difference in length between the longest and shortest insects. If your born on 1900 how old would have you been on 2009? One effect of the Haitian Revolution wasa)the end of slavery and independence of Haiti from Frenchb)the beginning of the Civil Warc)the decrease in the price of sugard)the overthrow of the French monarchy Select the correct navigational path to create the function syntax to use the IF function.Click the Formula tab on the ribbon and look in the ???'gallerySelect the range of cells.Then, begin the formula with the ????? click ?????. and click OK.Add the arguments into the boxes for Logical Test, Value_if_True, and Value_if_False.