A ball is thrown upward from the top of a 192-foot-high building. The ball is 240 feet above ground level after 1 second, and it reaches ground level in 6 seconds. The height above ground is a quadratic function of the time after the ball is thrown. Write the equation of this function.

Answers

Answer 1

Answer:

The equation of this function is [tex]h = -16\cdot t^{2}+64\cdot t+192[/tex].

Step-by-step explanation:

From Mechanical Physics we must remember that height reached by the ball as a function of time is a quadratic function if and only if ball is uniformly accelerated by gravity and viscous forces and Earth's rotation effects can be neglected. After assuming those considerations as true, the standard form of the quadratic function is:

[tex]h = a\cdot t^{2}+b\cdot t + c[/tex] (Eq. 1)

Where:

[tex]t[/tex] - Time, measured in seconds.

[tex]h[/tex] - Height of the ball, measured in feet.

[tex]a[/tex] - Second order coefficient, measured in feet per square second.

[tex]b[/tex] - First order coefficient, measured in feet per second.

[tex]c[/tex] - Zero order coefficient, measured in feet.

From Algebra, we can obtain a quadratic function by know three distinct points and solving the resulting system of linear equations:

[tex]A(t, h)= (0\,s,192\,ft)[/tex]

[tex]c = 192\,ft[/tex] (Eq. 2)

[tex]B(t,h) = (1\,s,240\,ft)[/tex]

[tex]a+b+c = 240\,ft[/tex] (Eq. 3)

[tex]C(t,h) =(6\,s,0\,ft)[/tex]

[tex]36\cdot a + 6\cdot b + c = 0[/tex] (Eq. 4)

By Algebraic methods, we get this unique solution:

[tex]a = -16\,\frac{ft}{s^{2}}[/tex], [tex]b = 64\,\frac{ft}{s}[/tex], [tex]c = 192\,ft[/tex]

The equation of this function is [tex]h = -16\cdot t^{2}+64\cdot t+192[/tex].


Related Questions

What is the equation of a line that is parallel to the line y = 2x + 7 and passes through the point (–2, 4)? A. y = −12x + 3 B. y = 2x + 4 C. y = −12x − 2 D. y = 2x + 8

Answers

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept)

y = 2x + 7 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, thus

y = 2x + c ← is the partial equation

To find c substitute (- 2, 4) into the partial equation

4 = - 4 + c ⇒ c = 4 + 4 = 8

y = 2x + 8 → D

1. Factor the expression completely 20x^4+80x^3-5x^2-20x

Answers

Answer:

5x(x+4)(2x+1)(2x−1)

Step-by-step explanation:

Suppose a person starts the day by drinking 3 cups of coffee containing 130 mg of caffeine EACH.

Let C = mg of caffeine remaining in the body and let t = hours since the 390 mg of caffeine was consumed. Write a function C(t) that expresses the amount of caffeine remaining in the body as a function of time.

Answers

Answer:

C = t * 3

Step-by-step explanation:

A container of coffee is 1/6 full. The container contains 2/3 a pound of coffee. a. Write a division expression that represents the capacity of the container. b.Write a multiplication expression that represents the capacity of the container. c.Find the capacity of the container.

Answers

Answer:

(a) [tex]x= \frac 2 3\div \frac 1 6[/tex]

(b) [tex]x= \frac 2 3\times \frac 6 1[/tex]

(c) 4 pounds

Step-by-step explanation:

Let the capacity of the container is [tex]x[/tex].

The container has coffee which is 1/6 of the capacity of the container and the amount of coffee is 2/3 pounds.

So, 1/6 of the capacity of the container has 2/3 pound of coffee, i.e

[tex]\frac 1 6 \times x = \frac 2 3\cdots(i)[/tex]

(a) From the equation (i), the required division expression for the capacity of the box, x, is

[tex]x= \frac 2 3\div \frac 1 6[/tex]

(b) The division expression can be changed to multiplication expression by interchanging the numerator and the denominator of the divisor. So, from part (a), the required multiplication expression for the capacity of the box, x, is

[tex]x= \frac 2 3\times \frac 6 1\cdots(ii)[/tex]

(c) From equation (ii), the capacity of the box is

[tex]x= \frac 2 3\times 6= 4[/tex] pounds.

1. What is 10% of 75?

Answers

Answer:

7.5

Step-by-step explanation:

i hope this helps!!

Which is the graph of the equation y-1=2/3(x-3)?

Answers

Answer:

The second graph ( one with the coordinates (3,1) and (6,3))

Step-by-step explanation:

Answer:

The answer is B.

Step-by-step explanation:

the sum of the 2 integers is -112. if one of them is -109 find the other​

Answers

Answer:

let x and be the two integers

x+y=-112

if one of them is -109

let x be one of the that is substitute-109 to the above equation

-109+y=-112

collect like terms to the left hand side.

-109+112=-y

3=-y

move the sigh to the constant

y=-3

If you could travel back in time one year, what advice would you give yourself?
10 sentence required for the brainlleist if 2 people answer
1

Answers

Answer:

To keep my head up and focus on the good instead of the bad. To understand that life gets hard. I would remind myself that I'm worth it and I am a strong person. I would tell myself that whatever bad happens, something good will come out of it. To remind myself that all the bad I've been through is only making me a stronger person. And I would remind myself that everything happens for a reason, whether I see it now or I see it later on down the road. I would remind myself that it's never too late to change for the better. I would tell my self "you made it this far, your strong". And I would tell myself that I can do whatever I put my mind to. And that nothing is impossible.

Hope this helps :)

Step-by-step explanation:

If someone could travel back in time one year, the advice I would give myself would be to embrace change and adaptability. The world is constantly evolving, and it is important to stay open-minded and flexible in order to thrive.

I would encourage myself to be proactive in seeking opportunities for growth and learning, even if they seem daunting or unfamiliar at first. Additionally, I would remind myself to prioritize self-care and mental well-being. It is easy to get caught up in the hustle and bustle of daily life, but taking time for oneself is crucial.

Whether it be spending time in nature, practicing mindfulness, or pursuing hobbies and interests, nurturing my own happiness should be a priority. Lastly, I would advise myself not to dwell on past mistakes or missed opportunities.

Every setback is an opportunity for growth, and it is important to learn from these experiences rather than letting them define me. By adopting a positive mindset and focusing on the present moment, I can ensure that I make the most of every opportunity that comes my way.

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PLS ANSWE PLS NEED HELP ASAP

Answers

Answer:

D. 75

Step-by-step explanation:

Bc they are congruent that means that DAY has angles 60 and 45 so you add them together to get 105 and bc triangles are 180 deg, the last angle is 75 (180-105 = 75)

180-105 = 75. Sorry if wrong

Fifty eighth graders attend a
charter school. If 1/10 are
home with the flu and 2/3 of
the remaining students are
on a field trip, how many are
in school?

Answers

Answer:

15

Step-by-step explanation:

1/10 of 50 is 5, so remove that.

2/3 of 45 is 30, so remove that too.

therefore, 15 kids are in school

hope this helps!! <3

Zevel overheard Bradley say he got a 66% on the last test. If Zevel only got one-third what
Bradley got, what is Zevel's score?

Answers

Answer:

22

Step-by-step explanation:

66 ÷3=22

3= one third

i believe it’s 1.98 because if you divide 60% by 1/3 You get 1.98

Express the following number as a decimal:
2 x 10^-6

Answers

Answer:

0.000002

Step-by-step explanation:

2* 10^-6

is the same as

2 * 0.000001

which is

0.000002

Answer:

The answer is: 0.000002

Step-by-step explanation:

Have a great day!

A really fast armadillo can cross a road that is 20.00 meters wide in 10.00 seconds. What is the speed of the armadillo?
A. 2.0 m/s
B. 10 seconds
c. 10 meters
D. 200 m/s

Answers

Answer:

A

Step-by-step explanation:

Speed= Distance/time

20m/10s=2 m/s

The Huggins family went out to dinner. The price of the meal was $62.95. The sales tax is 8% of the
price of the meal. The tip is 15% of the meal and the sales tax. How much money did the family
pay for the meal, including tax and tip?

Answers

Answer:

$62.95 (meal) + $5.03 (sales tax) +$.75 (sales tax tip) + $9.44 (meal tip)

Total: $78.17

Answer:

$78.19

Step-by-step explanation:

To find the total after the sales tax is charged you have to do

$62.95 x 1.08 (1 = to the total and .08 to add sales tax value) =$67.986  round*

Now you take $67.99 (has been rounded) and multiply but .15 to find out what is 15% of $67.99 , it comes out to be 10.1979 (Round)

Now to finish you add $67.99 +$10.20 = $78.19

ILL MARK BRAINLIST IF YOU GET IT RIGHT .which expression is equivalent to s - t?

Answers

Answer:

s(6)×t(6)

hope this helps

They are variables
Are there supposed to be answer choices?

) Write an integer that represents the following scenario: Jenna deposited (put in) forty dollars into her savings account..

Answers

Answer:

hi blair. we go to school together.

Step-by-step explanation:

Find two consecutive integers whose sum is eleven less than three times the smaller integer.

Answers

Answer:

If you call the smaller integer "x" and the greater integer "y", then:

x+y=3x-11             The sum of the two is 11 less than 3 times the smaller

y=x+1                    Because they are consecutive, the greater must be 1 more than the smaller

Then you can solve for x:

x+(x+1)=3x-11       Substitute x+1 for y

2x+1=3x-11            Combine like terms

2x+12=3x               Add 11 to both sides

12=x                      Subtract 2x from both sides

The smaller integer is 12, thus the greater integer is 1 more or 13.

Check:

12+13=3(12)-11

25=36-11

25=25                       Yes, so the integers are 12 and 13

Step-by-step explanation:

thats pretty much it

help!!!! due now ( right answer's only)

Answers

Answer:

Minimum, Vertex(1,-7) and sorry what do you mean by aos? i dont get that please type in the comments I'll answer that too. Hope you understand the rest

Step-by-step explanation:

The vertex of a parabola means the stationary point/turning point which is denoted by the following:

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

and for y we just simply put the value of x that we get into the equation so lets get started

The equation [tex]y=x^2-2x-6[/tex] is a quadratic equation

and if we compare it by the standard form [tex]y=ax^2+bx+c[/tex] we get the following values

a=1 , b=-2 , c=-6

and now for the vertex

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

[tex]x=\frac{-(-2)}{2(1)} \\x=\frac{2}{2} \\x=1[/tex]

and now for y

[tex]y=x^2-2x-6\\y=(1)^2-2(1)-6\\y=1-2-6\\y=-7[/tex]

so the vertex is (1,-7)

and the graph is minimum not maximum because the value of a is greater than 0 if the value of a>0 then the graph is minimum and if the value of a<0 meaning a is negative the graph is maximum and here in the equation a=1 which means a>0 then our graph is minimum.

Answer:

hey we were talking in the comment section with someone else 16 min ago and that chat maxed out so he made another one and wants you to come back. Just letting you know.

Step-by-step explanation:

What is the solution?

-6x - 1 =23

Answers

Answer:

X=-4

Step-by-step explanation:

the first thing you do is add 1 to both sides to make the variable be alone

-6x=24

now divide 6 on both sides the variable cancels out and your left with 24/-6

so your answer is -4

The area of a rectangular painting is 5734cm^2
If the length of the painting is 94cm , what is its width?

Answers

Answer: 61cm

Step-by-step explanation:

So to work out this question you do 5734÷94 which would work out the with which is 61

61×94=5734

Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-2, 2)A(−2,2)A, left parenthesis, minus, 2, comma, 2, right parenthesis, B(6, 2)B(6,2)B, left parenthesis, 6, comma, 2, right parenthesis, C(6, 3)C(6,3)C, left parenthesis, 6, comma, 3, right parenthesis, and D(-2, 3)D(−2,3)D, left parenthesis, minus, 2, comma, 3, right parenthesis.
What is the area of rectangle ABCDABCDA, B, C, D?

Answers

The area of rectangle ABCD with the given vertices is: 8 units².

What is the Area of a Rectangle?

Area of rectangle = (length)(width).

Given the following vertices:

A(-2, 2)B(6, 2)C(6, 3)D(-2, 3)

Area = (length)(width) = (AB)(BC)

AB = |-2 - 6| = 8 units

BC = |2 - 3} = 1 unit

Area of rectangle = (8)(1) = 8 units².

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Answer: 8

Step-by-step explanation:

CAN SOMEONE HELP ME ?

Answers

Answer:

sure ill help

Step-by-step explanation:

Answer:

a+b=f

Step-by-step explanation:

180-f= c

180-(a+b)= c

SO

a+b= f

Find the value for x that makes the given equation true. - -4(3x – 7) + 5x = -2x + 8​

Answers

Answer:

Okay this might be slightly confusing but I'll try to make it simple. x = -10

Step-by-step explanation:

-4 ( 3x - 7 ) + 5x = -2x + 8 1. get rid of parenthesis first. -4 times 3x = -12x and -4 times -7 is 28

-12x + 28 + 5x = -2x + 8 2. Combine any like terms on each side of the equation. -7x + 28 = -2x + 8 3. Get rid of the smallest x value by adding to both sides -7x

+7x +7x

28 = -2x + 8 4. subtract 8 from both sides to get rid of it. (you wanna get x alone)

-8 -8

20 = -2x 5. Divide both sides by -2 to get 1x (which is x)

/-2 /-2

x = -10

Kylie is studying the change in the water level of Sweetgum Pond as part of a summer science experiment. In the first week of June, the change in the water level was – 4 centimeters. The next week it stormed almost every day, so the water level rose 7 centimeters.

Answers

Answer:

3 centimeters

Step-by-step explanation:

The computation of the change in the water level over the first two weeks of June is shown below:

= Rise in the water level - changed in the water level

= 7 centimeters - 4 centimeters

= 3 centimeters

hence, the change in the water level is  3 centimeter and the same is to be considered

We simply applied the above formula so that the correct value could come

Answer:

3

Step-by-step explanation:

A baseball player starts the season with 77 career home runs. Ten games into the
season, he has hit 2 home runs. Assume he continues at this pace. Write an
equation for the number of career home runs he has hit. How many career home
runs would you expect him to have at the end of the season (162 games)?

Answers

If there are a total of 162 games, and every then games the player hits 2 home runs, we can divide the total amount of games by 10 then multiply the quotient by 2.

162 / 10 is approximately 16.

16 × 2 = 32

32 + 77 = 109 career home runs

Using the slope intercept relation, the required equation and the number of home runs at season end would be ;

y = 0.2x + 77109

Recall :

y = bx + c

c = initial number of hime runs = 77b = slope y = total career home runs x = number of games played

Slope, b = 2 home runs per 10 games = 2/10 = 0.2

The expression can be represented thus:

y = 0.2x + 77

Number of home runs at the end of the season :

x = 162

y = 0.2(162) + 77

y = 32.4 + 77

y = 109.4

y = 109

Hence, Total number of hime runs would be 109.

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hii i need help with a geometry problem. the picture is attached. i'll mark you brainliest!!

Answers

Answer:

i would wanna say the first one

Step-by-step explanation:

∆GAS ≅IOL by rule ASA , SAA

We say that ∆GAS ≅ ∆IOL because m∠G = mI , mA = m∠L and AS = LO ( which means that these triangles are congruent under the ASA or SAA congruence postulate . )

Therefore ,

∆GAS ≅ ∆ILO by rule ASA , SAA

Pleasssssse help meeeeee

Answers

Answer: [tex]x \geq 3[/tex]

The graph has a closed circle pointing to the right

If SV is a perpendicular bisector of RT, which statement is true?

Answers

The correct answer is A. :)).

Answer:

The correct answer is A

Step-by-step explanation:

PLEASE ANSWER FAST.
The question is in the picture.
(question 24)

Answers

Answer:

As the values of x increase both function decrease in value.

Step-by-step explanation:

Lerna's Hydra is a mythological character that appears in some stories such as the 12 Tasks of Hercules. The Hydra was a one-headed monster but when it is cut off, 2 more heads grow in its place. If a hero tried to conquer it by cutting off all of its heads every day, how many heads would the Hydra have on the third day? And at the end of 10 days of trying to kill it? *

Answers

Answer:

Step-by-step explanation:

Initially the monster is one-headed, when it is cut off, 2 more heads grow in its place, when the two heads are cut off, 4 will grow in its place. This will go on an on and the amount of heads that grows each day will form a geometric sequance as shown;

1, 2, 4...

The nth term of an arithmetic sequence is expresses as;

[tex]T_n = ar^{n-1}[/tex] where;

a is the first term

r is the common ratio

n is the number of terms

To get the number of heads that the Hydra have on the third day, we will have to find the fourth term of the sequence since the first cutting was done the next day (second day).

from the sequence above;

a = 1

r = 2/1 = 4/2 = 2

T4 = 1(2)^{4-1}

T4 = 2^3

T4 = 8

Hence the hydra will have 8 heads on the third day.

To know the number of heads at the end of 10 days, we will find the 11th term of the progression

T11 = 1(2)^{11-1}

T4 = 2^10

T4 = 1024

He will have 1024 heads after 10 days of trying to kill the monster.

The number of heads that would the Hydra have on the third day is 8

And, at the end of 10 days of trying to kill it is 1024.

The calculation is as follows:

a = 1

r = 2 by 1 = 2  

T4

= 8

So the hydra will have 8 heads on the third day.

Now  

To know the number of heads at the end of 10 days, we will determine the 11th term of the progression

= 1024

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