The height h (in feet) of an object dropped from a window after x seconds can be modeled by h(x)=−16x2+64 . The object is dropped a second time so that it hits the ground 1.5 seconds sooner. Write a function g that models the path of the object the second time it is dropped.

Answers

Answer 1

Answer:

g(x) = - 16x² + 4

Step-by-step explanation:

Given the model:

First drop:

h(x) = - 16x² + 64

Second drop hits the ground 1.5 seconds sooner

Function g(x) to model the second drop:

-16t² + V0t + h0

h(x) = - 16x² + 64

0 = - 16x² + 64

16x² = 64

x² = 64/16

x = 2

1.5 seconds sooner :

X = 2 - 1. 5

x = 0.5

0 = - 16(0.5)² + 0 + h0

0 = - 4 + h0

h0 = 4

Hence,

g(x) = - 16x² + 4


Related Questions

Which professional’s advice is Peter seeking?
Peter wants to buy office space for his new business. However, he is not sure if the current market is suitable for buying property. Hence, he consults his agent for advice.

Answers

Answer:Real estate agent

Step-by-step explanation:

got it right

Answer:

Real Estate Agent

Step-by-step explanation:

A ladder is resting against a wall. The foot of the ladder is `5`feet from the wall, and the top of the ladder is `16`feet from the ground. What is the slope of the ladder?

Answers

Step-by-step explanation:

that's wrong .....wait ...........

Rewrite the equation without absolute value.
y=|x-3|+|x-2|-|x-5|

Answers

Answer:

  y = {-x, x < 2; x-4, 2 ≤ x < 3; 3x -10, 3 ≤ x < 5; x, 5 ≤ x}

Step-by-step explanation:

The absolute value function is a piecewise linear function that changes its definition when its argument changes sign.

Here, the three different absolute value expressions will change their behavior at three different values of x. That is, this equation will be described by a piecewise linear function in four (4) pieces.

For x < 2:

  y = (3 -x) +(2 -x) -(5 -x) = -x

For 2 ≤ x < 3:

  y = (3 -x) +(x -2) -(5 -x) = x -4

For 3 ≤ x < 5:

  y = (x -3) +(x -2) -(5 -x) = 3x -10

For 5 ≤ x:

  y = (x -3) +(x -2) -(x -5) = x

In summary, the equation can be written ...

  [tex]y=\begin{cases}-x,&\text{for }x < 2\\x-4,&\text{for }2\le x < 3\\3x-10,&\text{for }3\le x < 5\\x,&\text{for }5\le x\end{cases}[/tex]

_____

Additional comment

The absolute value function itself can be described by ...

  [tex]y=|x-a|=\begin{cases}a-x,&\text{for }x < a\\x-a,&\text{for }a\le x\end{cases}[/tex]

The slope of a line is 2/3 . What is the slope of a line that is perpendicular to this line?


- 3/2

Answers

Step-by-step explanation:

for perpendicular:

m1×m2= -1

Which of the following differences could not give a distance between two points on a number
line? Explain why.

(1) 19-7
(3) -12 -(-7)
(2) -3-(-18)
(4) 14-(-6)

Answers

Answer:

Choice: (3) -12 -(-7)

Step-by-step explanation:

The distance between two points is by definition a positive number. If we wanted to know the distance between points 5 and 8, we should use the absolute value of the difference:

d=|5-8|=8-5=3

The same applies to negative points like -2 and -7:

d=|-2+7|=|2-7|=7-2=5

The only choice that does not result in a positive distance is (3) because

-12-(-7)=-12+7=-5

Thus this is not a distance between two points on a number line.

Choice: (3) -12 -(-7)

State the period, midline, amplitude, and range of the given graph. (I got them wrong, I will mark brainliest!)

Answers

Answer:

Period:  [tex]\pi[/tex]

Midline:  y = -3

Amplitude:  4

Range:   [-7, 1]

Step-by-step explanation:

Period - from one peak to the next (or from one trough to the next)

⇒ Period:  [tex]\pi[/tex]

Midline - center line

Range = -7 ≤ f(x) ≤ 1

[tex]\implies \sf midline =\dfrac{1-(-7)}{2}+(-7)=-3[/tex]

⇒ Midline:  y = -3

Amplitude - height from the center line to the peak (or to the trough)

Maximum height:  y = 1

center line:  y = -3

Therefore, amplitude = 1 - (-3) = 4

Range - the set of all values that the function takes

-7 ≤ f(x) ≤ 1  →  [-7, 1]

#Period

Find the distance between two peaks

It's π

#Midline

Range of the pitch (Peak to trough distance)

(-7,1)

Midline:-

[tex]\\ \tt\Rrightarrow \dfrac{1+7}{2}-7=4-7=-3[/tex]

Midline is y=-3

#Amplitude

Midline is y=-3Trough=y=-7

Distance:-

A=-3+7=4

#Range

The pitch

[-7,-1]

Please Help its A Math Problem!!! Please & thank you

Answers

Answer:

The last one is correct answer.

what is 0.6x + 4.8 = 7.2

Answers

Answer:

2.88x=7.2

x=7.2/2.88

x=2.5

=)

Answer:

x=4

Step-by-step explanation:

btw that's what M a t h w a y.

pleaase help meeeeee
³√125

Answers

Answer:

5

Step-by-step explanation:

hope this helps!

The correct answer is 5

AB←→is reflected to form ​​ ​A'B'←→−​.


The coordinates of point A are (0, 2) and the coordinates of point B are (2, 5).


Which reflection results in the transformation of AB←→​ to ​A'B'←→−?





reflection across the x-axis.


reflection across the y-axis


reflection across y = x.


reflection across y=−x.

Answers

Answer: reflection across y = x

Step-by-step explanation:

Answer:

Rotation of 180°

Step-by-step explanation:

solve for x (x+2)(x-1)

Answers

Answer:

See below.

Step-by-step explanation:

Given :-

x + 2x - 1

To Find :-

Values of x

Solving :-

x + 2 = 0x = -2x - 1 = 0x = 1

Solution :-

x = -2x = 1

A line with a slope of

6 passes through the points (

6,

5) and (

7,c). What is the value of c?

Answers

Answer:

c=11

Step-by-step explanation:

We have two points ( 6,5) and (7,c) and a slope of 6

The slope formula is

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

6 = (c-5)/(7-6)

6 = (c-5)/1

6 = c-5

Add 5 to each side

6+5 = c-5+5

11 =c

A tent has the shape of a pyramid on a rectangular base of length 6 meters and width 4 meters.How much space is inside the tent if its 5 meters high​

Answers

Answer:

Space inside tent is 60m³

Step-by-step explanation:

Given length 6m, width 4m is rectangular base and height of tent 5m

Space = Volume of Pyramid = × area of base × height

× 6 × 4 × 5 = 60m³

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

Determine the missing interior and exterior angles of the triangle shown below.

Answers

Answer:

∠c=50°, ∠1=95°, ∠2=135°, ∠3=130°

Step-by-step explanation:

Let's start with [tex]c[/tex]. We know that, universally, every angle in a triangle will add up to be 180°. Therefore, we do [tex]45+85=130[/tex]. Then, [tex]180-130=50.[/tex] This means ∠[tex]c[/tex] = 50°.

Then, for the other angles, we can use the rule that a straight line is equal to 180°. So for example, ∠1 + 85° = 180.

As a result:

∠1 = [tex]180-85=95[/tex]°

∠2 = [tex]180-45=135[/tex]°

∠3 = [tex]180-50=130[/tex]°

50 POINTS!
Determine which function has the greater rate of change, if either.


A. Function B has a greater rate of change because it's rate of change is 4/3

B. Function A has a greater rate of change because it's rate of change is 4/3

C. Neither function has a greater rate of change because their slopes are both 4/3

EXPLAIN

Answers

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

so let's get two points from each table to get their slope or rate

for function A hmmm (2 , -5) and (6 , -2), and for function B hmmm (-5, -46) and (7 , -30)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}}\implies \cfrac{-2+5}{4}\implies \stackrel{\textit{\Large A}}{\cfrac{3}{4}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-46})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-30})[/tex]

[tex]\stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-30}-\stackrel{y1}{(-46)}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{(-5)}}}\implies \cfrac{-30+46}{7+5}\implies \cfrac{16}{12}\implies \stackrel{\textit{\Large B}}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{\Large B}}{\cfrac{4}{3}}~~ > ~~\stackrel{\textit{\Large A}}{\cfrac{3}{4}}~\hfill[/tex]

What is the value of x in the equation −x = 6 − 4x + 18? (1 point) 24 8 −8 −24​

Answers

Answer:

-8

Step-by-step explanation:

-24=6-(4x24)+18= 6-96+18=-90+18=-72

-8=6-(4x8)+18= 6-32+18=-26+18=-8

Which of these is a reason an engineer may choose to use a prefabricated building component?

Answers

Answer: She wants to reduce costs

Step-by-step explanation:

Answer:

She wants the construction to move more quickly

Step-by-step explanation:

this was the correct answer as shown on the quiz. the choices were changed

PLEASE HELP! I WILL MAKE YOU BRAINLIST!

Answers

Answer: I think it is C

Step-by-step explanation: 32/4=8 so 1 cm = 8km

simplified?


0.018 + (3.1 × 10^-3)

Answers

Answer:

the answer is easy.. I'm glad to help you out. it is 0.018+ 3.1 × 10^-3. just simply remove the bracket

A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is x overbar, while the standard deviation is s. what is the 99% confidence interval for the population mean? use the table below to help you answer the question. confidence level 90% 95% 99% z*-score 1.645 1.96 2.58 x overbar plus-or-minus startfraction 0.90 times s over startroot n endroot endfraction x overbar plus-or-minus startfraction 0.99 times s over startroot n endroot endfraction x overbar plus-or-minus startfraction 1.645 times s over startroot n endroot endfraction x overbar plus-or-minus startfraction 2.58 times s over startroot n endroot endfraction

Answers

The 99% confidence interval for the population mean will be x± [tex]\frac{2.58 s}{\sqrt{n} }[/tex].

What is a confidence interval?

A confidence interval is a set of calculations for an unrecognized parameter that is specified as a range with a lower and upper bound.

If we take an n-sample from a normal population and wish to estimate the population mean, the confidence interval for the mean is:

[tex]\bar x[/tex]±[tex]Z_\frac{\alpha }{2} \times \frac{s}{\sqrt{n} }[/tex]

The level of significance is found by;

[tex]\rm \alpha =1- \ condifidence\ level \\\\\ \rm \alpha =1- 0.99 \\\\\ \rm \alpha = 0.001[/tex]

The value of z is

[tex]\rm Z_{\frac{\alpha}{2}} = \rm Z_{\frac{0.01}{2}} = Z_{0.005}=2.58[/tex]

Hence the 99% confidence interval for the population mean will be[tex]\frac{2.58 s}{\sqrt{n} }[/tex].

To learn more about the confidence interval refer to the link;

https://brainly.com/question/2396419

Answer:

x Overbar plus-or-minus StartFraction 2.58 times s Over StartRoot n EndRoot EndFraction

Step-by-step explanation:

The answer above is correct.

Solve for n.

11(n – 1) + 35 = 3nSolve for n.

11(n – 1) + 35 = 3n

Answers

Answer:

n is equal to -3

Step-by-step explanation:

11n - 11 + 35 = 3n

11n + 24 = 3n

11n - 3n = -24

8n = -24

n =-3

Answer:

n is equal to -3

Step-by-step explanation:

.

Which expression can you use to find 16÷45?

Answers

Answer:

☆<《HOPE IT WILL HELP YOU >

Step-by-step explanation:

Exprassion is 16/45--x=0

Answer:

16 x 5/4

Step-by-step explanation:

u change  division to multiplication then flip the fraction.

tada!

:)

Manny invested $1,200 at a simple interest rate of 5% (0.05). How much money would he have after 7 years?

Answers

Manny will have $1,620

Mike received 79 dollars and 9 movie tickets for his birthday. He went to
a sporting goods store and bought a baseball glove, baseball, and bat. He had
22 dollars left over, how much did he spent on the baseball gear?

Answers

Answer:

57

Step-by-step explanation:

79-22=57

Write the following quotient in scientific notation:

Answers

Step-by-step explanation:

Let's start by simplifying our light terms.

[tex]q = \frac{33 \times 10 {}^{9} }{11 \times 10 {}^{7} } [/tex]

33 is divisible by 11 so i can simplify up and down by 11.

[tex]q = \frac{3 \times 10 {}^{9} }{1 \times 10 {}^{7} } [/tex]

Now i have 10^9 in the numerator and 10^7 in the denominator. I can remove 10^7 from up and down to get;

[tex]q = \frac{3 \times 10 {}^{9 - 7} }{1 \times 10 {}^{7 - 7} } = \frac{3 \times 10 {}^{2} }{1 \times 10 {}^{0} } = \frac{3 \times 10 {}^{2} }{1 \times 1} [/tex]

[tex]q = 3 \times 10 {}^{2} [/tex]

And that is your scientific notation.

Given the sequence: 4.5, 5.75, 7, 8.25, Find the common difference

Answers

Answer:

1.25 is the common difference

Step-by-step explanation:

The difference of this equation is 1.25

Bob made 25 free throws out of 40 free throws he attempted every 5 minutes. How many free throw did bob make in 12 minutes

Answers

Answer: 300

Step-by-step explanation: 25 times 12 = 300. 20 times 12 = 240. 5 times 12 = 60. 60 + 240 = 300

Answer:

300

Step-by-step explanation:

25 times 12 = 300. 20 times 12 = 240. 5 times 12 = 60. 60 + 240 = 300

How many distinct permutations can be formed using the letters of the word believable?

Answers

Answer:

✒️Answer:

No. of Permutations=3360.

Step-by-step explanation:

#CarryOnLearning

[tex]watch.some.anime[/tex]

The number of distinct permutations that can be formed using the letters of the word believable is 15,1200.

What are permutation and combination?

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

It is given that:

The word is:

"believable"

Total number of letters = 10

b repeated two(2) times

e repeated three(3) times

l repeated two(2) times

No. of Permutations = 10!/(2!3!2!)

No. of Permutations = 15,1200

Thus, the number of distinct permutations that can be formed using the letters of the word believable is 15,1200.

Learn more about permutation and combination here:

https://brainly.com/question/2295036

#SPJ5

If h(x) = −2x − 10, find h(−4).

Group of answer choices

−16

−2

−18

−3

Answers

Answer:

-2

Step-by-step explanation:

h(x) = −2x − 10, find h(−4).

h(−4) = -2 × (-4) - 10

= 8 - 10

= -2

Answer:

-2

Step-by-step explanation:

did the test

Food cost for the last 5 months has been 600. What is the average amount spend?

Helppppppppp

Answers

Answer:

The average amount spent is $120

Step-by-step explanation:

To find the average, divide 600 by 5 to get 120.

Answer:

120

Step-by-step explanation:

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