Is the line perpendicular?
The situation is based on football. One player starts a couple of yards in the endzone while the other starts at the 8-9 yard line. The player in the endzone almost scores when he is tracked down by the guy on the 8-9 yard line. So does the starting position of these players form a perpendicular line?

[tex]\displaystyle\\Answer:\ sin(2\theta)=-\frac{4\sqrt{21} }{25} ,\ cos(2\theta)=\frac{17}{25}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\sin(\theta)=-\frac{2}{5} \ \ \ \ \ \ \ \ 270^0 < \theta < 360^0\\\\sin^2(\theta)+cos^2(\theta)=1\\\\cos^2(\theta)=1-sin^2(\theta)\\\\Hence,\\\\cos^2(\theta)=1-(-\frac{2}{5})^2 \\cos^2(\theta)=1-\frac{4}{25} \\\\cos^2(\theta)=\frac{25(1)-4}{25} \\\\cos^2(\theta)=\frac{21}{25} \\\\[/tex]

Extract the square root of both parts of the equation:

[tex]\displaystyle\\cos(\theta)=б\sqrt{\frac{21}{25} } \\\\cos(\theta)=б\frac{\sqrt{21} }{5} \\\\270^0 < \theta < 360^0\\\\Hence,\\\\cos(\theta)=\frac{\sqrt{21} }{5}[/tex]

[tex]\displaystyle\\a)\ sin(2\theta)=2sin(\theta)cos(\theta)\\\\sin(2\theta)=2(-\frac{2}{5})(\frac{\sqrt{21} }{5})\\\\sin(2\theta)=-\frac{4\sqrt{21} }{25}[/tex]

[tex]\displaystyle\\b)\ cos(2\theta)=cos^2(\theta)-sin^2(\theta)\\\\cos(2\theta)=(\frac{\sqrt{21} }{5})^2-(-\frac{2}{5})^2 \\\\cos(2\theta)=\frac{21}{25}-\frac{4}{25} \\\\cos(2\theta)=\frac{17}{25}[/tex]

Step-by-step explanation:

subtract the area of the phone from that of the phone

a) A recurrence relation for the number of bit strings of length n that contain three consecutive 0s :

a_n = a_(n-1) + a_(n-2) + a_(n-3) + 2^(n-3)   for n ≥ 3

b) The initial conditions are:

a_0 = a_1 = a_2 = 0 and a_3 = 1

c) There are 47 bit strings of length seven contain three consecutive 0s

Let s_n be a string of length n that does not have 3 consecutive 0's, and a_n be the number of strings  that contain three consecutive 0's

Consider a string of length n -1 that does not have 3 consecutive 0's, s_(n-1)

If we add 1 to this string, then we get a string s_n.

Consider a string s_(n-2)

If we add 10 at the end, then we get a string s_n

Now consider a string s_(n-3)

If we add 100 at the end we get a string s_n.

Now we got all possible strings s_n: that end in 1 (i.e. the last 3 digits could be 001, 011, 101 and 111),

Those strings that end in 10 (i.e. the last 3 digits could be 010 and 110)

and those strings  that end in 100. There are no other possibilities without having 3 consecutive zeros.

In the third case, there are a_(n-3) possibilities. And, in the fourth case, there are 2^(n-3) possibilities.

Hence the recurrence relation is

So, a_n = a_(n-1) + a_(n-2) + a_(n-3) + 2^(n-3)   for n ≥ 3

The initial conditions are a_0 = a_1 = a_2 = 0 and a_3 = 1

The recurrence gives the sequence of positive integers 0, 0, 0, 1, 3, 8, 20, 47, 107, 238, 520, 1121, 2391, . . . .

Hence there are a_7 = 47 bit strings of length seven that contain

three consecutive 0's.

Therefore, a) the recurrence relation:

a_n = a_(n-1) + a_(n-2) + a_(n-3) + 2^(n-3)   for n ≥ 3

b) Initial conditions: a_0 = a_1 = a_2 = 0 and a_3 = 1

c) there are 47 bit strings of length seven

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The mean absolute deviation over three period of time is 200

The absolute value of error in period 1 = 300

The absolute value of error in period 2 = 200

The absolute value of error in period 3 = -100

Total absolute value of error = The absolute value of error in period 1 + The absolute value of error in period 2 + The absolute value of error in period 3

Substitute values in the equation

Total absolute value of error  = 300 + 200 + 100

= 600

The mean absolute deviation = Total absolute value of error / 3

Substitute the values in the equation

The mean absolute deviation  = 600 / 3

= 200

Therefore, the mean absolute deviation is 200

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Answer:

The answer is B.

Step-by-step explanation:

Looking at the points gives you a x-axis and y-axis.

(x , y)

(-2 , 3) ,

(0 , 5) ,

(1 , 5) ,

(2 , 4) ,

(8 , -2)

Focus on the y-axis instead of the x-axis and list them.

{3 , 5 , 4 , -2}

Answer:

h

Step-by-step explanation:

because it shifts the graph to the left by 6 units

Type I errors (also known as a "false positive") occur when a test erroneously rejects a true null hypothesis. In other words, the test incorrectly concludes that the observed effect is significant or real when, in fact, it is not.

A type I error is a statistical mistake where the null hypothesis is rejected, despite it being true. This is also known as a false positive. This means that the test concluded that the observed effect was significant when in reality, it was not. Type I errors are more likely to occur when the sample size is small or when too many tests are conducted at once. To avoid type I errors, it is important to use an appropriate sample size and to consider the power of the test before conducting it.

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Yes, the starting position of these players form a perpendicular line.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Using Trigonometry

sin [tex]\theta[/tex] = 33.33/100

sin [tex]\theta[/tex] = 0.3333

[tex]\theta[/tex] = [tex]sin^{-1}[/tex] (0.3333)

[tex]\theta[/tex] = 19.469

cos 19.469 = B/ 100

0.9428 = B/ 100

B= 94.28

tan  [tex]\theta[/tex] = P/B

tan  [tex]\theta[/tex] = 94.28/ 33.33

[tex]\theta[/tex] = 70.5

Using Angle Sum property

< 3= 180 - (70.5 + 19.5)

<3 = 180 - 90

<3 = 90

Hence, they form perpendicular line.

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Answer:

7 feet

Step-by-step explanation:

Because they divided the length by 5 to get the scaled length so you would do the same for the width.

Answer:

26 inches squared

Step-by-step explanation:

If the real length is 30 feet and the scale drawing is 6 inches its 5:1

So if the actual width is 35 feet the scale drawing will be 7 inches

The perimeter is the sum of all sides of the rectangle, 2 sides have 6 inches and the other 2 sides are 7 inches

6+6+7+7= 26

One additional group would be required to conduct a 3 x 2 x 3 factorial design compared to a 3 x 2 x 2 design with independent variable.

A 3 x 2 x 3 factorial design requires three independent variables (x1, x2, and x3) with three levels each, for a total of 27 conditions. A 3 x 2 x 2 design, however, would only require two independent variables (x1 and x2) with two levels each, for a total of 12 conditions. To conduct a 3 x 2 x 3 factorial design, one additional group would be required, compared to the 3 x 2 x 2 design. This additional group would provide data for the additional 15 conditions that the 3 x 2 x 3 design would require.

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The time it take until 2000 people know about the rumor is 16 days.

The square root of a variety of is described because the value, which offers the variety while it's miles increased with the aid of using itself. The radical symbol √ is used to suggest the square root.  Radical is any other call given to the square root symbol. It is likewise called the surds. While Radicand is the variety gift beneath neath the square root symbol.

Find t, when N=200

N=5OO t^1/2

2000=500 t^1/2

t^1/2=4

t=16 days

Thus, the time it take until 2000 people know about the rumor is 16 days.

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Answer:

y = 4

Step-by-step explanation:

substitute x = 3 into the equation

y = 6(3) - (9 + 5) = 18 - 14 = 4

Answer: y=4

Step-by-step explanation:

y=6(3)-(9+5)

y=18-14

y=4

Writing the fraction 7/11 as a decimal gives a repeating decimal 0.636363 the sum of the first two digits is 90

The fraction 7/11 is written in fraction to give a repeating deicmal

Where decimal with repeats. Recurring decimal, often known as repeating  decimal, is a decimal number made up only of digits that repeat after the decimal at regular intervals.

The division inform of fraction when converted to decimal gives

0.636363

the sum of the first 20 decimals is 90

this is 6 ten times and 3 ten times

6 * 10 + 3 * 10

60 + 30

90

the sum is 20

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P(n) = 1³ +2³ +···+n³ = (n(n+1)/2)²

P(1) = 1³ = 1

According to statement P(n) = (n(n+1)/2)²

Checking for n = 1,

(n(n+1)/ 2)² = (1(1+1)/ 2)²

P(1) = (1 × 2/ 2)²

P(1) = 1² = 1

P(1) = 1³ = 1

So P(n) holds for n = 1.

The inductive hypothesis is that the statement holds for P(n). To prove this the inductive step under the assumption that the inductive hypothesis is true, we prove it is true for P(n + 1)

Let us assume P(n) = 1³ + 2³ + ... + n³ = (n(n+1)/ 2)²

Then P(n + 1) = 1³ + 2³ + ... + n³ + (n + 1)³ = (n(n+1)/ 2)² + (n + 1)³

P(n + 1) = (n(n+1)/ 2)² + n³ + 3n² + 3n + 1

P(n + 1) = ((n + 1)((n + 1) + 1)/ 2)²

As assuming P(n) holds, it is also true for P(n + 1) so it will be true for all values of n as it is proved already that P(1) is true.

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Answer: B

Step-by-step explanation:t+4+3−2.2t

Add 4 and 3 to get 7.

t+7−2.2t

Combine t and −2.2t to get −1.2t.

−1.2t+7

Answer: k=±`12

Step-by-step explanation:

[tex]ax^2-bx+c=0\\\\9x^2-kx+4=0\\\\D=b^2-4ac\\\\a=9\ \ \ \ b=-k\ \ \ \ c=4\\\\D=0\\\\Hence,\\\\D=(-k)^ 2-4(9)(4)=0\\\\k^2-144=0\\\\k^2=144\\\\k^2=12^2[/tex]

Extract the square root of both parts of the equation:

[tex]k=б\sqrt{12^2} \\\\k=б12[/tex]

Answer:

---------------------------------------------

A perfect square trinomial is:

Given trinomial:

Show this as:

Compare and find possible values of k:

the Central Limit Theorem, which states that as the sample size increases, the sampling distribution of the sample mean tends to become more normal.

The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean tends to become more normal. This means that the mean of the sample will be closer to the mean of the population, and the variability of the sample will be smaller. Since the sample proportion is just the mean of the sample, as the sample size increases, the distribution of the sample proportion will also become more normal. The larger the sample size, the more likely it is that the sample will accurately represent the population, and the more normal the distribution of the sample proportion will be. In other words, the sample proportion will be closer to the true population proportion, and the variability of the sample proportion will be smaller.

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The graph of the parabola declines through (-5, 2), (-3, 0), (-2, 0), (0, 1), (1, 2), (2, 3), (3, 5) on the x y coordinate plane represents the function.

A function is defined as the relation between the x and y coordinates such that no value of x maps to two values of y.

A vertical line test is a test used to determine whether the graph given is a function or not. This is a test where we draw a vertical line passing through a point x. If the graph is a function, then the vertical line will not intersects the graph at two points.

That is, no x coordinate maps to more than 1 y coordinate.

In the first graph of ellipse, the value -5 maps to two values 3 and 5. So this is not a function.

In the parabola all x values only maps to one y value. So this graph represents a function.

In the third graph, the value 3 maps to three values of y, 3, 2, and 1. So this is also not a function.

In the fourth graph, -2 maps to both 4 and 2, which also indicates that the given graph is not a function.

Hence the second graph of the parabola represents a function.

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Answer: B. X

Step-by-step explanation; I JUST DID IT(;

The area of the triangular dock is 19.5 square feet and the area of the rectangular box is 10 feet. The box will fit under the dock.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

Calculate the area of the triangle first,

Area = 1 / 2 x B x H

Area = 1/2 x 12 x 3.25

Area = 19.5 square feet

Calculate the area of the rectangle,

Area = L x W

Area = 2 x 5

Area = 10 square feet

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IT is found that the value of x is 4 and value of y is 5.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given system of equations are

2x-6y=22

-5x+y=1

The matrix form is

[tex]\left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}22\\1\end{array}\right][/tex]

Let as assume

[tex]A = \left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right]\\ \\X = \left[\begin{array}{ccc}x\\y\end{array}\right] \\B = \left[\begin{array}{ccc}22\\1\end{array}\right][/tex]

WE know that AX = B

Then we have;

[tex]\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}4\\5\end{array}\right][/tex]

Therefore, the value of x is 4 and value of y is 5.

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Answer:

Graph B

Step-by-step explanation:

First, simplify by subtracting 1 on both sides.

|x| + 1 - 1 < 3 - 1

|x| < 2

Using the absolute value definition, we know the inequalities are:

x < 2

-x < 2

Divide both sides by -1.

x < -2

If you multiply or divide both sides of an inequality by a negative number, you must flip the sign.

x > -2

x<2, x>-2

Graph B

Answer:

Graph A

Step-by-step explanation:

if x ≥ 0

x + 1 < 3

x < 3 - 1

x < 2

0≤ x < 2

if x < 0

-x + 1 < 3

-x < 3 - 1

-x < 2

x > -2

-2 < x < 0

Final solution

-2 < x < 2

The function that matches the graph is y(x)=(1-x)(x+2)^2

a function from a set X to the  set of Y assigns to each other element of X exactly one  element of Y. The set X is the  called the domain of to the  function of  the set Y is called as  the condominium of the functions.

From the graph the curve cross the x -axis at X=1

Therefore the expression is (x-1)

And at (-) x axis at X=-2 it is the turning point.

Therefore the expression is

(X+2)^2

And the point on y axis is (0,4)

Therefore the function can be written as

Y(x)=a(x-1)(x+2)^2

4= -4a≈a=-1

Therefore the function is y(x)

(-1)(x-1)(x+2)^2

= y(x)=(1-x)(x+2)^2

Therefore the function that matches the graph is y(x)=(1-x)(x+2)^2

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Answer:

C. The graph of the function does not form a straight line

The amount of taxes owed on a taxable income of $49,652 is $10,293.44.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Are the tax percentages for various amounts of income.

Now, From the given chart we conclude that $49,652 falls in the category of $41.176-$89.075 is 22% tax.

So, the Tax owed is 22% of $49,652.

∴ (22/100)×$49,652.

= $10,293.44.

So, an income of $49,652 owed 22% tax of the income which is $10,293.44.

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Answer:THE ANSWER IS B)6,600.44

Step-by-step explanation:

I got it right :)

Answer:

k = (-55) / 8

k = (-3005) / 8

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510((-255 + sqrt(65025 - 510(0.309016^2))) / 2)^2)) / 2)^2)) / 2

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510((-255 + sqrt(65025 - 1469.59)))))^2)) / 2)

To find the acute angle between two vectors, we can use the dot product formula:

angle = arccos((a * b) / (||a|| * ||b||))

where a and b are the vectors, * is the dot product, and ||a|| and ||b|| are the magnitudes of the vectors a and b, respectively.

In this case, the dot product of a and b is (i - kj) * (i + j) = i^2 - kj * i + kj * i + kj^2 = 2i - k^2j

The magnitudes of the vectors a and b are ||a|| = sqrt(i^2 + (-kj)^2) = sqrt(1 + k^2) and ||b|| = sqrt(i^2 + j^2) = sqrt(2).

Substituting these values into the formula above, we get:

angle = arccos((2i - k^2j) / (sqrt(1 + k^2) * sqrt(2)))

Since the angle is given to be 60 degrees, we can set this equal to 60 degrees and solve for k:

60 = arccos((2i - k^2j) / (sqrt(1 + k^2) * sqrt(2)))

We can use the inverse cosine function to solve for k:

k = sqrt(1 / (cos(60)^2 - (2i / sqrt(1 + k^2) * sqrt(2))^2))

Since cos(60) = 0.5, we can substitute this value in and solve for k:

k = sqrt(1 / (0.5^2 - (2i / sqrt(1 + k^2) * sqrt(2))^2))

k = sqrt(1 / (0.25 - (2i / sqrt(1 + k^2) * sqrt(2))^2))

k = sqrt(1 / (0.25 - (4i^2 / (1 + k^2) * 2)^2))

k = sqrt(1 / (0.25 - (16 / (1 + k^2))^2))

k = sqrt(1 / (0.25 - 256 / (1 + k^2)^2))

k = sqrt((1 + k^2)^2 / (256 - (1 + k^2)^2))

k = sqrt((1 + k^4) / (256 - 1 - 2k^2 - k^4))

k = sqrt((k^4 + 1) / (255 - 2k^2))

We can then solve for the roots of this equation to find the possible values of k:

k = sqrt((k^4 + 1) / (255 - 2k^2))

k^4 - (255 - 2k^2)k^2 + 1 = 0

This is a quartic equation and can be solved using the quartic formula:

k = sqrt((-b +- sqrt(b^2 - 4ac)) / 2a)

where a, b, and c are the coefficients of the polynomial. In this case, a = 1, b = -(255 - 2k^2), and c = 1.

Substituting these values into the quartic formula, we get:

k = sqrt((-(-(255 - 2k^2)) +- sqrt((-(255 - 2k^2))^2 - 4 * 1 * 1)) / 2 * 1)

k = sqrt((255 - 2k^2 +- sqrt((255 - 2k^2)^2 - 4)) / 2)

k = sqrt((255 - 2k^2 +- sqrt(255^2 - 510k^2 + 4k^4)) / 2)

k = sqrt((255 - 2k^2 +- sqrt(255^2 - 510k^2)) / 2)

k = sqrt((255 - 2k^2 +- sqrt(65025 - 510k^2)) / 2)

Solving for the roots of this equation gives us the possible values of k:

k = (-255 + sqrt(65025 - 510k^2)) / 2

k = (-255 - sqrt(65025 - 510k^2)) / 2

The first equation gives us one possible value of k:

k = (-255 + sqrt(65025 - 510k^2)) / 2

Substituting k = (-255 + sqrt(65025 - 510k^2)) / 2 into the second equation gives us the second possible value of k:

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510k^2)) / 2)^2)) / 2

Simplifying this expression gives us the final possible value of k:

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510((-255 + sqrt(65025 - 510k^2)) / 2)^2)) / 2)^2)) / 2

Therefore, the possible values of k are:

k = (-255 + sqrt(65025 - 510k^2)) / 2

k = (-255 - sqrt(65025 - 510((-255 + sqrt(65025 - 510k^2)) / 2)^2)) / 2

solve for k in each

To solve for k in the first equation, we can isolate k by moving everything else to the right side of the equation:

k = (-255 + sqrt(65025 - 510k^2)) / 2

2k = -255 + sqrt(65025 - 510k^2)

2k + 255 = sqrt(65025 - 510k^2)

(2k + 255)^2 = 65025 - 510k^2

4k^2 + 1020k + 65025 = 65025 - 510k^2

4k^2 + 1530k + 65025 = 0

This is a quadratic equation, and we can use the quadratic formula to solve for k:

k = (-b +- sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the polynomial. In this case, a = 4, b = 1530, and c = 65025.

Substituting these values into the quadratic formula gives us:

k = (-1530 +- sqrt(1530^2 - 4 * 4 * 65025)) / 2 * 4

k = (-1530 +- sqrt(3080400 - 2601000)) / 8

k = (-1530 +- sqrt(477900)) / 8

k = (-1530 +- sqrt(222725)) / 8

k = (-1530 + 1475) / 8

k = (-55) / 8

k = (-1530 - 1475) / 8

k = (-3005) / 8

Therefore, the solutions to the first equation are:

k = (-55) / 8

k = (-3005) / 8

The result of executing the code segment is -2

The complete question is added at the end of this solution as an attachment

The code in the question is given as

IF X > Y

  DISPLAY X + Y

ELSE

  DISPLAY X - Y

Given that

X = 3 and Y = 5

When x and y are compared, we have the truth value to be

Y > X

This means that the executed segment is

DISPLAY X - Y

So, we have

DISPLAY 3 - 5

Evaluate

DISPLAY -2

Hence. the displayed result is -2

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The equation of function for the given problem is y = 3x + 12.

What is point slope form of the line?

For linear equations, the general form is y - y1 = m(x - x1).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

Given:

A bathtub has some water in it. Mia turns on the faucet to add more water.

The total amount of water in gallons, y, is a function of the time in minutes since Mia turns on the faucet, a.

The graph of the linear function passes through the points (4, 24) and

(6, 30).

We have to find the equation of function.

Let the linear function passes through the points (4, 24) and (6, 30).

First to find the slope of equation using given points.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{30-24}{6-4} = \frac{6}{2} = 3[/tex]

Now to find the equation of function.

Consider the point slope form of the line,

[tex]y-y_1=m(x-x_1)[/tex]

Plug the values of m = 3 and [tex](x_1,, y_1) = (4, 24)[/tex]

⇒

[tex]y-24=3(x-4)\\y-24=3x-12\\y=3x-12+24\\y=3x+12[/tex]

Hence, the equation of function for the given problem is y = 3x + 12.

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Answer:

---------------------------------

Given function:

Find f(-7) by plugging in the value of x:

The distance the ball drops in the next 8 second is: 640 m. Using the concept of equation of motion.

An item is considered to be at rest when its position doesn't alter throughout time. An item is considered to be in motion if, over time, its location changes.

It is possible to build a relationship using a series of equations between the body's velocity, acceleration, and the distance it travels in a given amount of time when the body is travelling in a straight line with uniform acceleration. The term "motion equations" refers to these equations.

D = kt²  where D is the constant of proportionality.

D = 80 m

t = 4 seconds

Putting the values we get -

80 = k(4)²

or, k = 80 / 16

or, k = 5.

So the equation of motion is D = 5t²

When t = 8+4 = 12 seconds

now, D = 5(12)² =  5×144

or, D =  720 m

So, the distance the ball drops in the next 8 seconds = 720 - 80

= 640 m.

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