The product of the monomials is 32x^7y4
What is a monomial?A monomial is said to be a product of powers of variables with a non-negative integer exponents, or a product of variables.
Monomials include numbers, variables or multiple numbers or variables multiplied together.
Given the monomials;
(4x²y)(8x^5y³)
Finding the product is simply done by multiplying the two expressions, we have
The product of the numbers = 4 × 8 = 32
The product of the 'x' variables = x^2 + 5 = x^7
The product of the 'y' variables = y^1 + 3 = y^4
32x^7y4
Thus, the product of the monomials is 32x^7y4
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question in the picture
The salary after 6 years is $83,000.
The salary after tt years is 53,000 + 5000tt.
What is her total salary?The equation that can be used to determine Aisha's salary after a period of time can be represented by a linear equation. This is because that her salary increases by a constant rate each year.
A linear function represents a straight line when drawn on a coordinate plane. A linear function is a function that has a single variable raised to the power of 1. An example is y + 2. The variable y is raised to the power of 1. 2 is the constant term.
Total salary = beginning salary + (rate of increase x number of years)
Salary after 6 years: 53,000 + (5,000 x 6)
= 53,000 + 30,000 = $83,000
Salary after tt years: 53,000 + (5,000 x tt)
53,000 + 5000tt
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Find the seventh term of each geometric sequence. 1,-3,9, . . . . . . .
The seventh term of the given geometric progression is: 729.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Now,
Given GP: 1, -3, 9, .....
Here, a₁ = 1
a₂ = a₁ (r)
=> 3 = 1 (r)
=> r = 3
Thus, a₇ = a₁ (r⁷⁻¹) = 1 (3⁶) = 729.
Hence, The seventh term of the given geometric progression is: 729.
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-3(x + 2) > 15 or x-3 <-1
Answer:
-7
Step-by-step explanation:
-3x-6>15
-3x/-3>21/-3=-7
x<-1+3
x<2.
What is the value of x in the equation 6(x-4)=3 x ?
The value of x in equation is 8
To find the value of x, we will solve the given mathematical expression based on the sequence of signs and placement of bracket. Firstly bracket will be solved followed by subtraction or addition.
Rewriting the equation -
6(x - 4) = 3x
Performing multiplication on Left Hand Side of the equation to find the value of x
6x - 24 = 3x
Shifting 3x and 24 to other side of equation
6x - 3x = 24
Performing subtraction on Left Hand Side of the equation
3x = 24
Shifting 3 to other side of equation as denominator
x = 24 ÷ 3
Performing division on Right Hand Side of the equation
x = 8
Hence, the value of x is 8.
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f(x) = -x + 4 and g(x) = x2 - 5, then g(f(3)) = ?
Find two pairs of whole numbers with a geometric mean that is also a whole number. What condition must be met in order for a pair of numbers to produce a whole-number geometric mean?
2 and 18 are the two pairs of whole numbers with a geometric mean that is also a whole number.
The geometric mean is defined as the nth root of the product of n numbers, which means for a set of numbers x1, x2, ..., xn. The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc.
For example, we multiply them: 2 × 18 = 36
Then (as there are two numbers) take the square root: √36 = 6
Conditions: The square roots of the product of the pair of numbers must be whole-number. These two conditions must be met to have an exact geometric mean
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Martina has 16 cars available to rent. let c be the number of cars she would have left after renting r of them. write an equation relating c to r. then use this equation to find the number of cars she would have left after renting 14 of them.
If Martina has 16 cars available to rent, and if c is the number of cars she would have left after renting r of them, then the equation relating c to r will be c = 16 - r, and the number of cars she would have been left with after renting 14 of them is calculated to be 2.
An algebraic expression is a type of expression consisting of both numerals and letters.
If Martina has a total of 16 cars available to rent, then the equation or algebraic expression relating c to r is,
c = total number of cars available to rent - r
c = 16 - r
After renting 14 of the total cars available, then the number of cars left can be calculated using this equation,
c = 16 - r
c = 16 - 14
c = 2
Thus, the number of cars she would have been left with is calculated to be 2.
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BN.
Anna, Bob and Chris did will not disclose their weights but agree to be weighed in pairs. Anna and Bob together weigh 226 pounds. Bob and Christ together weigh 210 pounds. Anna and Chris together weigh 200 pounds. How
does each student weigh?
Anna , Bob , Chris weigh 108 pounds , 118 pounds , 92 pounds respectively .
Solve a linear equation in three variables by completing the following steps: Take any two equations and solve them for one variable Again, take two more pairs of equations and solve for the same variables. We have two systems of equations with two unknown variables. solve two equations Again, substitute the calculated values of the variables into one of the original equations and solve for the unknown variables.Let the Anna weigh = x pounds
Let the Bob weigh = y pounds
Let the Chris weigh = z pounds
According to the question Anna and Bob together weigh 226 pounds which can be written as [tex]x+y=226[/tex] ..(1)
According to the question Bob and Christ together weigh 210 pounds. which can be written as [tex]y+z=210[/tex] ...(2)
According to the question Anna and Chris together weigh 200 pounds. which can be written as [tex]x+z=200[/tex] ..(3)
From equation (1) [tex]y=226-x[/tex] putting this value in equation (2) , we get
[tex]226-x+z=210\\16=x-z\\16+z=x[/tex] ..(4)
Putting above value in equation (3) , we get
[tex]16+z+z=200\\2z=184\\z=92[/tex]
Putting z = 92 in equation (4) , we get
[tex]x=16+92\\x=108[/tex]
Putting x = 108 in equation (1) , we get
[tex]y=226-108\\y=118[/tex]
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The three interior angles of a triangle have a sum of 180°. If two of the three angles are complementary, which conclusion is accurate?
OA) The triangle is acute.
OB) The triangle is right.
OC) The triangle is obtuse.
OD) The triangle is isosceles.
The three interior angles of a triangle have a sum of 180°. If two of the three angles are complementary, then the triangle is right. The correct option is B
What is a triangle?A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.
Types of triangles are isosceles, scalene and equilateral triangles. Two angles are said to be complementary if their sum is 90 degrees.
The three interior angles of a triangle have a sum of 180°. If two of the three angles are complementary, then the triangle is right.
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Write an equation for each vertical translation of y=f(x) .
2 units up.
The equation for the vertical translation of y=f(x). 2 units up is y=f(x)+2.
Using equations of the form y=f(x), you may be able to modify the graph in various ways. For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. Understanding these transformations makes it easy to graph different functions. Start with a "basic model" and apply a series of transformations/modifications to change it to the desired function.
A point on the graph of y=f(x) has the shape (x,f(x)).
The points on the graph of y=f(x)+2 are of the form (x,f(x)+2).
So, the graph for y=f(x) +2 is the same as the graph for y=f(x) shifted up by 2 units.
The new equation is:
y=f(x)+2
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Sven is trying to find the maximum amount of time he can spend practicing the five scales of piano music
he is supposed to be working on. He has 80 minutes to practice piano and would like to spend at least 45
minutes playing songs instead of practicing scales. So, Sven sets up the following inequality, where t is
the number of minutes he spends on each scale, and solves it.
80-5t < 45
-5t -35
t≥7
Step-by-step explanation:
i thank the answer is 10.5 thanks for your question
The graph models the linear relationship between temperatures in degrees Fahrenheit and temperatures in degrees Celsius.
What is the rate of change of the temperature in degrees Fahrenheit with respect to the temperature in degrees Celsius?
According to the question, the model has linear relationship between the temperatures which are in degree Fahrenheit and in Celsius.
Now, to calculate the rate of change of the temperature which is defined in the ratio of y-axis and x-axis. Therefore, the expression can be written as:
Rate of change of the temperature = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
From the graph model, the coordinate values are (0,32) and (30,86)
[tex]x_{2} = 30; x_{1}=0; y_{2}=86; y_{1}=32[/tex]
Substituting the given values in the standard expression to calculate the rate of change of the temperature:
Rate of change of the temperature = [tex]\frac{86-32}{30-0}=\frac{54}{30} =\frac{9}{5}[/tex]
Hence, the rate of change of the temperature is 9/5.
What is rate of change in the graph?
In the graph, the rate of change of a quantity defines the relationship between the two quantities. The calculated values are either positive, negative or zero. It is a slope of a line in the form of ratio of vertical to horizontal axis.
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18. If ZW and ZV are supplementary angles and m2V = 49°, find m/W.
19. If 21 and 22 are vertical angles, <2 and <3 are complementary angles,
and m23 = 56°, find m21.
Answer:
Step-by-step explanation:
18. Supplementary angles add up to 180°therefore
∠W+∠V=180°
∠W+49°=180°
∠W=180°-49°
∠W=131°
19.Complementary angles are angles that add up to 360°
∠2+∠3=90°
∠2+56°=90°
∠2=90°-56°
∠2=34°
Vertical angles are equal therefore this tells us that ∠1 and ∠2 are equal
∠1=∠2
∴∠1=34°
20. Angles which are in a linear pair add up to 180°(supplementary)
Mathematically what the statement is sayin is :
∠1+∠2=180°
and ∠1=5(∠2)-18°
therefore we can plug in ∠1=5(∠2)-18° in ∠1+∠2=180°
(5(∠2)-18°)+∠2=180°
5(∠2)+∠2=180°+18°
6(∠2)=192°
[tex]\frac{6 < 2}{6} =\frac{198}{6} \\ < 2=33[/tex]
∠1=5(33°)-18°
∠1=165°-18°
∠1=147°
5) Diego had a pizza that was divided into 8 equal slices. He ate 3 of them. Hector has a pizza that
is the same size, but his is divided into 4 equal slices. He ate 3 slices of his pizza. Who ate more
pizza?
In 2006,500 million songs were legally downloaded from the Internet. In 2004, 200 million songs were legally downloaded.
b. Find the slope of the line, and interpret its meaning.
The slope of the line is 150.
It is given the number of songs (in million) downloaded from the internet in 2006 and 2004.
We actually need to graph this data which will be a straight line. We try to find two points in this graph using the given data.
Represent the years as x coordinates and the number of songs as y coordinates. Also take 2006 as 6 only and 2004 as 4 only for convenience.
Now we get two points [tex](x_1,y_1)[/tex] = (4, 200) and [tex](x_2,y_2)[/tex] = (6, 500)
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{500-200}{6-4}[/tex] = 300/2 = 150
Here the slope is positive, which means that the number of downloads are increasing with increase in years. The rate of change in number of downloaded songs from internet is 150 million in two years.
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Find the geometric mean between pair of numbers.
√20 and √80
The geometric mean between pair of numbers √20 and √80 is 6.32
We know that for a sequence of numbers x1, x2,.., xn
The formula of geometric mean is,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have been given two numbers √20 and √80
We need to find the geometric mean between pair of numbers, √20 and √80
Using the formula for the geometric mean,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have two numbers.
So, the value of n is 2.
[tex]\Pi=\sqrt{\sqrt{20}\times \sqrt{80} }\\\\ \Pi=\sqrt{\sqrt{1600} }\\\\ \Pi=\sqrt{40}\\\\ \Pi=6.32[/tex]
Therefore, the geometric mean between pair of numbers √20 and √80 is 6.32
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Find the 17 th term of each sequence. a₁₈ = 32, d=-4
36 is 17th term of sequence a₁₈ = 32, d=-4
Given the 18th term and the common difference, we subtract the common difference from the 18th term to determine the 17th term:
a₁₇ = a₁₈ - d
= 32 - (-4)
= 36
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Find the value of x to the nearest tenth. 228.4= πx
x = 73 is the value of x.
What exactly do we mean by a value?A value in mathematics is a number that indicates the result of a calculation or function.So, in the preceding example, you could tell your teacher that 5 x 6 equals 30 or that x + y equals 9 if x = 6 and y = 3.A value is another term for a variable or constant.To find the value of x:
Given: 228.4/x = πAfter we have entered the value of π, we will simplify the given equation to find the value of x.So,
228.4/x = π228.4/x = 3.14159228.4/3.14159 = xx = 72.702039Then rounding to the nearest tenths gives x = 73.
Therefore, x = 73 is the value of x.
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26 divided by 5 1/5 Help!!
You bought a total of 6 pens and pencils for 4 . If each pen costs 1 and each pencil costs .50 , how many pens and pencils did you buy?
I bought 2 pens and 4 pencils from given amount.
Let us represent the number of pens and pencils as x and y respectively. Forming the equation as per the given information -
Equation representing total number of pens and pencils bought
x + y = 6 - Equation 1
Rearranging the equation 1 as per the variable x
x = 6 - y - Equation 2
Equation representing cost of bought pens and pencils
1x + 0.5y = 4 - Equation 3
Keep the value of x from Equation 2 in Equation 3
1 (6 - y) + 0.5y = 4
6 - y + 0.5y = 4
Rearranging the equation for positive sign on each side -
y - 0.5y = 6 - 4
Performing subtraction on Right Hand Side of the equation to find the value of y
0.5y = 2
Shifting 0.5 to Right Hand Side of the equation and performing division
y = 2 ÷ 0.5
y = 4
Calculating the value of x by keeping the value of y in Equation 2
x = 6 - 4
x = 2
Hence, I bought 2 pens and 4 pencils from given amount.
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Compare and contrast function notation and vector notation for translations.
The comparison and contrast function notation and vector notation for translations are-
A transformation can be described using either notation. A equation to obtain the image from such a general point is shown in function notation. The vector notation indicates which direction to move in and the distance to move.What is termed as function notation?Function notation is a method for writing functions that are simple to comprehend and read.
When we employ function notation, the independent variable is typically x, as well as the dependent variable is F. (x). To use function notation to write a relation or equation, we must first ascertain if the relation is a function.What is termed as vector notation?Whenever a vector is simply a list of numbers, it can be represented by an arrow in space.
We divide the vector by its magnitude to discover a unit vector with the same direction as just a given vector. Consider the magnitude of a vector v = (1, 4) with a magnitude of |v|. When we divide evey component of vector v by |v|, we get the unit vector uv, which is oriented in the same direction as vector v.To know more about vector notation, here
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PLEASE HELP PLEASE PLEASE PLEASE!! Please show work for brainliest!!! :)
What is the factored form of the expression over the complex numbers? 16x^2+9y^2
The factored form of the expression 16x² + 9y² over the complex numbers is; (4x + 3iy)(4x − 3iy)
How to factorize expressions?We want to find the factored form of the expression 16x² + 9y² over the complex numbers.
We can rewrite the given expression 16x² + 9y² as perfect squares;
= (4x)² + (3y)²
Now, from using the difference of squares formula, we know that;
a² - b² = (a + b)(a - b)
Thus;
(4x)² + (3y)² = (4x)² - (√-9)²y²) can be expressed as;
(4x + 3iy)(4x − 3iy)
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what is the minimum value of g?
The quadratic opens upwards, so the minimum is at the vertex.
We can see that the minimum value of g is y = -1.
What is the minimum value of g?By looking at the given graph, can see that g(x) is a quadratic equation.
If the quadratic equation has a positive leading coefficient (it opens upwards) the minimum of the quadratic is on the vertex, and there is no maximum (as the function end behavior tends to infinity)
If the quadratic equation has a negative leading coefficient (it opens downwards). The maximum is at the vertex, and there is no minimum (similar like the case above).
Here we can see that the quadratic opens upwards, thus, the minimum is at the vertex, which we can see is located at x = 3 and y = -1, then the minimum value of the function g(x) is y = -1
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A coin is filmed using stop-motion animation so that it appears to move.
a. Describe the translation from A to B in function notation and in words.
The translation from A to B is described as-
In notation: From x = -3 to x = 0, the coin travels through y = (2/3)x + 1.In words: From A to B, the coin shifts three spaces to a right and then two spaces up.What is meant by translation?In mathematics, a translation is the movement of a shape to the left or right and/or up or down. The translated shapes appear to be the exact size as that of the original shape, therefore the shapes are congruent.
Replace x with x - k whenever a shape is moved to the left by k units.Replace x with x + k whenever a shape is moved to the right by k units.Replace y with y + k whenever a shape is moved up by k units.Replace y with y - k whenever a shape is moved down by k units.Now, according to the question.
Consider the equation for the shifting from A to B as y = k x+b
The coordinates of the location A and B are-(see the diagram)
A(-3,-1) and B(0,1)
Thus, A, B into y = k x+b
Substitute the value of A in the equation;
-1 = -3k + b
b = 1
So, k = 2/ 3
Put value of k in 'y'.
Hence, AB ; y = (2/3)x + 1
Thus, the coin moves thought y = (2/3)x + 1 from x = -3 to x = 0.
In words; Shifting from A to B, the coin moves 3 spaces to the right after that moves 2 space up.
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solve each equation(with explanation please)
-4+p=-7
x/10=-6
4-3(8n - 4) = -104
Answer:
1: P = -3
2: X = -60
3: N = 5
Step-by-step explanation:
Ok, for number one you are going to add 4 on the -4 canceling that out, and adding 4 on the -7 making that -3.
Number 2 you times 10 on the x/10 to cancel out the 10 (making it x) then you do -6 times 10, and then you get -60
Last one is a little tricky here's the equations I used to get the last one
-3 x 8n = -24x
New equation: 4-24x=-104
+4 + 4
___________________________
-24x = -100
___ ___
-24 -24
_
so the answer would be x = 5
1.
Solve each equation for the indicated variable.
a+m=n=p,
for a.
In linear equation, a = (n+p)/m is equation for the indicated variable.
What in mathematics is a linear equation?
A linear equation is an algebraic equation with the formula y=mx+b, . m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."In terms of algebra, writing "am" is the same as writing "a*m" or "a times m"
To undo the multiplication, we use division. We will divide both sides by m to get 'a' all by itself on the left side
So...
am = n+p
a*m = n+p
(a*m)/m = (n+p)/m .... divide both sides by m
a = (n+p)/m ... notice how the 'm's cancel out when we divide on the left side
a = (n+p)/m
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If a 45° -45° - 90° triangle has a hypotenuse length of 9 , find the leg length.
The leg length is 9/ root2
Here we are given a right angle triangle , and in a right triangle , sum of squares of sides is equal to the square of hypotenuse.
[tex]a^{2}+b^{2} =c^{2}[/tex]
This is right angle scalene triangle as the two angles other than right angle are 45° each.
Hence ,
In this case we have
[tex]a^{2}+a^{2} =c^{2}[/tex]
[tex]2a^{2}=c^{2}[/tex]
[tex]a^{2}=\frac{c^{2} }{2}[/tex]
Taking square roots on both sides
[tex]a=\frac{c}{\sqrt{2} }[/tex]
Here we have hypotenuse c given as 9
Hence, the leg length is [tex]a =\frac{9}{\sqrt{2} }[/tex]
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Which set of points represents a function which is not one-to-one?
choice 1:
{(3, 2), (9, 6), (0, 7), (6, 5), (2, 0)}
Choice 2:
{(9,6), (4,3), (5, 4), (8, 0), (7, 9)}
Choice 3:
{(4,3), (8,5), (8, 7), (0, 2), (1, 6)}
Choice 4:
{(2, 6), (0, 2), (8, 9), (1, 1), (4, 6)}
Answer:
Choice 4
Step-by-step explanation:
A one to one function has every domain with only one range as their individual output. Choice 4 has the output 6 mentioned twice for both 2 and 4 so therefore it's not a one to one function because the range 6 has two outputs 2 and 4.
A man who is 6 feet tall is walking at a rate of 4 feet/second, directly away from a light that is located 10 feet above the ground.
How long is the man's shadow t seconds after he starts walking? The answer will be in terms of t.
Answer:
2.5t
Step-by-step explanation:
Let the man be
x
feet away from the street light, and his shadow length be
y
, Let the tip of the shadow be
l
feet away from the light such that
l
=
x
+
y
and we are given that
d
x
d
t
=
2
By similar triangles:
y
6
=
x
+
y
30
∴
30
y
=
6
(
x
+
y
)
∴
30
y
=
6
x
+
6
y
∴
30
y
−
6
y
=
6
x
∴
24
y
=
6
x
∴
y
=
1
4
x
Now,
l
=
x
+
y
⇒
l
=
x
+
1
4
x
∴
l
=
5
4
x
Differentiating wrt
x
gives;
d
l
d
x
=
5
4
And by the chain rule we have:
d
l
d
t
=
d
l
d
x
d
x
d
t
∴
d
l
d
t
=
5
4
×
2
∴
d
l
d
t
=
2.5
feet/sec
a toy rocket is launched from a platform 6.3 meters above the ground in such a way that is a height, h (in meters) after t seconds is given by the equation h=-4.9t^2+43.4t+6.3. how long will it take for the rocket to hit the ground?
The toy rocket will take a time of 8.999 seconds to hit the ground.
How much time does the rocket take to hit the ground?
The height of the rocket (h), in meters, in terms of time (t), in seconds, is defined by a quadratic equation. In this question we must determine the time needed for the rocket to hit the ground, that is, a time t greater than zero such that the height is zero. Now we proceed to solve the polynomial:
- 4.9 · t² + 43.4 · t + 6.3 = 0
- 4.9 · (t² - 8.857 · t - 1.286) = 0
- 4.9 · (t - 8.999) · (t + 0.143) = 0
Only the first root offers a realistic value as time is a whole number. Hence, the toy rocket will take a time of 8.999 seconds to hit the ground.
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