The maximum height of the ball after its third bounce is equal to 3.568 feet.
What is the maximum height of a ball at the third bounce?
In this question we are aware that the maximum height reached by the ball decreases linearly after each bounce. To determine that height, we must take advantage of the recursive formula described in statement:
n = 0
a₀ = 10 ft
n = 1
a₁ = 0.85 · 10 - 1
a₁ = 8.5 - 1
a₁ = 7.5 ft
n = 2
a₂ = 0.85 · 7.5 - 1
a₂ = 5.375 ft
n = 3
a₃ = 0.85 · 5.375 - 1
a₃ = 3.568 ft
The maximum height of the ball after its third bounce is equal to 3.568 feet.
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The first one is 10 feet.
The second one is 6.141 feet.
Step-by-step explanation: Edge 2023
What is the end behavior of the graph
Answer:
as x is approaching positive infinity, y approaches positive infinity
as x is approaching negative infinity, y is approaching negative infinity
Problem: A piece of farmland is a watering plot of land in a circular pattern. A sewer line needs to be installed from a new housing project to a processing plant The city does not want the sewer line to cross the farm land. Can a direct line be installed?
● Let 1 unit = 100 feet.
● The entry to the sewer plant is at (2,3)
● The sewage exit from the housing project is at (12,6)
● The sprinkler system extends 200 ft and the center of the land is at (8,3)
Questions: (1) Will the sewer line cross the farmland? If so then at what points?
(2) If the farmer wants to maximize the farming area and does not want to cross the sewer line, what is the longest sprinkler system that could be installed?
The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;
(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)
(2) The longest installable sprinkler system is approximately 172.4 feet
How can the points where the line crosses the farmland be found?1. The slope of the sewer line is found as follows;
m = (6 - 3)/(12 - 2) = 3/10 = 0.3The equation of the sewer line can be expressed in point and slope form as follows;
(y - 3) = 0.3×(x - 2)y = 0.3•x - 0.6 + 3
y = 0.3•x + 2.4
The equation of the circumference of the sprinkler can be expressed as follows;
(x - 8)² + (y - 3)² = 2²Therefore;
(x - 8)² + (0.3•x + 2.4 - 3)² = 2²
Solving gives;
x= 6.53, or x = 8.48
y = 0.3×6.53 + 2.4 = 4.36
y = 0.3×8.48 + 2.4 = 4.9
Therefore;
The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)2. When the farmland does not cross the sewer line, we have;
sewer line is tangent to circumference of farmland
Slope of radial line from center of the land is therefore;
m1 = -1/0.3
Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;
y - 3 = (-1/0.3)×(x - 8)
Which gives;
y = (-1/0.3)×(x - 8) + 3
The x-coordinate is therefore;
0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3
x ≈ 7.5y = 0.3 × 7.5 + 2.4 ≈ 4.65The longest sprinkler system is therefore;
d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724
Which gives;
The longest sprinkler system is 1.724 × 100 ft. ≈ 172.4 ft.Learn more about the equation of a circle here:
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kể tên các cặp góc kề bù
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What is Permutations and Combinations?
Answer:
See below
Step-by-step explanation:
Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.
Permutation can be expressed in math as:
[tex]\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }[/tex]
where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.
Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:
Since there are 3 letters total and 3 selected letters to arrange then:
[tex]\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}[/tex]
Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:
ABC - 1
ACB - 2
BAC - 3
BCA - 4
CAB - 5
CBA - 6
Notice that if you do visually, you'll get the same answer as the calculation of permutation!
----
Combination can be expressed mathematically as:
[tex]\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }[/tex]
The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.
Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:
Since there are 3 letters total and 3 selected letters:
[tex]\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}[/tex]
Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.
Permutations and combinations have many practical applications in various fields such as statistics, Probability theory, and computer science.
Permutations and combinations are two concepts in mathematics that deal with counting and arranging elements in a set.
Permutations refer to the number of ways in which a set of objects can be arranged or ordered. In other words, permutations involve counting the number of possible ways in which a group of objects can be arranged in a particular order. For example, if we have three objects A, B, and C, the possible permutations would be ABC, ACB, BAC, BCA, CAB, and CBA. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects being arranged.
Combinations, on the other hand, refer to the number of ways in which a subset of objects can be selected from a larger set, without regard to the order in which they are selected. In other words, combinations involve counting the number of possible subsets that can be formed from a larger set. For example, if we have three objects A, B, and C, the possible combinations would be AB, AC, and BC. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects being selected.
The key difference between permutations and combinations is that permutations involve ordering objects, while combinations do not. Another important distinction is that in permutations, each arrangement is considered distinct, whereas in combinations, different arrangements that contain the same objects are considered identical.
Permutations and combinations have many practical applications in various fields such as statistics, probability theory, and computer science. For example, they are commonly used in solving problems related to probability, combinations of locks, and permutations of passwords. Understanding these concepts is essential in order to effectively analyze and solve problems in these fields.
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1. Find the product using Suitable Property a) 55×99
Answer:
5445
Step-by-step explanation:
We can use distributive property. a*(b - c) = (a*b) - (a *c)
99 = 100 - 1
55 * 99 = 55 * (100 - 1)
= 55*100 - 55*1
= 5500 - 55
= 5445
El rio Lempa sirve de linea fronteriza entre Honduras y El Salvador, mide 300km
de largo. ¿Cuántos metros mide este rio?
Answer:
El río mide:
300000 metros.
Step-by-step explanation:
1 km = 1000 metros
300 km = 300 * 1000 = 300000 metros
...
1. The perimeter of a rectangle is 16cm, and the area of the same rectangle is 8cm^2. What is the diagonal length of the rectangle?
2. Kendrick rides his bike x miles per hour to school and it takes him x + 15 minutes to get there. If Kendrick lives 5.4 miles from school, how many minutes does it take for Kendrick to ride to school?
Answer:
Step-by-step explanation:
A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 5 ftys along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole
25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path. This can be obtained by considering this as a right angled triangle.
How fast is the tip of his shadow moving?Let x be the length between man and the pole, y be the distance between the tip of the shadow and the pole.
Then y - x will be the length between the man and the tip of the shadow.
Since two triangles are similar, we can write
[tex]\frac{y-x}{y} =\frac{6}{15}[/tex]
⇒15(y-x) = 6y
15 y - 15 x = 6y
9y = 15x
y = 15/9 x
y = 5/3 x
Differentiate both sides
dy/dt = 5/3 dx/dt
dy/dt is the speed of the tip of the shadow, dx/dt is the speed of the man.
Given that dx/dt = 5 ft/s
Thus dy/dt = (5/3)×5 ft/s
dy/dt = 25/3 ft/s
Hence 25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path.
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y square plus 5y equals to 0
Answer:
y^2 + 5y = 0
y(y + 5) = 0
y = 0, -5
The answer is y = 0 and y = -5.
The given question :
y² + 5y = 0y (y + 5) = 0y = 0, y = -5what is the slope of -3x
Answer:
The slope is -3, in a y=mx+b equation the x coefficient is the slope
PLEASE ANSWER QUICKLY
Answer:
9
Step-by-step explanation:
See the attached image.
describe fully the single transformation which maps triangle A onto triangle B.
The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
The single transformation which maps triangle A onto triangle B is the reflection over the x axis, that is (x, y) ⇒ (x, -y)
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Solve:
2a + 6 = 12
a =
Answer:
8
Step-by-step explanation:
because hhhhhh
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vvvvv
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kkkkkk
lllll.ssss
Dad has 15 oak and maple boards from the lumber yard. each oak board is 6 centimetres thick. each maple board is 9 centimetres thick. when my dad stacks the boards, the stack is 96 centimetres thick. how many of each type of board does he have?
Answer:
He has 2 maple boards and 13 oak boards.
Step-by-step explanation:
Assuming all boards are oak : 6*15=90
Maple minus oak = 3
96-90=6 6/3=2 maple boards
Verification : 2*9+6*13 = 96
Answer:
13 oak, 2 maple
Step-by-step explanation:
o = oak
m = maple
o + m = 15
6o + 9m = 96
o + m = 15
o = 15 - m
6o + 9m = 96
6(15 - m) + 9m = 96
90 - 6m + 9m = 96
90 + 3m = 96
3m = 6
m = 2
o + 2 = 15
o = 13
6(13) + 9(2) = 96 (Yes, correct!)
Brainliest, please :)
Find the area of the figure.
Answer:
60 ft^2
Step-by-step explanation:
Richard wants to weed 33% of his garden today. The total garden is 144 square yards. How many square yards should Richard weed to reach his goal?
PLEASE HELP 50 POINTS
Step-by-step explanation:
The initial velocity of a particle moving along x−axis is u (at t=0 and x=0) and its acceleration a is given by a=kx.I can not factor the denominators on any online calculator so I'm unsure of how to do this. Please help!
Answer: 17/y-5
Step-by-step explanation:
DOES ANYONE KNOW THE ANSWER
Answer:
D. none
Step-by-step explanation:
we only know about the right angle at the bottom right.
that is not enough information.
we always need 3 pieces of confirmed information of each triangle to be able to say that the 2 triangles are indeed of the same shape and size.
like the other answer options would indicate :
SAS : side - angle - side.
2 sides and the enclosed angle. if we know they are equal, then the rest of the triangles follow automatically.
SSS : all 3 sides. with 3 defined sides there is only one possible shake and size for that triangle.
HL : Hypotenuse and a leg of a right-angled triangle (also 3 pieces of information - 2 sides and the right angle).
since we have only the right angle and nothing else, we cannot prove that the triangles are congruent.
X+y=5 7x+37=27 solve the system of equations: x=3; y=2 x=4; y=4 x=6;y=1 x=3; y=5
Answer:
(a) (x, y) = (3, 2)
Step-by-step explanation:
The correct answer to the given system of equations can be found by trying the offered choices.
The equations are ...
x + y = 57x +3y = 27Evaluating "solutions"The first equation tells you the sum of the x and y values is 5. Here's what we get for a sum from the different answer choices:
A: 3 +2 = 5 . . . . a viable choice
B: 4 +4 = 8 . . . . doesn't work
C: 6 +1 = 7 . . . . doesn't work
D: 3 +5 = 8 . . . . doesn't work
__
Checking (x, y) = (3, 2) in the other equation, we have ...
7(3) +3(2) = 21 +6 = 27 . . . . as required
The solution is x = 3; y = 2.
__
Additional comment
Often, the easiest way to find the answer to a multiple-choice question is to see which answer works to solve the problem. It can sometimes be easier to check the answer than to develop it in the first place.
Substitution can work for this problem to find the correct y-value. (The answer choices differ by y-values, so knowing y tells the answer.)
7(5 -y) +3y = 27 . . . . substitute x=5-y
35 -4y = 27 . . . . . . simplify
8 = 4y . . . . . . . . . add 4y-27
2 = y . . . . . . . . . divide by 2. Matches the first answer choice.
f(x) = (two-fifths) Superscript x
g(x) = (two-fifths) Superscript x – 3
Which statement about f(x) and its translation, g(x), is true?
The range of g(x) is , {y | y > 0} and the range of f(x) is {y | y > –3}.
The range of g(x) is , {y | y > 3} and the range of f(x) is {y | y > 0}.
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
The asymptote of g(x) is the asymptote of f(x) shifted three units up.
Answer: The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Step-by-step explanation:
Answer:
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Step-by-step explanation:
bc I said so
waheda purchased 8 textbooks each costing rupees 12 and 4 story books each question rupees 9 find the ratio of amounts she spent on the two types of books .
Answer:
8/3 or 2(2/3) Textbooks to storybooks
Step-by-step explanation:
Textbooks: (8 books)*(12 rupees/book) = 96 rupees
Storybooks: (4 books)*(9 rupees/book) = 36 rupees
Total is 132 rupees
Ratio: Textbook/Storybook = 96/36
96/36 = 8/3 or 2(2/3) Textbooks to storybooks
What is the value of the expression below when w = 9 and x = 5?
10w + 4x
Answer:
110
Step-by-step explanation:
10w + 4x
10 (9) + 4 (5)
90 + 20
110
The answer is 110.
Hope it helps!
Have a nice day:)
-6-5
(-5-4)
(-2,2)
2-
4
--2-1₁
4-
2
4 9
(0, -3)
X
What is the equation of the line that is parallel to the
given line and passes through the point (-2, 2)?
Oy=x+4
Oy = x + ¹/2
Oy = -5x + 4
Oy=-5x + ¹2
The equation of the line that is parallel to the given line and passes through the point (-2,2) is:
[tex]y = \frac{x}{5} + \frac{12}{5}[/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.When two lines are parallel, they have the same slope. In this problem, the given line passes through (-5,-4) and (0,-3), hence the slope is:
m = (-3 - (-4))/(0 - (-5)) = 1/5.
Hence the equation is:
[tex]y = \frac{x}{5} + b[/tex]
When x = -2, y = 2, then:
[tex]y = \frac{x}{5} + b[/tex]
[tex]2 = \frac{-2}{5} + b[/tex]
[tex]b = \frac{12}{5}[/tex]
Hence:
[tex]y = \frac{x}{5} + \frac{12}{5}[/tex]
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A system of three linear equations in three unknowns can have exactly three solutions.
The given statement is false. The option for the reason is the first option:
" The statement is false. A system of three linear equations in three unknowns can have one solution, an infinite number of solutions, or no solutions."
A system of linear equations is a grouping of one or more linear equations with the same variables.
A linear system solution is the assignment of values to variables in such a way that all of the equations are concurrently fulfilled.
For a system of equations, three types of solutions exist:-
One solution: When the lines (planes) intersect at a point.No Solution: When the lines (planes) are parallel.Infinitely many solutions: When the lines (planes) overlap each other.Thus, the given statement is false. The option for the reason is the first option:
" The statement is false. A system of three linear equations in three unknowns can have one solution, an infinite number of solutions, or no solutions."
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The question is incomplete. For the complete question, check the attachment.
A rectangle is 8 feet longer than it is wide. find the dimensions of the rectangle if its area is 345 sq-feet.
The width of rectangle is 15 feet and the length of rectangle is 23 feet.
According to the statement
Width of rectangle = x
Length of rectangle = x+10
Area of rectangle = 345 sq-feet.
we know that the area of rectangle is
Area of rectangle = L*W
Substitute the values in it then
345 = (x) (x+8)
345= (x)^2 + 8x
(x)^2 + 8x - 345 = 0
By factorisation
(x-15) (x+23) = 0
So, width of rectangle is 15 feet and the length of rectangle is 23 feet.
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On a plat map are two adjacent rectangular lots. Lot A has a square footage of 46,060, and Lot B has a square footage of 43,005. The common boundary they share is 235 feet long. What is the width of Lot B
The Width of plot B is 183 ft.
According to the statement
we have given that the Plot A has a square footage of 46,060, and Plot B has a square footage of 43,005. The common boundary they share is 235 feet long.
And we have to find the width of the Plot B
We know that
Area of plot A = 46,060 square footage.
Area of plot B = 43005 square footage.
Common area share by both Plot = 235 feet long.
So, Now
The width of Plot B = Area of plot B / Common area
Substitute the values in it then
width of Plot B = Area of plot B / Common area
width of Plot B = 43005 / 235
width of Plot B = 183 feet.
So, The Width of plot B is 183 ft.
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Find 20% of 150
A. 20
B. 130
C. 120
D. 30
For this, multiply 150 × .20 = 30
Therefore, 20% of 150 is 30.
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What is the multiplicative inverse of -13/14
The multiplicative inverse of -13/14 as in the task content is; -14/13.
What is the multiplicative inverse of -13/14?The multiplicative inverse of a number x is given as; 1/x.
On this same note, it follows that since, the number whose multiplicative inverse is to be found is: -13/14, the multiplicative inverse is; -14/13.
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Problem
Solve for x in the image below.
18
Solution
We can start with the pythagorean theorem:
(leg 1)² + (leg 2)² = (hypotenuse)²
Answer:
20.1246118
Step-by-step explanation:
hypotenus^2 - (leg1)^2 = (leg2) ^2
27^2-18^2 = (leg2)^2
729-324 = (leg2)^2
405 = (leg2)^2
20.1246118 = leg 2