a ball is dropped from a height of 20 feet. each time it drops h feet, it rebounds 0.89h feet, 343.63 feet the total distance traveled by the ball.
What is distance?The length of the line connecting any two places is known as their distance from one another. Subtracting the different coordinates will reveal the distance if the two locations are on the same horizontal or vertical line.
h₁ = 20 feet = h
h₂ = 0.89h
h₃ = 0.89²h
h₄ = 0.89³h
...........................
h(n) = 0.89ⁿh
Therefore, total distance travelled = 20 + 2 (0.89h + 0.89²h + 0.89³h +.....)
= 20 + 2h (0.89 + 0.89² + 0.89³ +.....)
Sum of (h.p)∞ = a/ (1-r)
Where, a = first term = 0.89
r = common ratio = 0.89
total distance travelled = 20 + 2 × 20 ×(0.89) × [1/(1 - 0.89)]
= 343.63 ft.
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Consider the points (-2,4), (-1, 1), (0, 0), (1, 1), and (2,4).
Does this represent a function?
A) Yes
Β) No
There is a sequence of numbers arranged in rows. Each row has six numbers. If the sequence begins as below, what is the fifth number on the 7853rd row?
0 1 2 3 4 5
6 7 8 9 10 11
12 13 14 15 16 17 ...
please help! I have a lot of points to give out lol
The fifth number in the 7853rd row as required to be determined is; 47,116.
What is the 7,853rd term of the arithmetic sequence?It follows from the task content that the fifth number on the 7853rd row of the sequence is to be determined. By observation, each column of the sequence of numbers represents an arithmetic sequence of numbers in which case;
The common difference is; 6 - 0 = 12 - 6 = 17 - 11 = 6.
Therefore, since the nth term of an arithmetic sequence is given by the formula;T (n) = a + (n - 1) d.
where a = does term
n = number of terms
d = common difference
In this scenario, the first term is the fifth number on the first row = 4.Therefore, the fifth number on the 7853rd row is; T (7853) = 4 + (7853 - 1) × 6T = 4 + (7852 × 6)T = 4 + 47,112T = 47, 116.
Therefore, the required number is; 47,116.
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. The graph shows the amount of cleaning
product dispensed when using a spray
bottle. Determine if the linear
relationship is proportional. Find and
interpret the slope. Then find the unit
rate and compare it to the slope.
The required proportional relationship is given as y = 3/2x.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
From the graph,
It seems that the relationship given is a proportional relationship,
Now locate two points on the graph, as (0, 0) and (2, 3)
The equation of the line function is given as,
y - 0 = [3 / 2] (x - 0)
y = 3/2x
Thus, the required proportional relationship is given as y = 3/2x.
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Which of the following equations represent linear functions?
a.) y=x2
b.) y=3x+2
c.) y=6
d.)y=x−−√
Answer:
b.) y=3x+2
Step-by-step explanation: The linear equation is y= mx + b
m is the slope and b is the y-intercept
Answer b is the linear equation!
If the derivative of y, dy/dx i the rate of change of y (alo known a the lope or gradient)
How can we ue the 2nd derivative of y, d2y/dx2 to determine whether the vertex of a quadratic i a maximum or minimum?
Why i thi the cae?
As d2y/dx2 is positive, the rate of change of gradient is positive, that means (2,-10) is a minimum point.
As stated in the video, the rate of change of dy/dx is the second derivative ( d2y/dx2 )
Thus, at a stationary point (dy/dx = 0), when d2y/dx2 < 0 meaning the rate of change of the gradient is negative the point is a maximum point. We can see that in the image below.
And at minimum points the rate of change of gradient is positive. Thus d2y/dx2 > 0 at minimum points.
A curve has equation y=x3 -12x +6 Find the coordinates of each stationary point, and the nature of these points (minimum or maximum).
Find when dy/dx = 0
dy/dx=3x2 -12
3x2 – 12 = 0
x2 =4
x = 2 or x=-2
when x = 2 y=-10 when x= -2 y=22
Thus, coordinates of stationary points are (2,-10) and (-2,22)
Now in order to find whether they are maximum or minimum points, we have to calculate d2y/dx2
d2y/dx2 = 6x
when x=2 d2y/dx2 = 12
As d2y/dx2 is positive, the rate of change of gradient is positive, that means (2,-10) is a minimum point.
when x= -2 d2y/dx2 = -12
As d2y/dx2 is negative, the rate of change of the gradient is negative, which means that (-2,22) is a maximum point
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If a firework is launched vertically upwards from a height of 20 feet above the ground. Its path is give by h(t)=-4t+16t+20, where h is the height of feet and t is the time in seconds.
can someone help me find the right answers for this with scratch work? i'm struggling quite a bit.
when is the firework at max height?
What was the highest point that the firework reached?
What is the starting point of the firework?
How high is the firework after 3 seconds?
When does the firework hit the ground?
The quadratic function defining the height of the firework in this problem after t seconds is given as follows:
h(t) = -4t² + 16t + 20.
From this definition, we can get the h-intercept giving the starting point of the firework, as follows:
h(0) = -4(0)² + 16(0) + 20 = 20 feet.
The height after 3 seconds is calculated with the numeric value as follows:
h(3) = -4(3)² + 16(3) + 20 = 32 feet.
The coefficients of the quadratic function are given as follows:
a = -4, b = 16, c = 20.
Due to the negative coefficient a, this is a concave down function, meaning that the vertex is a maximum point.
The t-coordinate of the vertex is given as follows:
tv = -b/2a = -16/2(-4) = -16/-8 = 2.
Then the maximum height of the firework is of:
h(2) = -4(2)² + 16(2) + 20 = 36 feet.
The firework hits the ground when h(t) = 0, hence, using a quadratic function calculator, the time is of:
5 seconds. (positive root).
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Find the nth term of this quadratic sequence 4, 7, 12, 19, 28, ...
Answer:
which grafde are you in and I think ur question is wrong
Given that ⧍PQR≅⧍TSU, name the corresponding angles and segments.
Answer: 5,1
Step-by-step explanation:
what is the value of x when y= -1
Answer:
x=+1
Step-by-step explanation:
the value of x will be positive 1 for we will take x=0 y=-1 where we inter change the values to be x=y-1=0
please help 30 points, giving brainliest!!! ( DO ONLY 5-8) (USE RISE OVER RUN) (FIND SLOPE)
picture is attached :) ty!!
Answer:
6. 4/1 7. 4/2
Step-by-step explanation:
that's all I got I hope it helps.
The perimeter of AABC= 15 cm. Given that AB = 7 cm and /BAC = 60°, find the lengths of AC and BC and the area of the triangle.
Step-by-step explanation:
Call AB side a...which is 7
therefore b+c = 8 (editted this part due toarithmetic slip)
sketch it, use the cosine rule knowing cos 60 = 0.5and set up a simultaneous equation for the sides b+ c
7^2 = b^2+c^2 - bc
then
a + b = 15
(as this 2bcCOSA cancels down)
2. What political hurdles did African American representatives have to face after they went into
office?
The political hurdles that African American representatives have to face after they went into office is Racism.
What is Racism?Racism is the belief that different groups of humans have different behavioral traits that correspond to inherited characteristics and that they can be divided based on the superiority of one race over another.
Racism stems from the belief that a person is superior to others because of the color of their skin. In the olden days, blacks were excluded from public schools, denied the right to vote, and faced racism and legal discrimination almost everywhere. This is still faces in politics as well.
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Please help me. I will give a brainliest AFTER 2 people message
Reason:
The scale factor 1.75 is what we'll multiply by each dimension of the blue figure, to get the green figure.
The "3" is multiplied by 1.75 to get 3*1.75 = 5.25 which is the value of x, since both involve the top side of each respective trapezoid.
In other words,
(preimage Length)*(scale factor) = (image length)
(3)*(1.75) = x
5.25 = x
x = 5.25
Use the diagram to the right to answer the
following questions.
a. Using parallel line relationships, find the value of
x. Use the relationship between the two marked
angles to set up your equation.
Show your work to support your answer. (
Answer:
a=14
b=166
c=166
d=166
e=166
f=14
x=5
12 divided by 127 show your work
Answer:
10.58
Step-by-step explanation:
dellana company tested 50 products for 75 hours each. during this time, it experienced four breakdowns. compute the number of failures per hour. what is the mean time between failures?
dellana company tested 50 products for 75 hours each. during this time, it experienced four breakdowns. compute the number of failures per hour, 937.50 hours is the mean time between failures.
What is mean time?The span of time before something occurs or before a given time frame expires. We can utilise the current computers while waiting for the new ones to arrive next week.
Given that,
dellana company tested 50 products
time =75 hours
Thus, total products in hours
= 50 products × 75 hours each
= 3750 product hours
Also said that, 4 breakdowns in 3750 product hours,
so, (4/3750) = 1.067 × 10⁻³ = 0.001067 breakdowns per hour.
Also, an average of 0.001067 breakdowns per hour = λ
therefore, mean time between failures:
= 1/ λ
= 1/0.001067
= 937.50 hours
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a container is in a shape of a cuboid
the container is 2/3 full of water
a cup holds 275ml of water
what is the greatest number of cups that can be completely filled with water from the container
The greatest number of cups that can be completely filled with water is 2.
What is the greatest number of cups that can be completely filled with water from the container?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
The greatest number of cups that can be completely filled with water will be:
1000ml = 1 liter
2/3l = 667ml
Therefore, the number of cups will be:
= 667 / 275
= 2
The greatest number of cups is 2.
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See the picture please
23. दुई अङ्कको एउटा सङ्ख्या त्यसका अङ्कहरूको योगको चार गुणा छ । यदि अङ्कहरूको गुणनफल 18 भए त्यो सङ्ख्या र त्यसको विपरीत सङ्ख्या बिचको भिन्नता पत्ता लगाउनुहोस् । A number of two digits is equal to four times the sum of the digits. If the product of the digits is 18 then find the difference between the number and its reversing number.
Answer:
hence the number is 24.
Step-by-step explanation:
Two Solutions:
1.10x+y=4(x+y)
2x=y
2.10x+y+18=10y+x
x−y=−2
x−2x=−2
x=2
y=4
two digit number =24
Todd is planning a vacation and is adding $5 per day towards his savings account for it. After 20 days he has a total of $150 in his savings
account.
a). Assuming this is linear relationship write an equation to model it.
b). How many days will it take Todd to build his savings up to a total of $250.
A) The equation of the model is 20x=100.
B) Todd will take 50 days to build his savings up to a total of $250.
What is meant by an equation?An assertion that two expressions containing variables or numerical values are equivalent is known as an equation. The first step in resolving a variable equation is to identify the values of the variables that lead to the equality being true. The variables that must be changed in order to solve the equation are referred to as the unknowns, and the unknown values that satisfy the equality are referred to as the equation's solutions.
1 day ------ $5
20 days -------?
x=20×5
x=$100
A) Let the savings per one day =$5
For 20 days it will be $100
And it is given as 20x=100
Where x=time in days
B) Todd has $150 dollars for 20 days
Actual savings for 20 days=100
? --------250
x=(20×250)/100
x=50 days.
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1. Which logarithm bases can you use to solve for x in the exponential equation 4^3+x= 25 ? (Select all that apply.)
log base 10
log base x
log base 4
log base 25
The logarithm bases can you use to solve for x in the exponential equation [tex]4^{3+x}[/tex]= 25 is log base 4. So, option 3 is correct.
What is meant by exponential equation?Finding the slope (m) and y-intercept (b) of a line's graph will allow us to build a linear function with the formula y=mx+ b. We may build an exponential function of the form y=a+ bx given an exponential curve graph by locating the common ratio (b) and y-intercept (a) on the graph. If your function has the formula y = a + b x, where and are constants, a 0 and b > 0 and b 1, then it must be exponential. Your functions in quadratic equations were always to the second power. The exponent of exponential functions is a variable.
Given equation is [tex]4^{3+x}[/tex]= 25
Applying logarithm with base 4 to both sides.
log [tex]4^{3+x}[/tex]=log 25
(3+x)log 4=log25/log 4
3+x=log 25/log 4
x=(log 25/log4)-3
So, we use log base 4.
Hence, option 3 is correct.
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Geometry work number 6
The geometry work number 6 has line MN parallel to line YX, line WY is parallel to line NX and line WX is parallel to line MO.
What are parallel linesIn geometry, parallel lines are straight lines that do not intersect or meet at any point.
Considering the triangle in the geometry work number 6,
the straight lines MN and YX can continue in same plene and will never meet at any point, so there are said to be parallel to each other.
the straight lines WY and NX can continue in their direction and will not intersect each other, so they are said to be parallel to each other.
and also, the straight lines WX and MO are parallel to each other because they can not intersect each other at any point.
Therefore, we can say that line MN is parallel to line YX, line WY is parallel to line NX and line WX is parallel to line MO.
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See screenshot below.
The union of the sets D and E, denoted by the expression, D ∪ E where, set D = {2, 5, 7}, and the set E = {2, 4, 5, 6} is D∪E = {2, 4, 5, 6, 7}
What is a set in set theory?A set comprises of a collection of members or elements which are objects in the set that together are taken as one object by itself.
The specified sets are;
D = {2, 5, 7}
E = {2, 4, 5, 6}
F = {1, 3, 4, 5, 7}
The union of two sets is the set of the elements in each of the set in the union, including the elements that are in both sets in the union.
The symbol used to indicate a union between two sets is the '∪'
The union of the set D and E is therefore;
D ∪ E = {2, 5, 7} ∪ {2, 4, 5, 6}
The elements in the union are therefore; 2, 2, 4, 5, 5, 6, 7
The numbers values are to be represented once in the set, such that the union of the set becomes; 2, 4, 5, 6, 7.
D ∪ E = {2, 4, 5, 6, 7}
The number of elements in the union of the set D and E is 5 elements, including 2, 4, 5, 6, and 7
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A shop has a sale of 1/3
off all items in stock.
If the original price of a dress is £42, what would be its sale price?
Answer:
£ 76
Step-by-step explanation:
Answer:
28
Step-by-step explanation:
Multiply 42 by 1/3 which is 14.
Then subtract 42-14 because your subtracting the discount from the original price which gives you 28.
Please help me! Find the value of X&Y for which ABCD must be a parallelogram!
Answer:
x = 8y = 6Step-by-step explanation:
You want the values of x and y that make the quadrilateral a parallelogram, given the halves of one diagonal are marked (3x-14) and (x+2), and the halves of the other diagonal are marked (4y-7) and (y+11).
ParallelogramThe diagonals of a parallelogram bisect each other. This means the marked segments on each diagonal are congruent.
x-value(3x -14) = (x +2)
2x = 16 . . . . . . . . . add 14-x
x = 8 . . . . . . . . divide by 2
y-value(4y -7) = (y +11)
3y = 18 . . . . . . . . . add 7-y
y = 6 . . . . . . . . divide by 3
The values of x and y are 8 and 6, respectively.
marcus is a gardener .he pulls weeds for 18 min waters for 13min and plants for 16 min.how many total min does he spent gardening
Answer: 47 mins
Step-by-step explanation:
18 min pulls weeds + 13min water + 16 min plant = 47 mins
A clothesline rope is 8 feet long. Which of these is another way to express 8 feetanother
Using the unit conversion concept of mathematics and converting the length provided into various units , There are multiple ways to express 8 feet such as in inches, meter or kilometer and many more.
What do you mean by unit?A unit is a reference value established by law or convention that is used as a benchmark to measure an object's physical characteristic.
What do you mean by unit conversion?By definition, unit conversion refers to the division or multiplication operation used to convert measurements of the same quantity between various units. The act of converting something from one form to another in mathematics, such as from inches to millimeters or from liters to gallons, is known as conversion.
l= 8 feet
In inches, l= 96 inches
In meter, l =2.43 meters
In kilometer, l = 0.0024 kilometers
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Using the unit conversion concept of mathematics and converting the length provided into various units , There are multiple ways to express 8 feet such as in inches, meter or kilometer and many more.
What do you mean by unit?
A unit is a reference value established by law or convention that is used as a benchmark to measure an object's physical characteristic.
What do you mean by unit conversion?
By definition, unit conversion refers to the division or multiplication operation used to convert measurements of the same quantity between various units. The act of converting something from one form to another in mathematics, such as from inches to millimeters or from liters to gallons, is known as conversion.
l= 8 feet
In inches, l= 96 inches
In meter, l =2.43 meters
In kilometer, l = 0.0024 kilometers
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Use Newton's method to find all roots of the equation correct to six decimal places. e^x = 9 - 2x
1.716762 is the correct solution up to 6 decimal places by using Newton's method.
What is Newton's method?The Newton's method is a potent tool, and in general, the convergence is quadratic: as the procedure approaches the root, the discrepancy between the root and the approximation squares, almost doubling the number of accurate digits at each step. The approach does, however, have significant drawbacks. The phrase "Newton's method" refers to Isaac Newton's explanation of a particular application of the method in his books De analysi per aequationes numero terminorum infinitas, which he wrote in 1669 and had William Jones publish in 1711, and De metodis fluxionum et serierum infinitarum (written in 1671, translated and published as Method of Fluxions in 1736 by John Colson).
Given,
f(x)=eˣ+2x-9
f'(x)=eˣ+2
ˣₙ₊₁=ˣₙ-f(ˣₙ)/f'(ˣₙ)
Let, n=1
x₂=1.9074740
x₃=1.7299338
x₄=1.716825
x₅=1.7167621
x₆=1.716762
x₅≈x₆
Therefore, 1.716762 is the correct solution up to 6 decimal places.
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If you buy a 7.25
pound pumpkin that
costs 59 cents per
pound, how much will
you have to pay?
Answer:
you will have to pay 427.75 cents.
Step-by-step explanation:
Multiply 7.25 by 59.
Which equation represents how to determine the speed of an object?
The equation that the speed of an object is speed = distance/time
How to determine the equation of an objectFrom the question, we have the following parameters that can be used in our computation:
Parameter = Object
Argument = Speed
By definition, the speed of an object is the ratio of the distance moved by the object and the time travelled by the object
Mathematically, this can be represented as
Speed = Distance : Time
Express as fraction
Speed = Distance/Time
Hence, the equation is Speed = Distance/Time
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