The total distance traveled by the pendulum when it comes to rest is 10,000 cm.
Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of a pendulum has a length of 100 cm and the return swing is 99 cm .
Now,
Given,
On the first swing, the distance traveled is 100, and on the second swing, the distance is 99.
The first term of the geometric sequence is, a1 = 100
The second term of the sequence is, a2 = 99
The common ratio r = 99/100
Therefore, the expression for the n-t h term of the sequence is:
a_n = 100*(99/100)^(n-1)
Theoretically, using this formula, it would take an infinite number of trips to come to rest.
Hence we need to find the sum of the series a_n = 100*(99/100)^(n-1) from n=1 to n=infinity.
The sum of an infinite series is given by S = a/(1-r) where a=the first term and r=the common ratio.
Therefore,
the total distance traveled is S = 100/(1-(99/100) = 100/0.01 = 10,000 cm
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Determine whether each statement is always, sometimes, or never true. (Lesson 1-5 )
If two angles are supplementary, then one of the angles is obtuse.
If two angles are supplementary, then one of the angles is obtuse: Never TRUE
What do we mean by obtuse angles?An obtuse angle is one that is less than 180 degrees but greater than 90 degrees. Obtuse angle degrees include 110°, 135°, 150°, 179°, 91°, and others. As a result, all angles ranging from 90° to 180° are obtuse. The hypothesis that if two angles are supplementary, one is obtuse and the other acute is false. This is due to a situation in which two angles are supplementary but neither is acute or obtuse. When we have two right angles, we get this. A supplementary angle cannot be formed by two obtuse angles. Obtuse angles are defined as angles that are greater than 90° in length. The sum of two obtuse angles will be larger than 180°. When we add obtuse angles, the property of supplementary angles is violated.Therefore, the statement "if two angles are supplementary, then one of the angles is obtuse" is never TRUE.
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Kristen goes hiking every 3 days and swimming every 2 days. She did both kinds of exercise today. How many days from now will she next go both hiking and swimming again?
Kristen will do both the exercises together, 6 days from now.
We are told that Kristen goes hiking every 3 days and swimming every 2 days.
The day she will do both the exercises together will be the day which is a multiple of the LCM of 2 and 3.
Now, since 2 and 3 are both prime numbers, their LCM (lowest common multiple) will simply be their product, which comes out to be-
LCM (2, 3) = 2 * 3
= 6
Thus, Kristen will do both the exercises on every 6th day.
Thus, if she went for both swimming and hiking today, she will do both the exercises together again 6 days from now.
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solve for x.
also write the equation needed please
Answer:
x = 12
Equation: 6x + 8 = 80
Step-by-step explanation:
A triangle's angles add up to 180 degrees. Knowing this, the angle represented by the "6x + 8" must equal 80 degrees since the other two angles add to 100 degrees.
Quanto e {2×-3y=34×-y=11
Answer: x=4
Step-by-step explanation:
is √196 rational or irrational
Answer:
rational
Step-by-step explanation:
the square root of 196 is 14 ( whole number) therefor it is rational
ls 1.0227 a rational number Explain
At a little-known vacation spot, taxi fares are a bargain. A36 -mile taxi ride takes 42 minutes and costs $25.20. You want to find the cost of a 47 - taxi ride. What unit price do you need?
Answer:
it will cost $32.9 for a 47 mile taxi ride
Step-by-step explanation:
Since 36 miles takes 42 minutes and Costa $25.20 then 47 miles taxi rides will take
42/36 = per minute = 1.17
1.17 × 47 = 54.83
In order to find cost per minute = $25.2/42 = 0.6
then 54.83 × 0.6 = $32.898
∴it will cost $32.9 for a 47 mile taxi ride
What is 36/-4+2(10-8)
Answer:
36/-4+2(10-8)
36/-4+2(2)
-9+2(2)
-9(4)
-36
Step-by-step explanation:
Determine whether each sequence is arithmetic. If so, identify the common difference. 97,86,75,64, ...........
The given sequence is arithmetic progression AP. The common difference is found to be (-11).
What is the sequence called arithmetic progression AP?Arithmetic Progression (AP) is a number sequence in which the difference between two numerical order is a constant value. Arithmetic Sequence is another name for it.
We would then come across some key terms in AP, that are denoted as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)Some formula use in AP are-
The AP could also be expressed in concepts of common distinctions, as shown below; a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) dThe terms used in this progression for a given series are the first term, this same common difference, and the nth term. If a1, a2, a3,................, an is an AP, then the common difference " d " can be calculated as; d = a2 – a1 = a3 – a2 = ……. = an – an – 1.The formula for determining the n-th term of an AP is as follows: an = a + (n − 1) × dIf the first term, common difference, and total terms are known for an AP, the sum of the initial n terms can be calculated. The arithmetic progression sum formula is given below: Sn = n/2[2a + (n − 1) × d]Now as per the given question;
The given sequence is 97,86,75,64, ...........
Let the first term is'a₁' = 97.
Let 'a₂' = 86 is the second term.
Let the third term is 'a₃' = 75.
Let the fourth term be 'a₄' = 64.
As we know, in the AP, the difference between two consecutive terms is equal and therefore is referred to as the common difference.
d = a₂ - a₁
Substitute the values;
d = 86 - 97 = -11 ........(equation 1)
Now consider other pair;
d = a₃ - a₂
d = 75 - 86 = -11 .......(equation 2)
Put the values;
Thus, both the two equation are equal. It means the common difference is same that is (d = -11).
Therefore, the stated sequence is found to be in AP and the value of the common difference is found to be (d = -11).
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Simplify by combining like terms. -(2x + y) -2(-x-y)
The Simplified expression for -(2x + y) -2(-x-y) is y.
Like terms in an algebraic expression is defined as those terms that have same variable and that variable has the same power .
Algebraic Operation is only possible with Like terms .
For Example ; 3x , 9x are like terms .
According to the given Algebraic expression
= -(2x + y) -2(-x-y)
= -2x-y+2x+2y
Combining like terms together
We get ,
= (-2x+2x)+(2y-y)
= 0+y
=y
Therefore , the Simplified expression for -(2x + y) -2(-x-y) is y.
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Determine whether the following are mutually exclusive. Explain.
choosing a quadrilateral that is a square and a quadrilateral that is a rectangle
A quadrilateral can be both a square and a rectangle, or a rectangle but not a square, because squares are rectangles but rectangles are not always squares. They do not conflict with one another.
What is termed quadrilateral?
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.What types of quadrilaterals are examples?
A closed, two-dimensional figure with four sides, four angles, and four vertices is called a quadrilateral. Square, rectangle, and trapezium are a few examples of quadrilaterals.
The two events are mutually exclusive if they cannot occur at the same time.
A quadrilateral can be both a square and a rectangle, or a rectangle but not a square, because squares are rectangles but rectangles are not always squares.
They do not conflict with one another.
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How can -6 be expressed as the sum of its integer and fractional parts?
The sum of its integer and fractional parts is (-6) + (-1/3).
What are fractions?Fractions are numerical values that represent a subset of a larger whole. A fraction is a portion or section of a whole quantity, which can be any number, a specific value, or a thing.
What Are Mixed Fractions, exactly?A mixed fraction is made up of both a whole number and a fraction. If 8 is a whole number and 1/2 is a fraction, the result is a mixed fraction.
The given expression is -6 1/3.
The integral part is -6, and the fractional part is 1/3.
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The correct question is: " How can - 6 1/3 be expressed as the sum of its integer and fractional parts? "
What is three x plus five x
Write a recursive definition for each sequence. 2,-4,8,-16, . . . .
A recursive definition of the given Geometric progression is: [tex]a_{n}=a_{n-1}r[/tex], with a₁ = 2 and n > 1.
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: 2, -4, 8, -16, ...
Here, [tex]r = \frac{-4}{2} = -2[/tex] and a₁ = 2.
Thus, a recursive formula for this geometric progression can be: [tex]a_{n}=a_{n-1}r[/tex], with a₁ = 2 and n > 1.
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Find the slope of the line through each pair of points. (2,7) and (-3,11)
The slope of line passing through points (2,7) and (-3,11) is -4/5.
What is the slope of line?Slope of a Line
The slope of a line is defined as the increase divided by the run, or as the ratio of the rise to the run. It describes the slope of the line in the coordinate plane. Calculating the slope of a line and determining the slope between two different points are similar activities.
The following formula is used to determine slope:
The slope of the line between two points is given by y2 - y1 / x2 - x1.
Given points are -
(2,7) and (-3,11)
Slope of the line is -
= 11 - 7 / -3 -2
= 4 / -5
So the slope of the line is -4/5
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Q is in the interior of right PRS. if m PRQ is 4 times larger as m QRS,what is m PRQ
Activity
Brayden, Howard, and Vincent are on the football team. During a game, Brayden gains 1 less than 5 times the average number of yards gained per play during the game. Howard runs for 1 more than 5 times the average number of yards gained per play during the game. Vincent runs for 5 more than 4 times the average number of yards gained per play during the game.
Question:
Is it possible that all three players gained the same number of yards? Explain your response.
Answer:
The equation for Brayden and Howard gaining the same number of yards has no solution. So, they could not have gained the same number of yards. Because Brayden and Howard could not have gained the same number of yards, all three could not have gained the same number of yards.
Step-by-step explanation:
(This is straight from Edmentum)
help
I will be using your answer in the question so follow the prompt carefully.
Answer:
1/5 as a fraction can be turned into 20/100. (Multiply the top and bottom by 20). 20/100 can be turned into 0.2.
0.2 multiplied by something will end up as 20% of the original value. So 0.2 and 20% are the same.
Therefore, they are all equal.
Step-by-step explanation:
1/5 as a fraction can be turned into 20/100. (Multiply the top and bottom by 20). 20/100 can be turned into 0.2.
0.2 multiplied by something will end up as 20% of the original value. So 0.2 and 20% are the same.
Therefore, they are all equal.
Select the correct answer.
A triangle with vertices at A(0, 0), B(0, 4), and C(6, 0) is dilated to yield a triangle with vertices at A10, 0), B(0, 10), and C115, 0). The origin is the
center of dilation. What is the scale factor of the dilation?
OA. 1.5
OB. 2
OC. 2.5
D. 3
Reset
Next
the scale of dilation is 2.5 for the triangle ABC.
We are given the coordinates of triangle ABC as:
A(0, 0), B(0, 4), and C(6, 0)
Coordinates of dilated triangle A'B'C' is:
A' (10, 0), B'(0, 10), and C' (15, 0).
The scale of dilation can be calculated as:
k · ( 0, 0 ) = ( 0 , 0 )
k · ( 0 , 4 ) = ( 0 , 10 )
k · ( 6, 0 ) = ( 15, 0 )
k = 15 / 6 = 10 / 4 = 2.5
The scale of dilation is 2.5 for the triangle.
Therefore, the scale of dilation is 2.5 for the triangle ABC.
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Ms. Turner drove 100 miles in January. She drove 3 times as many miles in March as she did in January. She drove 4 times as many miles in February as she did in March. How many miles did Ms. Turner drive in February?
Step-by-step explanation:
100x4=400miles
400miles in February
OR
300x4=1200 miles
1200 miles in February
I don't know what is the correct one tho
Answer:
Step-by-step explanation:
1200 miles
What is 38 plus negative 17 in integers?
Answer:
Step-by-step explanation:
38 + (-17) = 21
Answer:
The answer would be 55
Step-by-step explanation:
38-(-17)
38+ +17
55
do i set them equal to each other since they are opposite from one another? or do i set it equal to 180? Can someone help? thanks !
Answer:
Step-by-step explanation:
Okay so this is fun, let's lable the angle just under 72, but still on the right side B. now, side b is corresponding or equal to (2y+48). So you set them to equal 180 because it makes a straight line....
(2y+48) + 72 = 180
2y + 48 + 72 = 180
2y + 120 = 180
2y = 180 - 120
2y = 60
y = 60/2
y = 30
plug this back in and ...
2(30)+48 =
(60+48) =
108
No we'll use 108 + 72 to make sure that the y is correct and....
108 + 72 = 180 so.. CORRECT! :)
Which quantity decreases as the sample size increases?
a. the standard deviation
b. the standard error
c. the population mean
d. the mean of all the sample means
The standard deviation decreases as the sample size increases.
What is standard deviation?The degree of data dispersion from the mean is measured by the standard deviation. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
A region containing 68 percent of the total number of data points would be defined by one standard deviation, or one sigma, shown above or below the average value on that normal distribution curve. Ninety-five percent of the data would be covered by two sigmas above or below, whereas three sigmas would cover 99.7 percent.
The standard deviation is significant because it reveals the degree of dispersion of the values in a particular dataset. Every time we examine a dataset, we look for the following metrics: the dataset's geographic center.
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In Triangle ABC, the measure of angle B is 50 degrees. Select all (there may be one or more) possible measure angles of A and C if ABC is a right triangle.
By using angle sum property, The value of ∠ A = 40° and ∠ C = 90°
A triangle's total angle is 180°.
Using angle sum property,
∠A+∠B+∠C = 180°
assuming B = 50°
replacing in the formula
∠A+50+∠C = 180°
Due to the triangle's right angle, A+90=180-50
∠A = 130° - 90
∠ A = 40°
The angles A and C must be more than 90 degrees since the ABC is a right triangle.
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Complete question -In triangle ABC, the measure of angle B is 50 degrees. Select all possible values for the measures of A and C if ABC is an right triangle. m\angle∠A= 58 degrees; m\angle∠C= 72 degrees m\angle∠A= 100 degrees; m\angle∠C= 30 degrees m\angle∠A= 80 degrees; m\angle∠C= 50 degrees m\angle∠A= 60 degrees; m\angle∠C= 70 degrees m\angle∠A= 90 degrees; m\angle∠C= 40 degrees m\angle∠A= 105 degrees; m\angle∠C= 25 degrees
Answer:
m∠A = 40°, m∠B = 75°, m∠C = 65° (A)
m∠A = 136°, m∠B = 28°, m∠C = 16° (B)
m∠A = 60°, m∠B = 60°, m∠C = 60° (E)
Step-by-step explanation:
i did the assignment and got it wrong at first then it showed me the right answers
what is f(2)= for the piecewise?
Answer:
Piece wise
Step-by-step explanation:
Piecewise function definition A piecewise function is a function that is defined by different formulas or functions for each given interval. Its also in the name: piece. The function is defined by pieces of functions for each part of the domain.
Which expressions are equivalent to (d^1/8)^5
Using exponent properties we can get two equivalent expressions:
⁸√d^5
d^(5/8)
Which expressions are equivalent to (d^1/8)^5?Here we need to use two properties, these are:
ⁿ√x = x^(1/n)
(x^n)^m = x^(n*m)
Now, if we use the first property, we can rewrite the expression as:
(d^1/8)^5 = ⁸√d^5
Which is an equivalent expression.
If we use the other property we can get:
(d^1/8)^5 = d^( (1/8)*5) = d^(5/8)
Which is another equivalent expression.
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Lisa has $375 left after paying her total expenses for the month. She wants to buy an exercise machine for$660. How much would she have to save for three months to have enough to buy this new exercise machine? For four months? For six months?
Answer:
Step-by-step explanation:
285 dollars. the left money = 660 - 375 =285
PLEASE HURRY THIS IS TIMED!!! I WILL CHOOSE BRAINLIEST!!!
Step-by-step explanation:
A=M
B=N
E=P
AB=MB
BE=NP
AE=MP
I don't know about the blanks sorry
Refer to ®N . If EN = 13 feet, what is the diameter of the circle?
EN is a radius and the diameter is twice the radius. The diameter of the circle is 26 ft.
What is meant by diameter?In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.
The diameter is twice the radius because the greatest distance between two points on a circle must be a line segment through the center of the circle.
Here, CF is a radius and the diameter is twice the radius.
Diameter of a circle = 2r
d = 2r
Where, r = 13
Diameter of a circle, d = 2r
Diameter of a circle = 2(13)
Diameter of a circle = 26
Therefore, the diameter of the circle is 26 ft.
Here, EN is a radius and the diameter is twice the radius.
Therefore, the diameter is 26 ft.
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Are collinearity and betweenness of points maintained under rotation? Explain.
Yes , Are collinearity and betweenness of points maintained under rotation.
A rotation is a transformation that maintains congruence of the original figure and its image.
What does "collinearity" mean?
Collinearity is the statistical term for the correlation of predictor variables (or independent variables) in a regression model to represent a linear connection. They are unable to independently estimate the value of the dependent variable when predictor variables in the same regression model are coupled.What is an example of collinearity?
We have perfect multicollinearity if there is a precise linear relationship between two or more independent variables. Incorrect use of dummy variables (falling into the dummy variable trap), repeating the same information (weight in pounds and weight in kilograms), etc.Learn more about collinearity
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