Answers
The figure with the least surface area is the cube.
How to find the surface area of a figure?The surface area of a 3 dimensional figure or solid figure is the sum of the area of the whole surface.
Therefore,
surface area of the cube = 6a²
where
a = side lengthsurface area of the cube = 6 × 6²
surface area of the cube = 6 × 36
surface area of the cube = 216 units²
surface area of the second rectangular prism = 2(lh + lw + hw)
where
l = lengthw = widthh = heightTherefore,
surface area of the second rectangular prism = 2(54 + 54 + 16)
surface area of the second rectangular prism = 2(124)
surface area of the second rectangular prism = 248 units²
Therefore,
surface area of the third rectangular prism = 2(13.5 + 216 + 16)
surface area of the third rectangular prism = 2(245.5)
surface area of the third rectangular prism = 491 units²
Therefore, the least surface area is the cube.
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Related Questions
Logan mows (L) lawns each week for 8 weeks. Eve mows 2 fewer lawns than Logan each week.
a. Write an expression that represents the number of lawns Eve mows in those 8 weeks.
b. Evaluate the expression from part (a) when (L) = 3. Interpret the result
c. Write an expression equivalent to the one from part (a) by using a tabular model.
d. If Logan mows 5 lawns each week, how many lawns does Eve mow in 8 weeks?
(Must show work)
Answers
a)
The expression that represents the number of lawns Eve mows in those 8 weeks is 8(L- 2)
b)
The value of the expression is 8.
c)
The tabular table is given above.
d)
Eve mowed 24 lawns in 8 weeks.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Logan:
Number of lawns each week = L
Number of lawns 8 weeks = 8L
Eve:
Number of lawns each week = )L - 2)
Number of lawns 8 weeks = 8(L- 2)
a)
The expression represents the number of lawns Eve mowed in those 8 weeks.
= 8(L -2)
b)
When L = 3,
8 (L - 2)
= 8 (3 - 2)
= 8 x 1
= 8
c)
Tabular table
Number of weeks Number of lawns
Logan x xL
Eve x x(L - 2)
d)
Logan:
Number of lawns in one week = 5
L = 5
Eve:
Number of lawns in 8 weeks.
= 8 (L - 2)
= 8 (5 - 2)
= 8 x 3
= 24
Thus,
a) 8(L- 2)
b) 8
c) Tabular table is given above.
d) Eve mowed 24 lawns in 8 weeks.
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A sign company is building a sign with the dimensions shown.
What is the area of the sign? Question 4 options:
A. 60 square feet
B. 240 square feet
C. 120 square feet
D. 260 square feet
Answers
TLDR: Your answer is D. 260 square feet.
To find the area of a triangle, you must use the formula "1/2 B ⋅ H."
In this problem, your values are the following:
B = 20
H = 26
Now, you just plug these values in and solve.
1/2 (20) ⋅ 26 > 10 ⋅ 26 = 260 ft
Dottie went to the movies with her friends. She bought a soda for $2.35, a pack of bubble gum for $1.15, and a chocolate bar for $1.65. How much did Dottie spend in total?
Answers
Answer:
Step-by-step explanation:
The candy bar cost, in dollars, is $1.05
Say the price of a piece of bubble gum is x.
This means that we can represent our scenario with the equation (x+1)+x=1.10, with (x+1) representing the price of a candy bar.
We can then solve from there.
We have given that,
(x+1)+x=1.10
Simplify above expression
2x+1=1.10
2x=0.10 - Subtract From Both Sides
x=0.05 - Divide From Both Sides
So now we have the price of the piece of bubble gum, but we want the cost of the candy bar.
What is the cost?
Cost is the value of money that a company had to spend to produce its goods or services.
Fortunately, we know it costs one dollar more than the piece of bubble gum, so just do 0.05 + 1. This means our candy bar costs $1.05.
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Answer:
Soda = 2.35
Pack of bubble gum = 1.15
Chocolate bar = 1.64
2.35 + 1.15 + 1.64 = 5.15
Answer: Dottie spent a total of $5.15.
66th term of the arithmetic sequence 3, 13, 23,
Answers
The 66th term of this arithmetic sequence is equal to 653.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference as follows.
Common difference, d = a₂ - a₁
Common difference, d = 13 - 3
Common difference, d = 10.
Substituting the given parameters into the formula, the 66th term of this arithmetic sequence is given by;
a₆₆ = a₁ + (n - 1)d
a₆₆ = 3 + (66 - 1)10
a₆₆ = 3 + (65)10
a₆₆ = 3 +650
a₆₆ = 653.
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The 66th term of the arithmetic sequence is 653
What are arithmetic sequence?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.
The nth term of an arithmetic sequence is given as:
a(n) = a1 + (n-1) d
a1 is the first term and d is common difference
d =10, a = 3
a(66) = 3 + ( 66-1) 10
a(66) = 3+ 65 ×10
a(66) = 3 + 650
a(66) = 653
therefore the 66th term of the sequence is 653
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a sample is a subset of all possible data values for a given subject under consideration.
Answers
False. A sample is a subset of all possible data values for a given subject under consideration, not the set of all possible data values.
What is sample space?
The set of all potential outcomes for an experiment is referred to as the sample space S in a random experiment. The results of a random experiment, also known as sample points, are incompatible (i.e., they cannot occur simultaneously).
According to question:A sample is a portion of a larger set of data that is selected for analysis or representation. It is not the entire set of all possible data values for a given subject, but rather a smaller subset chosen for the purpose of study.
Sampling is important because it allows researchers to study and make inferences about a larger population with a smaller, more manageable amount of data.
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jim has received scores of 69 and 82 on his first two 100 point tests. what score must he get on his third 100 point test to keep an average of 85 or greater?
Answers
Jim needs a score of 97 on his third test to keep an average of 85 or greater.
Average refers to the sum of a set of numbers divided by the count of numbers in the set. It gives a typical or central value that represents the set of numbers.
Given,
The average of his first two tests is (69 + 82) / 2 = 75.5.
To get an average of 85,
he needs the sum of his three tests to be 3 * 85 = 255.
So, the sum of his first two tests is 255 - x, where x is the score he needs on the third test.
Therefore, x = 255 - (69 + 82) = 255 - 151 = 104.
So, he needs a score of 104 on his third test.
Jim needs a score of 97 on his third test to keep an average of 85 or greater.
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3.35x + 115 = 3.25x + 125
Answers
For the given expression 3.35x + 115 = 3.25x + 125 the value of x is 100.
What is an equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
The given expression is:
3.35x + 115 = 3.25x + 125
Regroup all the terms with variable x on one side of the equation:
3.35x - 3.25x = 125 - 115
0.1x = 10
x = 100
Hence, for the given expression 3.35x + 115 = 3.25x + 125 the value of x is 100.
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michael is 3 33 times as old as brandon. 18 1818 years ago, michael was 9 99 times as old as brandon. how old is brandon now?
Answers
Brandon is currently 6 81 years old.
Let M be Michael's age and B be Brandon's age.
We are given that Michael is 3 33 times as old as Brandon. This means that M = 3 33 × B
We are also given that 18 1818 years ago, Michael was 9 99 times as old as Brandon. This means that M - 18 1818 = 9 99 × (B - 18 1818).
We can combine these two equations to solve for Brandon's current age:
3 33 × B = (9 99 × B) + 18 1818
2 66 × B = 18 1818
B = 18 1818 / 2 66 = 6 81.
Therefore, Brandon is currently 6 81 years old.
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Can someone help me ive been stuck on this for a bit
Keenan opens a savings account with $740
that earns 6% interest per year, not compounded.
How much money, to the nearest penny, will Keenan have in 8 years? Give your answer in dollars.
Answers
Answer: $1095.20
Step-by-step explanation: Multiply 6% by 740 and then times that number by 8 and add it to 740, lmk if it is wrong though.
Answer:
1095.20
Step-by-step explanation:
Take the 8 for the amount of time and multiply it by .06 because .06 is repeating each year.
You get .48 when you multiply it. Take that decimal and multiply it by 740.
He will get an extra 355.20. Add that with 740.
He has $1095.20 in his account.
Evaluate each expression if d = –24, e = –4, & f = 8.
f+8/-4
Answers
Answer:
d=-28 and e=-20
Step-by-step explanation:
d×1=-24×1=e=4
d=-24-4=-28
three consecutive even integers are such that the sum of the smaller two is 52 less than three times the largest. what are the integers?
Answers
Three consecutives even integers are 42, 44, and 46.
The three consecutives even integers can be represented as x, x+2, and x+4. We can create an equation to solve for x, using the given information.
3(x+4) = 52 + x + (x+2)
3x + 12 = 54 + 2x
x = 42
Therefore, the three consecutives even integers are 42, 44, and 46. To explain this answer, we can use the equation we created. We know that the sum of the smaller two integers is 52 less than three times the largest. We can represent this as 3(x+4) = 52 + x + (x+2). We can then solve for x by subtracting 2x from both sides and adding 12 to both sides, resulting in x = 42. This means that the three consecutives even integers are 42, 44, and 46.
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East Middle’s football team has 20.9 liters of sports drink on the field during the game. Each player receives the same amount of sports drink.
If East Middle’s football team consists of 22 players, how much sports drink, in liters, does each player receive?
(Write the answer as a decimal to the nearest hundredth.)
Answers
Taking the quotient between the volume of sports drink and the number of players we will see that each player gets 0.95 liters.
How much sports drink, in liters, does each player receive?We know that East Middle’s football team has 20.9 liters of sports drink on the field during the game. Now we want to divide that evenly among all the players of the team, and we know that the team has 22 players.
Then we just need to take the quotient between these two numbers, it is:
20.9/22
We can rewrite that as:
(209/10)*(1/22)
(209/220)
Each player receives (209/220) liters of sports drink.
We can also simplify that as (209/220) liters = 0.95 liters.
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Among fatal plane crashes that occurred during the past 70 years, 503 were due to pilot error, 90 were due to other human error, 326 were due to weather, 382 were due to mechanical problems, and 643 were due to sabotage.What is the most serious threat to aviation safety, and can anything be done about it?
A. Sabotage is the most serious threat to aviation safety. Airport security could be increased.
B. Mechanical problems are the most serious threat to aviation safety. New planes could be better engineered.
C. Weather is the most serious threat to aviation safety. Weather monitoring systems could be improved. D. Pilot error isPilot error is the most serious threat to aviation safety. Pilots could be better trained.
Answers
Sabotage is the most serious threat to aviation safety. Airport security could be increased.
The relative normal probability plot of aeroplane crashes is derived by using its concept:
Error of the pilot: 503/1944 = 0.258.
90/1944 erroneous by humans: 0.046.
326/1944 = 0.167 for weather.
issues with the mechanics: 382/1944 = 0.196.
643/1944 = 0.330 sabotage.
Sabotage provide the chief concern as a result of the higher relative frequency; therefore, airport security could be increased.
Define Relative Frequency.
The number of desired outcomes divided by the total number of outcomes yields a relative frequency.
The total number of accidents in this problem is provided by:
503+90+326+382+643 = 1944
Following are the relative frequencies of each cause:
Error of the pilot: 503/1944 = 0.258.
90/1944 erroneous by humans: 0.046.
326/1944 = 0.167 for weather.
issues with the mechanics: 382/1944 = 0.196.
643/1944 = 0.330 sabotage.
Due to Sabotage provide the greatest concern as a result of the increased relative frequency; therefore, airport security should be increased.
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Graph g(x) = |x + 3|.
Answers
the graph of the function g(x) = |x + 3| will not have a negative value. graph of the given function is attached below.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given a function g(x) = |x + 3|.
Since the modulus of a function is a function that gives the absolute value of a number or variable. It produces the magnitude of the number of variables. It is also termed an absolute value function. The outcome of this function is always positive, no matter what input has been given to the function.
Thus,
The domain of this function g(x) is - infinite to + infinite
And range will be [0, ∞)
So the graph of the function g(x) = |x + 3| will not have a negative value.
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the process of using sample statistics to draw conclusions about population parameters is called: group of answer choices calculating the confidence level. calculating descriptive statistics. finding the significance level. doing inferential statistics.
Answers
Option D. Doing inferential statistics. Inferential statistics is the process of using sample statistics to draw conclusions about population parameters.
This involves making inferences about a population based on data collected from a sample, and using statistical methods to estimate the true values of population parameters, such as the mean or proportion.
Descriptive statistics, on the other hand, involves summarizing and describing the characteristics of a sample or population, without making any inferences about the larger population.
Calculating the confidence level and finding the significance level are important components of inferential statistics, as they help to assess the accuracy and reliability of the estimates made based on the sample data. However, these are not the primary processes involved in using sample statistics to draw conclusions about population parameters.
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The process of using sample statistics to draw conclusions about population parameters is called: group of answer choices
A. Calculating the confidence level.
B. Calculating descriptive statistics.
C. Finding the significance level.
D. Doing inferential statistics.
Find the slope of a line parallel to the line whose equation is 3x+18y=-4863x+18y=−486. Fully simplify your answer.
Answers
The slope of the parallel line is given by the equation m = ( -1/6 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
3x + 18y = -486 be equation (1)
On simplifying the equation , we get
Subtracting 3x on both sides of the equation , we get
18y = -3x - 486
Divide by 18 on both sides of the equation , we get
y = ( -3/18 )x - ( 486/18 )
On further simplification , we get
y = ( -1/6 )x - 27
Now , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
Slope m = -( 1/6 )
Hence , the slope of the line is m = -1/6
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to start her old lawn mower, rita has to pull a cord and hope for some luck. on any particular pull, the mower has a 20% chance of starting. what is the probability that it takes her exactly 3 pulls to start the mower?
Answers
Rita's old lawn mower will start after exactly three pulls 12.8% of the time,
The binomial probability formula states that the probability of success occurring precisely x times in n trials is equal to the product of the probability of success (p) and the probability of failure (1-p) raised to the power of n-x. This can be used to calculate this. The probability of success occurring exactly three times is equal to 0.2 x 0.8 x 0.8, or 12.8%, given that the number of trials (n) and the probability of success (p) is both 20 percent.
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Avery decides to take her puppy for a walk. After 90 feet, they stop to smell some roses. Then, Avery runs into a friend 200 yards up the road. They start talking, and soon it's time for Avery to go home. So, she and her puppy head back to her house. How many feet long was Avery's walk?
Answers
Answer:
Below
Step-by-step explanation:
90 feet + 200 yrads = 90 feet + 200 *3 feet = 690 feet EACH direction for a total of 690 * 2 = 1380 ft
Answer:
1380 ft long
Step-by-step explanation:
1. You would convert 200 yds to feet. (3ft in a yd so 600 ft.)
2. Add 600+90 to figure out how far she walked to her friend.
3. Double it because she walked the same distance to get home.
Whole numbers are _____ integers. always, sometimes, never
Answers
Answer:
Always
Step-by-step explanation:
A whole number will always be an interger.
HELP
There are 6p+18 fiction books and 4p+12 non-fiction books in a bookcase.
Work out the fraction of the books in the bookcase that are non-fiction.
Give your answer in its simplest form.
Answers
The fraction of the books in the bookcase that are non-fiction is 2/5.
What is fraction?A fraction is a part of a whole number, and a way to split up a number into equal parts.
Given that, there are 6p+18 fiction books and 4p+12 non-fiction books in a bookcase, we need to find the fraction of the books in the bookcase that are non-fiction.
Therefore,
Number of fictional books = 6p+18
Number of non-fictional books = 4p+12
Total books = 6p+18+4p+12 = 10p+30
Therefore,
the fraction of the books in the bookcase that are non-fiction is given by,
Number of non-fictional books / Total books
= 4p+12 / 10p+30
= 4(p+3) / 10(p+3)
= 4/10
= 2/5
Hence, the fraction of the books in the bookcase that are non-fiction is 2/5.
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Which is more, 97 ounces or 6 pounds?
Answers
Answer:
97oz
Step-by-step explanation:
16oz per lb
16x6=96
96oz<97oz
Answer: They are equal
Step-by-step explanation:
the distance from the ground of a person riding on a ferris wheel can be modeled by the equation d equals 20 times the sine of the quantity pi over 30 times t end quantity plus 10 comma where d represents the distance, in feet, of the person above the ground after t seconds. how long will it take for the ferris wheel to make one revolution?
Answers
It takes approximately 26.56 seconds for the ferris wheel to make one revolution.
The ferris wheel makes one complete revolution when the distance of the person above the ground returns to the original value after completing a full circle.
This occurs when the sine function returns to its maximum value, which is 1.
Thus, we have the following equation:
20 * sin(π/30 * t) + 10 = 20
Solving for t,
we will get:
sin(π/30 * t) = 0.5
Taking the inverse sine of both sides:
(π/30 * t) = sin^-1(0.5)
Multiplying both sides by 30/π,
we will get the following:
t = (30/π) * sin^-1(0.5)
Now solving the value of t
We will get it as: t ≈ 26.56 seconds.
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A system of equations is made up of an ellipse and a hyperbola. Part A: Create the equation of an ellipse centered at the origin, with a horizontal major axis of 8 units and a minor axis of 6 units. Show your work. (3 points) Part B: Create the equation of a hyperbola centered at the origin, with a horizontal transverse axis, vertex at (–7, 0), and asymptotes of y equals plus or minus six sevenths x period Show your work. (4 points) Part C: Determine the domain of each conic section and use it to explain why there is no solution to the system. (3 points)
Answers
The equation of the ellipse and the equation of the hyperbola can be derived from the given information and the general form of the equations.
Part A: The equation of the ellipse is [tex]\frac{x^2}{3^2} + \frac{y^2}{4^2} = 1[/tex]
Part B The equation of the hyperbola is [tex]\frac{x^2}{(-4)^2} - \frac{y^2}{(-7)^2} = 1[/tex]
Part C: The domain of the ellipse is; [-3, 3]
The domain of the hyperbola is; (-∞, -4]
The domains of the ellipse and the hyperbola do not intersect, therefore, the system of the equation has no solution.
What is an Ellipse?A planar curve with two focal points is called an ellipse if at every point on the curve the sum of the two distances from the focal points is constant.
The domain of the hyperbola = x < The negative vertex
∴ The domain of the hyperbola = x < -4 = (-∞, -4]
The above domain of the ellipse does not extend to the hyperbola, therefore there is no solution to the system
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you plant two flowers in a garden. The equations y= 13.6x + 21 and y=9.4x+ 21 model the heights y of the flowers, in millimeters, after x days. what does the y-intercept of each equation represent? Will the flowers ever be the same height?
Answers
The y-intercept represents the initial height when the were planted.
The height of both plants will never be the same.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
The equations y = 13.6x + 21 and y = 9.4x + 21 represent the heights of two flower plants in a garden in millimeters.
We know y-intercept is when x = 0,
Therefore, y = 21 and y = 21 represent the initial height when they were planted.
The height of the plants will never be the same because the initial height was the same but one plant is growing faster than the other.
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What is the volume of this prism?
Answers
Answer:
560
Step-by-step explanation:
7*20*4=560
Solve x²+bx+c = 0 by completing the square. Your answer will be an expression for x in terms of b and c.
Answers
The roots of the given quadratic function would be -
x = {- b - √(b² - 4c)}/2 & x = {- b + √(b² - 4c)}/2
What is a function? What is a quadratic function?A function describes a relationship between a dependent and independent variable. Example -
y = f(x) = 5x + 9
A quadratic function is of the form -
y = f(x) = ax² + bx + c
Given is the quadratic equation as -
x² + bx + c = 0
Using the quadratic formula, we can write the roots as -
x = {- b ± √(b² - 4c)}/2
We can write the two distinct roots as -
x = {- b - √(b² - 4c)}/2 & x = {- b + √(b² - 4c)}/2
Therefore, the roots of the given quadratic function would be -
x = {- b - √(b² - 4c)}/2 & x = {- b + √(b² - 4c)}/2.
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Write an explicit formula for a,, the nth term of the sequence 14,16,18,….
Answers
The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.
What is the explicit formula for the nth term of the sequence?Since the sequence increases by 2, it is an arithmetic sequence.
The formula the nth term an arithmetic sequence is expressed as;
aₙ = a₁ + d( n - 1 )
Given the sequence; 14,16,18,….
First term a₁ = 14
Common difference d = 16 - 14 = 2
Now, plug the values into the above formula and simplify.
aₙ = a₁ + d( n - 1 )
aₙ = 14 + 2( n - 1 )
aₙ = 14 + 2n - 2
aₙ = 14 - 2 + 2n
aₙ = 2n + 12
Therefore, the explicit formula is aₙ = 2n + 12.
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Amelia selects a pupil from the list at random 300 times and records the
number of pupils who studies Spanish, Italian, French or German.
Subject Spanish Italian
Frequency 90
60
French German
30
120
Amelia selects a pupil from the list at random 300 times.
Work out the relative frequency that a pupil studies French.
Submit Answer
Answers
The relative frequency that a pupil studies French is 0.1
What is Relative Frequency?This refers to the proportion of one event's frequency to all events' frequencies in a statistical experiment.
Given that:
The total number of data values is 300
The frequency of a pupil that studies French is 30
The relative frequency is 30/300 = 0.1
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The triangle on the right is a scaled copy of the triangle on the left. Identify the scale
factor. Express your answer as a whole number or fraction in simplest form.
Answers
Scale-factor of copy to original is 3/2.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Given,
Right side triangle is scaled copy of left side triangle
Ratio of side of copy to side of original = (57/2) / 19 = 3/2
So, Scale factor = 3/2
Hence, 3/2 is the scale-factor in making copy of original triangle.
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now, let's consider the effects of time dilation. how far would the pion actually travel before decaying?
Answers
To get the number of half-lives passed, we divide the time of flight from part a by the length of a half-life, as
given in the statement of the problem:
Number of half lives = 2×10−4
1.5×10−6 ≈ 133
The fraction of remaining muons will decrease by 1/2
every half life, so the fraction after a given number N of
half-lives will be:
1/2 × 1/2 × 1/2
· · · N times · · · × 1/2 = ( 1/2)N .
This makes the fraction remaining equal to 1/2 to the power 133:
fraction remaining = ( 1/2)
133 ≈ 10−40. That’s not very many muons
First-generation quarks are what make up pions, which are mesons with no spin. An anti-down quark and an up quark are described in the quark model. In addition to vector, rho, and omega mesons, the exchange of virtual pions also explains why there is still a strong interaction between nucleons. Pions are typically created in high-energy collisions between hadrons and are not created during radioactive decay. In some matter-antimatter annihilation processes, pions are also produced.
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Note that the full question is:
Ne of the many fundamental particles in nature is the muon mu. This particle acts very much like a "heavy electron." It has a mass of 106 MeV/c^2, compared to the electron's mass of just 0.511 MeV/c^2. (We are using E = mc^2 to obtain the mass in units of energy and the speed of light c).Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (nu). We'll ignore the neutrinos throughout this problem.
If the muon is at rest, the characteristic time that it takes it to decay is about 2.2 microseconds. Most of the time, though, particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects.
Cosmic rays are constantly raining down on the earth from outer space. (Figure 1)The majority of these cosmic rays are protons, and when upper atmosphere, they can convert into particles called pions (), which subsequently decay into muons with a characteristic lifetime of T.
Suppose that a cosmic-ray proton crashes into a nitrogen molecule in the upper atmosphere. 45 km above the earth's surface, producing a pia a muon. Assume that the pion has a velocity of 99.99% the speed of light and decays into a muon, which, owing to kinematics, has a downward velocity of 99.9943% the speed of light.
now let’s consider the effect of time dilation how far would the pion actually travel before decaying?