Answers
The period of time during which the projectile is at least 240 feet above the ground is 3 seconds <= t <= 5 seconds.
What is time of projectile motion?
Vertical motion totally determines the time for projectile motion.
The height of the projectile above the ground after t seconds is given by s = -16t^2 + 128t. To find the period of time during which the projectile is at least 240 feet above the ground, we need to find the values of t for which s >= 240.
Solving for t:
-16t^2 + 128t >= 240
-16t^2 + 128t - 240 >= 0
t^2 - 8t + 15 >= 0
(t - 5)(t - 3) >= 0
So t must be between 3 and 5 seconds, inclusive.
Therefore, the period of time during which the projectile is at least 240 feet above the ground is 3 seconds <= t <= 5 seconds.
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Related Questions
A stone is projected vertically so that its position above ground level after t
seconds is given by h(t)=100t−5t2
meters, t≥0
.
Which one of the following is the maximum height the stone can reach?
Answers
Answer: The height of the stone after time "t" is given by the function h(t) = 100t - 5t^2, where t is in seconds. To find the maximum height, we need to find the value of t for which the height is greatest.
To do this, we can take the derivative of h(t) with respect to t, which gives us the rate of change of height with respect to time. Then, we can set this derivative equal to 0 and solve for t. The value of t that satisfies this condition will be the time at which the height is at its maximum.
h'(t) = 100 - 10t
Setting h'(t) = 0, we get:
100 - 10t = 0
10t = 100
t = 10
So, the maximum height is h(10) = 100 * 10 - 5 * 10^2 = 100 - 500 = -400 meters.
Since the height cannot be negative, the maximum height the stone can reach is 100 meters.
Step-by-step explanation:
Solve the following system of equations:
-2x + 5y = −11
4x - 3y = 15
Answers
Answer: (x,y)=(3,-1)
Step-by-step explanation:
Juan's mother gave him a recipe for trail mix. What is the order of the ingredients from least to greatest?3/4 cup raisins1/3 cup almonds2/3 cup peanuts1/2 cup cereal
Answers
The answer to question of trail mix in ascending order would be, 1/2 cup cereal, 3/4 cup raisins, 1/3 cup almonds, 2/3 cup peanuts.
The order of ingredients from least to greatest for Juan's trail mix recipe is: 1/2 cup cereal, 3/4 cup raisins, 1/3 cup almonds, and 2/3 cup peanuts. Juan's mother provided the recipe which consists of a combination of dried fruits, nuts, and cereal. The recipe calls for 1/2 cup of cereal, which is the least amount of any of the ingredients. The next ingredient is 3/4 cup of raisins, followed by 1/3 cup of almonds, and finally 2/3 cup of peanuts, which is the greatest amount of any of the ingredients. These ingredients can be combined and enjoyed as a snack.
Hence the answer is, 1/2 cup cereal, 3/4 cup raisins, 1/3 cup almonds, 2/3 cup peanuts.
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Which of the following describes a situation in which it is reasonable to reach a cause-and-effect conclusion based on data from a statistical study?answer choices- The study is based on a random sample from a population of interest.- The study is observational, and the sample used is not a convenience sample.- The study is an experiment that uses random assignment to assign volunteers to experimental conditions (treatments).- It is never reasonable to reach a cause-and-effect conclusion based on data from a statistical study.- It is always reasonable to reach a cause-and-effect conclusion based on data from a statistical study.
Answers
The correct answer is: The study is an experiment that uses random assignment to assign volunteers to experimental conditions (treatments).
What is statistical study?A sample is an analytic subset of a larger population in statistics. The utilization of samples enables researchers to conduct investigations with more manageable data and more quickly. Randomly chosen samples exhibit little bias if they are large enough, but obtaining such a sample can be costly and time-consuming.
Here,
A study that uses random assignment to assign volunteers to experimental conditions (treatments) is considered the best design to establish cause-and-effect relationships. In this type of study, researchers can control the variables and minimize extraneous factors that could confound the results. By using random assignment, the volunteers in the experimental and control groups are similar on average, making it more likely that any observed differences between the groups are due to the treatments.
The correct answer is: The research is an experiment in which volunteers are randomly assigned to experimental settings (treatments).
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What is the quotient when the dividend is 40 and the divisor is 2.5?
Answers
Answer:
16.00
Step-by-step explanation:
400 divided by 25 is also 16, so divide that and it should be the same as 40 divided by 2.5
QUOTIENT-
The answer to a division problem
40/2.5 =
16
Which function is the same as y = 3 cosine (2 (x + StartFraction pi Over 2 EndFraction)) minus 2?
y = 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
y = negative 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
y = 3 cosine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
y = negative 3 cosine (2 (x + StartFraction pi Over 2 EndFraction)) minus 2
Answers
The function as the same as y = 3 cosine (2 (x + Start Fraction pi Over 2 End Fraction)) minus is y = -3 sin(2(x + π/4)) - 2 Option B
How to find the function?Sine and cosine have the following relationship:
cos(θ) = sin (π/2 - θ)
y = 3 cos(2 (x + π/2)) - 2
y = 3 cos(2x + π) - 2
Let θ = 2x + π,
therefore using Sine and cosine have the following relationship:
cos(2x + π) = sin (π/2- (2x + π))
= sin (π/2 - 2x - π)
= sin (-2x - π/2)
= sin (-2(x + π/4))
but sin(-θ) = -sin (θ)
Therefore:
sin (-2(x + π/4)) = -sin (2(x + π/4))
= - sin (2(x + π/4)) = cos(2x + π)
y = 3 cos(2x + π) - 2 = 3[ - sin (2(x + π/4))] -2
y = -3 sin (2(x + π/4)) -2
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MBUL with diagonals BL and MU intersecting at point A is shown. Find the value of x that makes MBUL a kite if BA=3x-1, LA=17, MA=2x, and UA=23
Answers
The value of x that makes MBUL a kite is given as follows:
x = 6.
How to obtain the value of x?For MBUL to represent a kite, the following lengths have to be congruent:
BA and AL.
The lengths for this problem are defined as follows:
BA = 3x - 1.LA = 17.As the sides are congruent, the equation is given as follows:
BA = LA.
Hence the value of x that makes MBUL a kite is obtained as follows:
3x - 1 = 17
3x = 18
x = 18/3
x = 6.
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An animal shelter needs to buy 8 pounds of cat food for every cat
they have. Complete the following table of cats to pounds of cat food.
Answers
the food needed for 10 cats will be 80 pounds.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem. Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers
An animal shelter needs to buy 8 pounds of cat food for every cat
they have.
So per pound, it food needed for 10 cats will be 8*10 = 80 pounds.
Hence the food needed for 10 cats will be 80 pounds.
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Assign a variable solveEquation with a function expression that has three parameters (x, y, and z) and returns the result of evaluating the expression 2 * x * y Z?
Answers
The program for assigning variable and solving expression 2 * x * y - z is -
def func1(x, y, z):
return 2*x*y - z
x= int(input("Enter x"))
y= int(input("Enter y"))
z= int(input("Enterz"))
solveEquation=func1(x, y, z)
print (solveEquation)
What is Expression in Code?
Expressions in computer science are written by developers, interpreted by computers, and 'evaluated.' The evaluation yields a result or return. Expressions in code include simple mathematical equations like 2 + 2. They are commonly referred to as arithmetic expressions.
The program for the condition given is -
def func1(x, y, z):
return 2*x*y - z
x= int(input("Enter x"))
y= int(input("Enter y"))
z= int(input("Enterz"))
solveEquation=func1(x, y, z)
print (solveEquation)
Therefore, the coding has been done.
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6x^2 − 5x + 6 = 6x + 3
Answers
Answer:
x=1/3;3/2
Step-by-step explanation:
6x^2-5x+6 = 6x+3
-6 -6
6x^2 -5x = 6x - 3
+5x +5x
6x^2 = 11x -3
6x^2 + 11x - 3 = 0
(3x-1)(2x-3)=0
3x-1=0
3x=1
x=1/3
2x-3=0
2x=3
x=3/2
Given A= {{4,1,6},{-7,5,3},{9,-3,3}}
Observe that the first column plus twice the second column equal the third column. Find a nontrivial solution Ax=0
Answers
The nontrivial solution to the equation Ax = 0 is x = [1, 1, 1]^T.
What is the nontrivial solution?
To find a nontrivial solution to the equation Ax = 0, where A is the given matrix, we need to find a vector x that satisfies the equation and is not the trivial solution x = 0.
We can start by using the observation that the first column plus twice the second column equal the third column:
4x1 - 7x2 + 9x3 = 0
x1 + 2x2 - 3x3 = 0
6x1 + 3x2 + 3x3 = 0
Applying row reduction to the matrix A, we find:
{{4,1,6},{-7,5,3},{9,-3,3}}
{{1,1/2,-3/2},{-7,5,3},{9,-3,3}}
{{1,1/2,-3/2},{0,11/2,15/2},{0,11/2,15/2}}
The rank of the matrix A is 2, which is less than the rank of the matrix of the system of linear equations, which is 3. This means there is a nontrivial solution to the equation Ax = 0.
One such nontrivial solution can be found by setting x3 = 1 and solving for x1 and x2:
x1 + 2x2 - 3(1) = 0
x1 + 2x2 = 3
x1 = 3 - 2x2
Setting x2 = 1, we find:
x1 = 3 - 2(1) = 1
x2 = 1
x3 = 1
Hence, a nontrivial solution to the equation Ax = 0 is x = [1, 1, 1]^T.
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whats the liner expression for 2h - 1 and 3h + 4
Answers
The linear expression for 2h - 1 and 3h + 4 is 5h + 3. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
According to mathematicians, the four fundamental operations, also referred to as "arithmetic operations," can be used to describe all real numbers. Division, multiplication, addition, and subtraction are the four mathematical operations that result in the terms quotient, product, sum, and difference, respectively.
We are given two expressions as 2h - 1 and 3h + 4.
On adding both, we get
2h - 1 + 3h + 4 = 5h + 3
Hence, the linear expression for 2h - 1 and 3h + 4 is 5h + 3.
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For y=f(x)=7x^3, x=5, and Ax=0.06 find
A) Ay for the given x and Ax values,
B) dy=f’ (x)dx,
C) dy for the given x and Ax values
Answers
The functions and equations y = f(x) = 7·x³, x = 5, Δx = 0.06, indicates that we get;
a) Δy = 31.879512
b) dy = 21·x²dx
c) dy = 31.5
What is a function?A function is a rule that maps input variables to output variables in a relationship in which an input is assigned to exactly one output.
a) The value of the function y = f(x) = 7·x³
The value of x = 5
Value of the change in x, Δx = 0.06
The change in y, Δy is therefore;
Δy = f(x + Δx) - f(x), from which we get;
Δy = f(5 + 0.06) - f(5) = f(5.06) - f(5)
Δy = f(5.06) - f(5)
Plugging in the values of x = 5.06, and x = 5 in the function f(x), we get;
f(5.06) = 7 × (5.06)³ = 906.879512
f(5) = 7 × 5³ = 875
Therefore; Δy = f(5.06) - f(5) = 906.879512 - 875 = 31.879512
Δy = 31.879512
b) dy = f'(x)dx
f'(x) is the derivative of the function f(x)
dy/dx = f'(x) = 3 × 7 × x² = 21·x²
dy/dx = f'(x) = 21·x²
dy = f'(x)dx = 21·x²dx
dy = 21·x²dx
c) dy for the given x and Δx values can be found by plugging in x = 5 and dx = Δx = 0.06 in the equation, dy = 21·x²dx, as follows;
dy = 21 × 5²× 0.06 = 31.5
dy = 31.5
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Will mark BRAINLY ASAP
Solve the quadratic x2+10x=−25.
-10
10
5
-5
Answers
X = -5
Step by Step explanation:
By rearranging the equation to be solved for zero and then factoring as illustrated, this problem is simply resolved:
x2+10x=−25
x2+10x+25=0
(x+5)(x+5)=0
Since both elements are identical, there is only one way to solve this issue.
x+5=0
x=−5
Hope it helps! :)
Step by step: move the constant to the left which would give you, x2+10x+25=0
Then you would use a2+2ab+b2=(a+b)2 to factor the expression which would then give you, (x+5)2=0.
The only way a power can be 0 is when the base is zero so your expression should know look like this… x+5=0
Now you must move the constant to the right hand side which will change its sign to a negative.
Which gives you your answer of x=-5
Choice A: $0.10 on January 1, $0.20 on January 2, $0.40 on January 3, $0.80 on January 4, doubling the amount each day, or
Choice B: $5.00 on the first day, $10.00 on the second day, $15.00 on the third day, getting $5.00 more each day.
Which of the choices can be defined using an exponential function? explain
Answers
Step-by-step explanation:
Choice A.
Choice A is exponentially because the amount is double each day. In other words each day the amount gets larger. One day it increased by 10 cents, the next day 20 cents, the next day 40 cents and so on... eventually it'll be a day where it increases by a million cents.
Choice B is not exponentially, it is linearly because each day the amount increase stays the same. One day is $5.00 more, the next day it's $5.00 more, the next day it's $5.00 more... and so on.
Because of that, we can get rid of those two choice B options.
Both Choice A's look the same. The only difference is that one has a 2 and the other doesn't. That 2 indicates that we're doubling. Makes sense because that's what we associate with doubling.
Making the second Choice A the correct formula.
Company XYZ's Computer can execute a program of an input size n in one minute.
Company ABC claims that their computer runs 100 times faster than XYZ's.
What size input can ABC's computer execute in one minute for each algorithm for the following growth rates?
a.n
b. n^2
c. n^3
d. 2^n
Answers
The size input which ABC's computer can execute in one minute for each algorithm for the following growth rates are given below:
a. For a growth rate of "n", ABC's computer can execute an input size of 100n in one minute.b. For a growth rate of "n^2", ABC's computer can execute an input size of (100n)^(1/2) in one minute.c. For a growth rate of "n^3", ABC's computer can execute an input size of (100n)^(1/3) in one minute.d. For a growth rate of "2^n", ABC's computer can execute an input size of log2(100n) in one minute.How are the execution times gotten?For a growth rate of "n", it means the execution time increases linearly with the size of the input. In this case, XYZ's computer takes 1 minute to execute an input size of "n".
Company ABC claims that their computer is 100 times faster, so they can execute an input size of 100n in one minute.
For a growth rate of "2^n", it means the execution time increases exponentially with the size of the input.
In this case, if we double the input size, the execution time increases two times. So, if XYZ's computer takes 1 minute to execute an input size of "n", it would take 2 minutes to execute an input size of "2n".
Company ABC claims that their computer is 100 times faster, so to execute an input size of "2n" in 1 minute, the input size must be log2(100n).
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a triangle has two side lengths of 3.5 inches and 7.75 inches. which of the following could be the length of the third side
Answers
The length of the third side could be 5.26 inches.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
There are 2 possible triangles that can arranged one being the 8 the longest side, and another one being the 5 and 8 the sides of the triangle
Given that triangle has two side lengths of 3.5 inches and 7.75 inches.
Using the pythagorean theorem to solve.
3.5² + 7.75² = x²
x² = 12.25 + 15.5
x² = 27.75
x = 5.26
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Write the answer is (x,y) form
Answers
The translation in the form (x,y) is (-3, -10)
How to determine the translation that maps from T to T'?In geometry, translation is a type of transformation that moves each point of a figure to a new location, while preserving the shape and size of the figure. A translation is defined by a displacement vector, which specifies the direction and magnitude of the movement.
T is the initial position of the object and T' is the image (new position) of the object after translation. We can use this equation:
T + translation = T'
translation = T' - T
translation = (6, -2) - (9, 8)
translation = (6-9, -2-8)
translation = (-3, -10)
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URGENT PLS HELP
stats standard deviation
Answers
The sample standard deviation of the given data will be 10.058.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.
[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}[/tex]
The table is given below.
M f Mf M²f
15 8 120 1,800
25 18 450 11,250
35 20 700 22,050
45 13 585 26,325
55 7 385 21,175
The variance is given as,
Var = 1 / (66 - 1) [82600 - 2240² / 66]
Var = 101.16
Then the standard deviation is given as,
SD = √ Var
SD = √101.16
SD = 10.058
The sample standard deviation of the given data will be 10.058.
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Given a simplified rate of (1.99), determine the percent change.
Answers
Therefore , the solution of the given problem of percentage comes out to be 19.9% is the percent change.
Define percentage.In mathematics, a percentage is any value that can be written as a proportion of 100. There are also sporadic uses of the abbreviations "pct.," "pct," or "pc." However, it is commonly indicated by the "%" mark. The proportional amount is flat and lacks any dimensions. Since percentages have a numerator of 100, they can be thought of as fractions. The cent symbol (%) must come after a number to denote that it is a percentage.
Here,
Given:
You can compute 1.99 as a percent of a given number x by dividing 1.99 by x and multiplying the outcome by 100.
For instance,
if 1.99 is expressed as a percentage of 10,
then
=> 1.99 x 100% = 19.9%
Therefore , the solution of the given problem of percentage comes out to be 19.9% is the percent change.
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Match each formula on the left side to an equivalent formula on the right side A=BC+D
Answers
We can see that matching each formula on the left side to an equivalent formula on the right side, we have:
A = BC + D ------ B = A - D/C
A = B + CD ------ B = A - CD
A = BD - C ------- B = A + C/D
A = CD - B ------- B = CD - A
What is formula?A formula is a mathematical expression that represents a set of instructions for solving a specific problem or calculating a desired value. It often uses symbols and variables to represent values, and can include operations such as addition, subtraction, multiplication, and division.
Formulas can be used in a variety of fields, including physics, chemistry, finance, and engineering.
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Logan says, “140 millilitres is more than 1.2 litres”. Is he right?
Answers
A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
First, because we are dealing with different units here, we need to know how many milliliters are in a litre.
1000 milliliter = 1 litreSo, an equation we can use is:
1 litre × 1000 = the amount in millilitersIf we look at 1.2 litres, we can now convert it to milliliters.
1.2 × 1000 = 1200Comparing 1200ml to 140ml, we can see that 1200ml is bigger.
Therefore, 1.2 litres are greater.
help
Find an equation of the line that contains the given pair of points.
(25, 26), (6, 7)
Answers
Answer:
y = x + 1
Step-by-step explanation:
Since we have two points, we can find the equation of the line in slope-intercept form or y = mx + b, where m is the slope and b is the y-intercept.
We can find the slope using the slope formula, which is:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where y2 and x2 are one point on the line and y1 and x1 are the other point on the line:
Thus, we have:
[tex]m=\frac{7-26}{6-25}\\ m=\frac{-19}{-19}\\ m=1[/tex]
Now that we have the slope, we choose one of the points and plug in the slope to find the y-intercept:
[tex]26=1(25)+b\\26=25+b\\1=b[/tex]
Your Shadow measures 8 ft your father's Shadow is 9 ft if you are 5.5 ft how tall is your father in inches? I need problem wrote out please.
Answers
Check the picture below.
An experienced roofer with Stark Vegas roofing company can install a new roof in 24
hours. Together with a new trainee they can install a new roof in 15 hours. How long
would it take the trainee working by himself to install a new roof? Round to the nearest
tenth.
Answers
Answer:
40 hours
Step-by-step explanation:
This is an example of a work-rate-time problem
Since the experienced roofer can finish the job in 24 hours, his rate of work would be 1/24 (of the roof) per hour
Let the time taken by the trainee alone be x hours
His rate of work = [tex]\dfrac{1}{x}[/tex]
Together they finish the roof in 15 hours
So combined work rate = [tex]\dfrac{1}{15}[/tex]
Since combined rate = sum of individual rates we get
[tex]\dfrac{1}{24} +\dfrac{1}{x} = \dfrac{1}{15}[/tex]
Move 1/24 to the right side:
[tex]\dfrac{1}{x} = \dfrac{1}{15} - \dfrac{1}{24}[/tex]
[tex]\dfrac{1}{x} =\dfrac{24 - 15}{24\cdot 15} = \dfrac{9}{360}\\\\[/tex]
Taking reciprocals on both sides
[tex]x = \dfrac{360}{9} = 40 \;hours[/tex]
Given f(x)=(8/x+13)+2 find the inverse
Answers
Answer:
Step-by-step explanation:
da fact that it sometimes get me wrong but it do works ngl
Consider the following three random experiments: Experiment 1: Toss a coin. Experiment 2: Toss a die. Experiment 3: Select a ball at random from an urn containing balls numbered 0 to 9. (a) Specify the sample space of each experiment. (b) Find the relative frequency of each outcome in each of the above experiments in a large number of repetitions of the experiment. Explain your answer.
Answers
The sample space of the tossed coin: head or Tail =[ HT ]
The sample space of the die : [1, 2, 3, 4, 5,6 ]
The sample space of the ball {0 , 1, 2, 3, 4, 5, 6, 7, 8, 9]
What is the relative frequency?experiment 1: In a large number of repetitions of the experiment, the relative frequency of each outcome (Heads or Tails) would be approximately 0.5 or 50%.
Experiment 2: In a large number of repetitions of the experiment, the relative frequency of each outcome (1 to 6) would be approximately 0.1667 or 16.67%.
Experiment 3: In a large number of repetitions of the experiment, the relative frequency of each outcome (0 to 9) would be approximately 0.1 or 10%.
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show that in any set of six classes there must be two that meet on the same day, assuming that no classes are held on weekends.
Answers
There must be two that meet on the same day, assuming that no classes are held on weekends.
What is Set?
Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
According to question:Let us show that in any set of six classes, each meeting regularly once a week on a particular day of the week, there must be two that meet on the same day, assuming that no classes are held on weekends.
Since there are 5 working days by a week and 6 classes, by Pigeonhole Principle there must be two that meet on the same day.
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What type of variable is a coin flip?
Answers
The coin flip is random variable.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
A variable at random The value of the variable X is subject to chance. Imagine that you flip a coin. If the coin lands on its head, you win one dollar; otherwise, you lose one. You can never predict how much money you'll make from one coin toss.
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The coin flip is random variable.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
A variable at random The value of the variable X is subject to chance. Imagine that you flip a coin. If the coin lands on its head, you win one dollar; otherwise, you lose one. You can never predict how much money you'll make from one coin toss.
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A washer 4mm wide is to be made as indicated in the drawing. Find the area of the washer in term of the outer radius ( in expanded form ).
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Answers
The required area of the washer is 8πr - 16π square millimeter.
How to find area of circle?A = π r², where r is the circle's radius, is the formula for calculating a circle's surface area. The square unit, such as m², cm², in², etc., is the unit of area.
Circle Area Formulas;
Area is equal to π r², where r stands for radius.
Area is equal to ( π /4) d², where d stands for diameter.
Area is equal to C²/4 π where C stands for circumference.
According to question:The area of a washer with outer radius "r" and inner radius "r-4" can be found as follows:
Area = π * (outer radius² - inner radius²)
= π * (r² - (r-4)²)
= π * (r² - r² + 8r - 16)
= 8πr - 16π square millimeter.
Thus, required area of washer is 8πr - 16π,Option(B) is correct.
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