The length of the shadow of a pole on level ground increases by 90 metres when the angle of elevation of the sun changes from 58 degrees to 36 degrees. calculate and correct to three s.f , the height of the pole
Answers
Answer:
120 m
Step-by-step explanation:
Let the length of the pole be a and the shadow be b at 58° and b+90 at 36°.
Then, as the pole and its shadow form a right triangle, we have:
a/b = tan (58°) a/(b+90) = tan (36°)As,
tan (58°) ≈ 1.6tan (36°) ≈ 0.727The equations change to:
a = 1.6ba = 0.727 (b+90)Comparing the two equations:
1.6b = 0.727b + 0.727*901.6b - 0.727b = 65.430.873b = 65.43b = 65.43/0.873b ≈ 75Then
a = 1.6b = 1.6*75 = 120 m
Related Questions
For two days in a row, Windstone rescued tadpoles from a puddle. He rescued 54 on Friday. This is 17 less Then the number he rescued on Saturday. Write and solve a subtraction equation to find how many tadpoles he rescued on Saturday.
Answers
Answer:
71 tadpoles
Step-by-step explanation:
Windstone rescued 54 on Friday.
Let the number rescued on Saturday =x
The number rescued on Friday is 17 less than the number he rescued on Saturday.
This is written as:
54=x-17To solve for x, we add 17 to both sides of the equation
54+17=x-17+1771=xx=71Windstone Rescued 71 tadpoles on Saturday
Answer:
71 tadpoles
Step-by-step explanation:
let 't' represent the number of tadpoles he rescued on Saturday.
According to the problem,
Windstone rescued 54 on Friday.
If the number rescued on Friday is 17 less than the number he rescued on Saturday.
The equation to find the number of tadpoles he rescued on Saturday will be:
t-17 = 54
Further solving for 't'
t= 54+17
t= 71
Therefore, Windstone Rescued 71 tadpoles on Saturday
Part A
in the table describe the shape of the cross section formed when a particular plane passes through the cone
Answers
Answer:
plane parallel to the circular base, not passing through the tip of the cone: circle
plane parallel to the circular base, passing through the tip of the cone: A point
plane not parallel to the base, not passing through the base, and making an angle with the horizontal that is less than that made by the slant height of the cone: an oval that becomes more elongated as the angle with the horizontal increases
plane making an angle with the horizontal that is greater than that made by the slant height, passing through the tip of the cone : an isosceles triangle
Step-by-step explanation:
What is the cross section of a shape?A cross-section is a plane section that is a section of a three-dimensional object that is parallel to one of its planes of symmetry or perpendicular to one of its lines of symmetry. Describe shapes formed by cross-sections (square, rectangle, triangle, etc.)
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Venus is the planet that comes nearest to Earth. It's closest position is about 38.000,000 kilometers from Earth. Write this number expressed as a product of 38 and a power of 10. I am in 5th grade and this is for math.
Answers
Answer:
The distance as product of 38 and a power of 10 is [tex]38*10^{6}[/tex]
Step-by-step explanation:
In math when we're dealing with big numbers like this we express them in power of 10, since it'll be easyer to read that way. We take the parts of the number to the left that are not equal to "0", in this case 38, and multiply it by a power of 10. The expoent to this power of 10 will be the number of "0" after the 38 and before the ",". In this case the closest distance from Earth to Venus is 38,000,000 (there's a typo in the question). So we take the 38 and multiply it by [tex]10^{6}[/tex], since there are 6 zeros.
The distance as product of 38 and a power of 10 is [tex]38*10^{6}[/tex]
which function BEST expresses the linear relationship displayed by the scatter plot? A) y = 1.4x − 11.2 B) y = 0.7x − 10.8 C) y = 1.4x + 11.2 D) y = 0.7x + 10.8
Answers
Answer:
d
Step-by-step explanation:
Lu is making a quilt that is 20 squares wide and has 18 rows the border of the quilt is made by using each toy design equally as often there are a total of 6 toy designs each square can hold 1 design how many of each design does she use for the border?
Answers
Answer:
The correct answer is two designs are used 12 times each and other four designs are used for 13 times each.
Step-by-step explanation:
Width of the quilt Lu is making is 18 rows of 20 squares each.
Thus the perimeter of the quilt is 20 + 20 + 18 + 18 = 76.
We can also say there are 76 square as the boundary which are to be bordered with toy designs.
Each square can hold 1 design of toy and there are 6 different designs of toys.
Thus number of times each design is used [tex]\frac{76}{6}[/tex] = 12 [tex]\frac{4}{6}[/tex].
Thus there are two designs used 12 times each and other four designs are used for 13 times each.
A manufactured lot of buggy whips has 20 items, of which 5 are defective. A random sample of 5 items is chosen to be inspected. Find the probability that the sample contains exactly one defective item (a) if the sampling is done with replacement. (b) if the sampling is done without replacement.
Answers
Answer:
a. 39.55%
b. 44.02%
Step-by-step explanation:
We have the following data:
n = 5
x = 1
p = 5/20 = 0.25
to. If the sampling is done with replacement.
We apply the binomial distribution formula, which is as follows:
P = nCx * (p ^ x) * ((1-p) ^ (n-x))
Where nCx, is a combination, and is equal to:
nCx = n! / x! * (n-x)!
replacing we have:
5C1 = 5! / 1! * 4! = 5
replacing in the main formula:
P = 5 * (0.25 ^ 1) * ((1- 0.25) ^ (5-1))
P = 0.3955
that is, without replacing the probability is 39.55%
b. if the sampling is done without replacement.
Here it is a little different from the previous one, but what you should do is calculate three cases,
the first was the one at point a, when n = 5 and x = 1
5C1 = 5! / 1! * 4! = 5
the second is when n = 20 and x = 5, this is all possible scenarios.
20C5 = 20! / 5! * 15! = 15504
and the third is when n = 15 (20-5) and x = 4 (5-1), which corresponds to the cases when none were damaged
15C4 = 15! / 4! * 11! = 1365
In the end, it would be:
P = (5C1 * 15C4) / 20C5
Replacing:
P = 5 * 1365/15504
P = 0.4402
Which means that without replacing the probability is 44.02%
what is the probablility of flipping a coin tails all three times and all three time you get tails?
Answers
Answer:
If the coin is fair, then the odds of getting heads or tails should be equal, 12. Then 3 tosses of tails will have a chance of 12⋅12⋅12=18. Tossing of the coin is an independent event. The probablility of each event is 12.
Each vertex of the polygon shown below forms a right angle. The side measurements given are inches. What is the area of the figure?
Answers
Given:
Given that each vertex of the polygon forms a right angle.
The measurements of the sides of the polygon were given.
We need to determine the area of the polygon.
Let us divide the polygon into 3 rectangles.
Area of the rectangle can be determined using the formula, [tex]A=length \times width[/tex]
Area of rectangle 1:
The length of rectangle 1 is 17 inches.
The width of rectangle 1 is 8.5 inches.
The area of rectangle 1 is given by
[tex]17 \times 8.5 =144.5 \ in^2[/tex]
Area of rectangle 2:
The length of rectangle 2 is 16.5 inches.
The width of rectangle 2 is (17 - 9) = 8 inches.
The area of rectangle 2 is given by
[tex]16.5 \times 8 =132 \ in^2[/tex]
Area of rectangle 3:
The length of rectangle 3 is 13 inches.
The width of rectangle 3 is 11 inches.
The area of rectangle 3 is given by
[tex]13 \times 11=143 \ in^2[/tex]
Area of the polygon:
The area of the polygon can be determined by adding the areas of the three rectangles.
Thus, we have;
[tex]Area=144.5+132+143[/tex]
[tex]Area=419.5 \ in^2[/tex]
Thus, the area of the figure is 419.5 square inches.
Hence, Option B is the correct answer.
(X+1)(x+8) in standard form
Answers
x²+9x+8
Step-by-step explanation:Rewrite
(x+1)(x+8)
Distribute
x²+8x+1x+8
Simplify
x²+9x+8
Answer:
[tex]x^{2}[/tex] + 9x + 8 i hope this helps! :)
Step-by-step explanation:
distribute the x to the x and 8 [tex]x^{2}[/tex] + 8x
distribute the 1 to the x and 8 x + 8
put the two together [tex]x^{2}[/tex] + x + 8x + 8
combine like terms [tex]x^{2}[/tex] + 9x + 8
4.
How can you use a graph of a linear relationship to predict an unknown
value of y for a given value of x within the region of the graph?
Answers
Step-by-step explanation:
Take a look at this graph (sorry, it's small). The graph shows three data points, (0, 1), (2, 6), and (4, 8). The line is called the "line of best fit" or "regression line."
The equation for the line is y = 1.75x + 1.5 .
The data did not include a point for x = 3, but it can be predicted by finding the y-coordinate on the line that corresponds to x = 3.
Substituting x = 3 into the line's equation gives
y = 1.75(3) + 1.5 = 6.75
That's the predicted value of y for x = 3 given the linear relationship shown.
Find the value of the unknown
Answers
Answer:
a= 35°
b=70
c=70
Step-by-step explanation:
if u need explanation comment and I'll explain
. Classify ABC if the vertices are A(-12,5), B(12,5), and C(10, 17).
A-right scalene'
B-obtuse scalene
C- acute scalene
D-none of these
Answers
Answer:
acute scalene
Step-by-step explanation:
Andy promises opie that he will give him 5000 upon his graduation from college at mayberry u. How much must andy invest today to make good on his promise, if opie is expected to graduate in 12 years and andy can earn 5% on his money?
Answers
Answer: Andy should invest RS. 2784.19 for 12 years .
Step-by-step explanation:
Since we have given that
Amount = Rs. 5000
Time = 12 years
Rate of interest = 5%
So, We need to find the sum:
Using "Compound interest" , we get :
[tex]A=P(1+r)^t\\\\5000=P(1+0.05)^{12}\\\\5000=P(1.05)^{12}\\\\\dfrac{5000}{1.05^{12}}=P\\\\2784.19=P[/tex]
Hence, Andy should invest RS. 2784.19 for 12 years .
Final answer:
To find out how much Andy needs to invest today to fulfill his promise to Opie in 12 years with a 5% interest rate, we use the present value formula. Andy needs to invest approximately $2475.64 today to ensure he can fulfill his promise to Opie.
Explanation:
To calculate how much Andy must invest today to fulfill his promise to Opie, we can use the concept of present value.
First, we need to find the present value of $5000 that Opie will receive in 12 years with a 5% interest rate.Using the present value formula: P = F / (1 + r)^n, where P is the present value, F is the future value, r is the interest rate, and n is the number of years, we can plug in the values and calculate the amount Andy must invest today.By calculating the present value, Andy needs to invest approximately $2475.64 today to ensure he can fulfill his promise to Opie.A university wants to estimate the average distance that commuter students travel to get to class with an error of ±3 miles and 90 percent confidence. What sample size would be needed, assuming that travel distances are normally distributed with a range of X = 0 to X = 50 miles, using the Empirical Rule μ ± 3σ to estimate σ.
Answers
Answer:
A university wants to estimate the average distance that commuter students travel to get to class with an error of ±3 miles and 90 percent confidence. What sample size would be needed, assuming that travel distances are normally distributed with a range of X = 0 to X = 50 miles, using the Empirical Rule μ ± 3σ to estimate σ.
The required sample size, n=(zσ/E)² = 21.0
Step-by-step explanation:
The estimated σ here = (range)/6 = (50/6) = 8.33
In the case of 90 % , CI value of z = 1.64
standard deviation, σ= 8.33
margin of error E = 3
The required sample size, n=(zσ/E)² = 21.0
Answer:
n = 21
Step-by-step explanation:
Solution:-
- Let denote a random variable "X" : average distance that commuter students travel to get to class.
- The population is given to be normally distributed, such that:
Range X: [ 0 , 50 ] miles
- We will use the given range coupled with the empirical rule for normal distribution to determine the mean (u) and standard deviation of population (σ):
P ( μ - 3σ < X < μ + 3σ) = 0.997 ..... (Empirical Rule)
- According to the standardized results for Z-table:
P ( -3 < Z < 3 ) = 0.997
So, P ( Z ≤ 3 ) = 1 - (1 - 0.997) / 2 = 0.9985
P ( Z ≥ -3 ) = 1 - (1 - 0.997) / 2 = 0.9985
- The standardized values for the given data can now be determined:
P ( X ≥ μ - 3σ ) = P ( Z ≥ -3 ) = 0.9985
X ≥ μ - 3σ = Upper limit - 0.9985*( Range )
X ≥ μ - 3σ = 50 - 0.9985*( 50 )
μ - 3σ = 0.075 ..... Eq1
P ( X ≤ μ + 3σ ) = P ( Z ≤ 3 ) = 0.9985
X ≤ μ + 3σ = Lower limit + 0.9985*( Range )
X ≤ μ + 3σ = 0 + 0.9985*( 50 )
μ + 3σ = 49.925 ..... Eq2
- Solve the Eq1 and Eq2 simultaneously:
2μ = 50 , μ = 25 miles
3σ = 24.925
σ = 8.30833
- Hence, the normal distribution parameters are:
X ~ N ( μ , σ^2 )
X ~ N ( 25 , 8.308^2 )
- The standard error in estimation of average distance that commuter students travel to get to class is E = ±3 miles for the confidence level of 90%.
- The Z-critical value for confidence level of 90%, Z-critical = 1.645
- The standard error estimation statistics is given by the following relation with "n" sample size.
E = Z-critical*σ /√n
n = [ Z-critical*σ /E ]^2
- Plug in the values:
n = [ 1.645*8.308/3]^2
n = 20.75306 ≈ 21
Answer: The sample size needed to estimate average distance that commuter students travel to get to class with error of ±3 miles and 90 percent confidence, is n = 21.
At Sandy's Beauty Salon, a haircut costs $15.00 and a permanent costs $30.00. Which graph represents the amount of revenue the salon will earn in one day for x haircuts?
Answers
The amount of revenue Sandy's Beauty Salon will earn in one day for x haircuts is represented by a linear graph.
Explanation:The graph that represents the amount of revenue Sandy's Beauty Salon will earn in one day for x haircuts is a linear graph. This is because the revenue is directly proportional to the number of haircuts. The equation that represents this relationship is y = 15x, where y is the revenue and x is the number of haircuts.
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what is 5x-(x-2)>2x-4(x-8)
Answers
Answer:
x > 5
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(4x + 2) - (2x - 4 • (x - 8)) > 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
6x - 30 = 6 • (x - 5)
Equation at the end of step 3 :
6 • (x - 5) > 0
Step 4 :
4.1 Divide both sides by 6
Solve Basic Inequality :
4.2 Add 5 to both sides
x > 5
The amount of a sample remaining after t days is given by the equation , where A is the initial amount of the sample and h is the half-life, in days, of the substance. A scientist has a 10-mg sample of a radioactive isotope. The isotope has a half-life of 8 days. After 16 days, how much of the radioactive isotope remains? 1.2.0 mg2.2.5 mg 3.5.7 mg 4.7.1 mg
Answers
Answer:
2.5 mg
Step-by-step explanation:
We are given that
A=Initial amount=10 mg
Half life,h=8 days
We have to find the mass of radioactive isotope remains after 16 days.
t=16 days
We know that the amount of radioactive isotope after t days is given by
[tex]P(t)=A(1\frac{1}{2}^{\frac{t}{h})[/tex]
Using the formula
[tex]P(t)=10(\frac{1}{2}^{\frac{16}{8}})[/tex]
[tex]P(t)=10\times (\frac{1}{2})^2[/tex]
[tex]P(t)=2.5 mg[/tex]
Answer:
its b on edg
Step-by-step explanation:
its B I answered the question on my test and got it correct
I dont know how to do this, i mean i do but its hard
Answers
Answer:
Step-by-step explanation:
opposite= 8 : the length opposite angle c
adjacent=15 : the length next to angle c, not the hypotenuse
hypotenuse= 17 : the hypotenuse will always be opposite the right angle
[tex]sinC=\frac{opposite}{hypotenuse}\\ \\sinC=\frac{8}{17}[/tex]
[tex]cosC=\frac{adjacent}{hypotenuse}\\\\cosC=\frac{15}{17}[/tex]
[tex]tanC=\frac{opposite}{adjacent} \\\\tanC=\frac{8}{15}[/tex]
Which represents a quadratic function
Answers
answer:
it's the second one -7^2-x+2
explanation:
in order to be a quadratic function it has to meet this criteria: ax² + bx + c
it can't be the first one because there is no bxit can't be the third one because there has to be at least an exponent of 2it can't be the last one because a CANNOT be 0, hoped this help pls lmk if i'm right lolThe quadratic function is -7x²-x+2. Therefore, option B is the correct answer.
What is a quadratic function in standard form?The standard form of a quadratic equation is given as:
ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.
A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.
Here, the quadratic function is -7x²-x+2
Therefore, option B is the correct answer.
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PLSSSSSSSSSS HELLLPPPPPP!!! ASAP!!!! 6th GRADE MATH!!!!!!!!!! ITS FOR MY COUSIN!!!!!!FIRST TO ANSWER BOTH GETS MARKED BRAINLIEST!!!!
Answers
Answer:
I believe its 15
Step-by-step explanation:
Answer for 12+7+(-4)= 15
Answer for -1.75+(-6.25)+6= -2
I hope this helps
A company is designing a new cylindrical water bottle. The volume of the bottle will be 211 cm^3. The height of the water bottle is 7.9 cm. What is the radius of the water bottle? Use 3.15 for pi
Answers
Answer:
The correct answer is 2.912 cm.
Step-by-step explanation:
A company is designing a new cylindrical water bottle.
Volume of a cylinder is given by π × [tex]r^{2}[/tex] × h, where h is the height of the cylinder and r is the radius of the cylinder.
The volume of each bottle will be 211 [tex]cm^{3}[/tex].
The height (h) of the water bottle be 7.9 cm.
Let the radius of the bottle be r cm.
∴ π × [tex]r^{2}[/tex] × h = 211 ; (π = 3.15)
⇒ [tex]r^{2}[/tex] × 24.885 = 211
⇒ r = 2.912
The radius of the water bottle is 2.912 cm.
PLEASEEEEEEEEEE HELPPPPPPPPPPP
Answers
Answer:
I would just guess, but if i were to actually think about it, i would think C. I hope it helps, and blame it on me if you fail.
Step-by-step explanation:
Hannah is at an arcade where each game requires her to use 2 tokens. She buys 40 tokens to begin. Let n be the number of games Hannah has played. Find the number of games Hannah has played if she has 16 tokens left.
Answers
Answer:
n = 12, she has played 12 games
Step-by-step explanation:
40 = 16 + 2n
24 = 2n
24/2 = n
n = 12
The division is one of the four fundamental arithmetic operations. The number of games that Hannah has played is 12.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that Hannah is at an arcade where each game requires her to use 2 tokens. Also, the total number of tokens Hannah has is 40.
Therefore, the number of tokens that Hannah has used is,
Number of tokens Hanna used
= Total number of toke - Number of tokens left
= 40 - 16
= 24
Now, the number of games that Hannah has played is,
Number of games Hannah has played = Number of tokens used / Number of token per game
n = 24 / 2
n = 12 game
Hence, the number of games that Hannah has played is 12.
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In a test of the effectiveness of garlic for lowering cholesterol, 36 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) have a mean of 0.9 and a standard deviation of 15.8. Use a 0.01 significance level to test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic treatment? Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
Answers
Answer: We do not sufficient evidence that mean is greater than 0.
Step-by-step explanation:
Since we have given that
n = 36
mean = 0.9
Standard deviation = 15.8
at 0.01 level of significance,
Hypothesis would be:
[tex]H_0:\mu =0\\\\H_1=\mu\neq 0[/tex]
Standard error of mean would be :
[tex]\dfrac{\sigma}{\sqrt{n}}=\dfrac{15.8}{\sqrt{36}}=\dfrac{15.8}{6}=2.63[/tex]
statistic value would be :
[tex]t=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\t=\dfrac{0.9-0}{2.63}\\\\t=\dfrac{0.9}{2.63}\\\\t=0.342[/tex]
Degree of freedom = df = 36-1=35
So, p value = 2.4377
Since 2.4377 > 0.342, we will not reject null hypothesis.
Hence, We do not sufficient evidence that mean is greater than 0.
Which expressions represent the area of the entire shaded
region, including the light and dark shading? Select three
options.
12a cm2
2b cm
(6a - b) cm
(12a + 2b) cm
(6a + b) cm
Answers
Answer:
12a cm2
2b cm2
(6a + b) cm2
Step-by-step explanation:
The complete question is
The figure consists of 12 congruent equilateral triangles. The area of one equilateral triangle is a cm2. The area of the hexagon, shaded slightly darker, is b cm2.
Which expressions represent the area of the entire shaded region, including the light and dark shading? Check all that apply.
12a cm2
2b cm2
(6a - b) cm2
(12a + 2b) cm2
(6a + b) cm2
The picture of the question in the attached figure
we know that
The area of the entire shaded region is equal to the area of the the light and dark shading
so
step 1
Find the area of the light shading
The area is equal to the area of six congruent equilateral triangles
[tex]A_1=6a\ cm^2[/tex]
step 2
Find the area of the dark shading
The area is equal to the area of the regular hexagon
[tex]A_2=b\ cm^2[/tex]
step 3
1) Find the total area
[tex]A=A_1+A_2=(6a+b)\ cm^2[/tex]
2) Remember that the figure consists of 12 congruent equilateral triangles
so
[tex]A=12a\ cm^2[/tex]
3) The area of the light shading is the same that the area of the dark shading
so
6a=b
therefore
[tex]A=2b\ cm^2[/tex]
Answer: 1 2 5
Step-by-step explanation:
What is the mean for this data. Plz explain
Answers
Answer:
18
Step-by-step explanation:
Mean is the average of the data.
There is one 7.
Three 9's.
Two 10's
7+9+9+9+10+10=54
There are only 3 numbers with actual data so 6 and 8 don't matter.
54÷3=18
Select all solutions for the equation (3x + 5)(2x + 8) = 0
Answers
Answer:
x=-1.67 or x=-4
Step-by-step explanation:
3x+5=0 and 2x+8=0
3x=0-5 2x=-8,,,divide both sides by 2, the two's cancel then x=-4
3x=5 Divide by 3 to hve x on one side,,, thus the answer is -5÷3=1.666...
Answer:
-5/3 and -4
Step-by-step explanation:
I got it correct.
Amy deposited $460 into a savings account that pays 3.2% annual interest. In 5 years, how much interest will she have earned?
Answers
Answer:
$73.60
Step-by-step explanation:
take 460 times .032 witch is 14.72 then times that by 5
Wayne owns a house with a value of $215,000. He has a mortgage of $175,000 on the house. He has a car worth $12,500 with a loan of $4,000 outstanding. He has $1,875 worth of electronic equipment and a saving account of $2,400. He owes $1,275 on his credit card.
What is the amount of his assets?
What is the amount of his liabilities?
What is Wayne's net worth?
Answers
Answer:
Assets: $231,775
Liabilities: $180,275
Net worth: $51,500
Step-by-step explanation:
- Assest is something of value. ex. house, barns, tractors. To find this take...
215,000+12,500+1,875+2,400=$231,775
(All these numbers are good things he has, not debt.)
- Liability is debt you will need to repay. ex. loans or accounts payable. To find this take...
175,000+4,000+1,275=$180,275
- Net worth is the difference between your total assests and total liabilities. Knowing difference is subtraction, we should subtract assests minus liablities. To find this take...
$231,775-$180,275=$51,500
- Hope this helps! If you have any further questions or other problems you need help on please let me know as I would be glad to help.
A coin has a radius of 10 mm. How long will it take the coin to roll through the given angle measure at the given angular velocity? How far will it travel in that time? Round to the nearest tenth.
180°; 4 rev/sec
Answers
Step-by-step explanation:
The coin roll revolution = 4 rev / sec
Angle = 180° which is 1/2 of a revolution(360°).
The circumference of a circle is 2πr.
Radius of the circle, r = 10 mm
The circumference of this coin = 20π mm.
Again 180° is half of a roll,
the circumference = [tex]\frac{20\pi }{2}[/tex] = 10π
The coin travels 31.42 mm.