It is difficult to accurately predict the number of days a favorite radio or TV station will correctly forecast whether it will be cloudy over the next 30 days.
Forecasting weather accurately is a challenging task, and even the most advanced weather models are subject to errors. The accuracy of a station's forecasts depends on various factors such as the quality of their data sources, the skill and experience of their forecasters, and the complexity of the weather patterns in the region. Therefore, it is not possible to determine the exact number of days a station will make correct forecasts about whether it will be cloudy or not. However, it is important to note that modern weather forecasting has come a long way in recent years, and many stations now provide fairly accurate predictions. It is always a good idea to consult multiple sources and use personal judgment when making plans based on weather forecasts.
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If x is the average (arithmetic mean) of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, what is the average of x, y, and z in
terms of m?
A) m+ 6
B) m+ 7
C) 2m + 14
D) 3m + 21
The calculated value of the average of x, y, and z is (b) m + 7
Calculating the average of x, y, and zFrom the question, we have the following averages that can be used in our computation:
x to m and 9y to 2m and 15z to 3m and 18Using the formulas of arithmetic mean and average, we have
x = (m + 9)/2
y = (2m + 15)/2
z = (3m + 18)/2
The average of x, y, and z is then represented as
Average = [(m + 9)/2 + (2m + 15)/2 + (3m + 18)/2]/3
Evaluate
Average = m + 7
Hence, the average of x, y, and z is (b) m + 7
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due sometime very soon
Answer:
D. Yes
Step-by-step explanation:
a 95onfidence interval for the ages of six consecutive presidents at their inaugurations is about (,). either interpret the interval or explain why it should not be interpreted_____________________.
Without that information, I cannot interpret or evaluate the validity of the interval. However, I can provide general guidance on how to interpret a confidence interval.
A 95% confidence interval for a parameter (such as the mean age of the six presidents at their inaugurations) is an interval estimate calculated from sample data that has an associated probability of capturing the true population parameter. Specifically, it means that if we were to repeat the sampling process many times and construct 95% confidence intervals each time, approximately 95% of those intervals would contain the true population parameter.
Therefore, if the confidence interval you provided was calculated correctly and is valid, it means that we are 95% confident that the true mean age of the six presidents at their inaugurations falls within the given interval. However, if there are any issues with the data or the assumptions made in calculating the interval, it may not be appropriate to interpret it in this way.
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What is the formula for finding the circumstance of a circle
with just the diameter?
A.πx D
B.b x h
C.L×W×H
D.4x1
Answer: A.) π x D
Step-by-step explanation:
The diameter of a circle is 2x the radius
Answer:
A.πx D
Step-by-step explanation: The formula for the circumference of a circle is C=π×d, or it can be written as C=2×π×r.
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Answer the Question: 3v−(7.9w−9.3)
The answer to the question is 3v - 7.9w + 9.3.
We are given that;
The expression 3v−(7.9w−9.3)
Now,
we need to simplify the expression by applying the distributive property and combining like terms. Here are the steps:
First, we need to distribute the negative sign to the terms inside the parentheses. This gives us 3v - 7.9w + 9.3.
Next, we need to combine any like terms that have the same variable or are constants.
In this case, there are no like terms, so we cannot simplify further.
3v - 7.9w + 9.3.
Therefore, by the given expression the solution will be 3v - 7.9w + 9.3.
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Consider the third order polynomial
3x^3 + 13x^2 + 18x - 12
To provide a solution for this problem, we can factor the polynomial or find its roots using the rational root theorem.
One possible factorization of the polynomial is:
3x^3 + 13x^2 + 18x - 12 = (x+1)(3x^2 + 10x - 12)
To obtain this factorization, we can start by trying factors of the constant term -12 that might work as roots of the polynomial.
One such factor is -1, so we can use synthetic division or long division to divide the polynomial by x+1. This gives us a quotient of 3x^2 + 10x - 12, which can be factored using the quadratic formula or other methods.
The roots of the polynomial can be found by setting each factor equal to zero and solving for x. This gives us:
x+1 = 0 or 3x^2 + 10x - 12 = 0
The first equation has a single root of x = -1. The second equation can be solved using the quadratic formula or factoring, giving us two more roots:
x = (-10 ± sqrt(100 + 4312)) / (2*3) = (-10 ± 2sqrt(19)) / 3
Therefore, the roots of the polynomial are -1, (-10 + 2sqrt(19))/3, and (-10 - 2sqrt(19))/3.
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Students at a large university have four places to get lunch: the cafeteria, the hut, the taco wagon, or the pizza place. An article in the school newsletter states that 70% of students prefer to get lunch in the cafeteria and the other three options are preferred equally. To investigate this claim, a random sample of 150 students is selected. It is discovered that 118 prefer to eat in the cafeteria, 10 prefer the hut, 12 prefer the taco wagon, and 10 prefer the pizza place. Someone may want to know if these data provide convincing evidence that the distribution of lunch location preference differs from the claim in the article. What is the value of the chi-square test statistic and P-value?
χ2 = 0.74, P-value is between 0.10 and 0.15
χ2 = 0.74, P-value is greater than 0.25
χ2 = 5.54, P-value is between 0.10 and 0.15
χ2 = 5.54, P-value is between 0.20 and 0.25
The value of the chi-square test statistic and P-value are χ2 = 5.54 and between 0.10 and 0.15 respectively.
To determine the chi-square test statistic and P-value, we need to perform a chi-square test of independence using the observed frequencies and the expected frequencies based on the null hypothesis.
The null hypothesis states that the distribution of lunch location preference is as claimed in the article: 70% prefer the cafeteria, and the remaining options are preferred equally.
To calculate the expected frequencies, we need to assume that the null hypothesis is true. Since there are four lunch options, each option would be expected to have an equal probability of 0.10 (or 10%) if the null hypothesis is true.
Using the observed and expected frequencies, we can calculate the chi-square test statistic using the formula:
χ2 = Σ((O - E)² / E)
Substituting the values:
χ2 = ((118-105)²/105) + ((10-15)²/15) + ((12-15)²/15) + ((10-15)²/15)
= 5.54285714286
≈ 5.54
To determine the degrees of freedom, we subtract 1 from the number of categories (4 - 1 = 3).
Using the chi-square test statistic and degrees of freedom, we can find the P-value from a chi-square distribution table or using statistical software.
Based on the given answer choices, the correct option is:
χ2 = 5.54, P-value is between 0.10 and 0.15
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Let T3 be the Maclaurin polynomial of f(x) = ex.Use the error bound to find the maximum possible value of | f(1.3) − T3(1.3)|. (Round your answer to three decimal places. Let K = e1.3.)|f(1.3) - T_3(1.3)| <= ?
Using the error bound formula for Maclaurin polynomials, the maximum possible value of | f(1.3) - T3(1.3)| is approximately 0.038.
The Maclaurin polynomial for f(x) = ex up to degree 3 is T3(x) = 1 + x + x^2/2 + x^3/6. The error bound formula for Maclaurin polynomials is given by |Rn(x)| <= K^(n+1) / (n+1)! * |x^(n+1)|, where K is an upper bound for the (n+1)th derivative of f(x) on the interval of interest. For this problem, K = e^1.3, n = 3, x = 1.3, and the maximum possible value of | f(1.3) - T3(1.3)| is given by |R3(1.3)| <= K^(4) / 4! * |1.3^(4)| = 0.038. Therefore, we can conclude that the maximum possible error in approximating f(1.3) with T3(1.3) is approximately 0.038.
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a researcher wishes to survey student opinions on a proposed increase in fees at her university. she decides to select a sample for telephone interviewing by selecting every 20th name in the student directory. what is this type of sampling called?
The type of sampling described in the scenario is known as systematic sampling.
Systematic sampling involves selecting elements from a population in a systematic and predetermined manner. In this case, the researcher is selecting every 20th name from the student directory to form her sample. This method of sampling is relatively simple to execute and can be less time-consuming compared to other methods such as random sampling. However, it is important to ensure that the selected interval does not coincide with any underlying patterns in the population that may bias the results.
Overall, systematic sampling can be a useful method for obtaining a representative sample from a large population, but it is important to consider the potential limitations and biases associated with this approach.
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helpppppppppppppppppp 40pts
Answer:
43,5311
Step-by-step explanation:
Cos A= 6²+10²-7²/2×6×10
this is the cosin theorem in triangle
When testing joint hypothesis, you should use the F-statistics and reject at least one of the hypothesis if the statistic exceeds the critical value use t-statistics for each hypothesis and reject the null hypothesis once the statistic exceeds the critical value for a single hypothesis use t-statistics for each hypothesis and reject the null hypothesis is all of the restrictions fail None of them use the F-statistic and reject all the hypothesis if the statistic exceeds the critical value
The F-test should only be used to test the joint significance of multiple variables or restrictions, and should not be used to reject all the hypotheses.
When testing joint hypothesis, you should use the F-statistics and reject at least one of the hypothesis if the statistic exceeds the critical value.
This is because the F-test is designed to test the joint significance of multiple variables or restrictions. In other words, it tests whether the combination of the hypotheses is statistically significant.
Alternatively, you can use t-statistics for each hypothesis and reject the null hypothesis once the statistic exceeds the critical value. However, this approach is not ideal when testing joint hypotheses as it does not account for the multiple hypotheses being tested simultaneously.If all of the restrictions fail, you should use t-statistics for each hypothesis and reject the null hypothesis for each individual hypothesis that fails. This approach allows you to identify which specific hypotheses are not supported by the data.Finally, it is incorrect to use the F-statistic and reject all the hypotheses if the statistic exceeds the critical value.Know more about the critical value
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HELP FAST! WILL GIVE BRAINLIEST
The amount of money a movie earns each week after its release can be approximated by the graph below where n is the number of weeks after opening, and a(n) is earnings (in millions)
(see picture)
Part A: Write a function that represents the arithmetic sequence.
Part B: In what week will the movie earn $16 million?
Part C: How much money does the movie earn overall?
Part A:
The arithmetic sequence will be approximately,
42 , 36 , 30 , 24 , ....
Given,
The graph of amount of money a movie earns each week after its release where n is the number of weeks after opening, and a(n) is earnings (in millions).
Now,
After reading the graph carefully it can be judged that the the graph is decreasing linearly. Thus the sequence can be framed as,
42 , 36 , 30 , 24 , ....
here the common difference is 6.
Part B:
The movie will earn $16 million in approximately 3.5 -4 weeks.
As from the graph we can see that the earnings will further decline to $15 million in 3.5 weeks.
So for $16 million the required time will be 3.5 to 4 weeks.
Part C:
The movie will approximately earn
Arithmetic sequence,
41 , 34 , 27 , 20..
Complete the sequence,
42 , 36 , 30 , 24 , 18 , 12 , 6 , 0
For total earning,
Add the earning of the respective weeks.
$(42 + 36 + 30 + 24 + 18 + 12 + 6 + 0) million = $168
Hence the total earning of the movie is approximately $168 million.
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Find the volume of the prism
The volume of the prism in the image attached is 27cm³. This type of prism is called Trapezoidal.
Understanding Trapezoidal PrismThe attached image shows a Trapezoidal prism. To calculate the volume of the prism, we need to multiply the area of the base by the height.
Given dimensions:
Top width = 2 cm
Base width = 4 cm
Length = 6 cm
Height = 1.5 cm
To find the area of the base, we need to consider the average of the top width and base width.
average width = (2 + 4)cm / 2 = 6 cm / 2 = 3 cm.
The area of the base (A) can be calculated as follows:
A = Length × Width = 6 cm × 3 cm = 18 cm²
Now, we can calculate the volume (V) of the prism:
V = A × Height = 18 cm² × 1.5 cm = 27 cm³
Therefore, the volume of the prism is 27 cm³
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what would be the value of the autonomous expenditure multiplier if all taxes are autonomous
The value of the autonomous expenditure multiplier would be equal to 1 divided by (1 minus the tax multiplier).
The value of the autonomous expenditure multiplier would depend on the size of the tax multiplier.
The tax multiplier is the inverse of the marginal propensity to consume (MPC) from taxes, which is the portion of each dollar of taxes that households and businesses will spend.
If all taxes are autonomous, this means that taxes are not influenced by changes in income or other economic factors, and will remain constant.
In this case, the tax multiplier would be equal to the MPC from taxes.
The autonomous expenditure multiplier is calculated by dividing 1 by the marginal propensity to save (MPS), which is the portion of each dollar of income that households and businesses will save.
Since the MPC and MPS always add up to 1, we can use the tax multiplier to calculate the MPS from taxes as 1 minus the tax multiplier.
Therefore, the value of the autonomous expenditure multiplier would be equal to 1 divided by (1 minus the tax multiplier).
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If dy/dx= (x^3+1)/y and y=2 when x=1, then, when x=2, y=I am very confused as to what to do. all i know is when youplug in for x and y with the y=2 and x=1, the answer is 1since is is 2/2. what then do you do?
The value of y is ± (3√6/2) when x =2
To find the value of y when x = 2, we can use the given differential equation and initial condition.
Given: dy/dx = (x³ + 1)/y
Let's solve the differential equation using the separation of variables:
Separating the variables, we have:
y dy = (x³ + 1) dx
Integrating both sides, we get:
∫ y dy = ∫ (x³ + 1) dx
Integrating the left side:
(1/2) y² = (1/4) x⁴ + x + C
Now, using the initial condition y = 2 when x = 1, we can solve for C:
(1/2) (2²) = (1/4) (1)⁴ + 1 + C
2 = 1/4 + 1 + C
2 = 5/4 + C
C = 2 - 5/4
C = 3/4
Substituting the value of C back into the equation:
(1/2) y² = (1/4) x⁴ + x + 3/4
Multiplying both sides by 2 to eliminate the fraction:
y² = (1/2) x⁴ + 2x + 3/2
Now, we can substitute x = 2 into the equation to find y:
y² = (1/2) (2)⁴ + 2(2) + 3/2
y² = 8 + 4 + 3/2
y² = 27/2
y = ± (3√6/2)
Therefore, The value of y is ± (3√6/2) when x =2
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In a group of 50 executives, 27 have a type A personality. If one executive is selected at random from this group, what is the probability that this executive has a type A personality?
The probability of selecting an executive with a type A personality can be calculated by dividing the number of executives with a type A personality by the total number of executives in the group. the probability of selecting an executive with a type A personality from this group is 0.54, or 54%.
P(type A) = number of executives with type A personality / total number of executives
P(type A) = 27 / 50
P(type A) = 0.54 or 54%
Therefore, the probability of selecting an executive with a type A personality from this group is 54%. Probability = (Number of desired outcomes) / (Total number of possible outcomes)
Probability = 27 / 50
Now, we can simplify the fraction:
Probability = 0.54
So, the probability of selecting an executive with a type A personality from this group is 0.54, or 54%.
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Harold had some pencils he gave his friend carl 17 of them then he let his teacher have 35 for the classroom he now has 48 pecils left how many pencils did harold have originally?
Harold had originally 100 pencils.
Let X be the number of pencils Harold had originally. After giving 17 to his friend Carl, he had X-17 left. Then, after giving 35 to his teacher, he had X-17-35 left, which is equal to 48.
Therefore, we can set up an equation: X-17-35=48. Solving for X, we get X=100 pencils.
Thus, Harold originally had 100 pencils. To check, we can verify that after giving 17 to Carl and 35 to his teacher, he is left with 48, which matches the information given in the problem.
This problem can also be solved by using algebraic equations, but since there are only two steps involved, we can use simple arithmetic to arrive at the answer.
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Help on this question.
Answer: [tex](x+4)^2 + (y+2)^2 = 9[/tex]
Step-by-step explanation:
The general form for the equation of a circle is:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex], where (h,k) is the center, and r is the radius:
We see the center to be at the point (-4,-2). and the radius can also be seen to be 3 units:
with this in mind:
[tex](x-(-4))^2 +(y-(-2))^2 = 3^2[/tex]
[tex](x+4)^2 + (y+2)^2 = 9[/tex]
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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
y=−16x^2+125x+147
The maximum height reached by the rocket is approximately 441.2 feet to the nearest tenth of a foot.
To find the maximum height reached by the rocket, we need to determine the vertex of the parabola represented by the equation y = -16x^2 + 125x + 147. The vertex formula for a quadratic equation in the form y = ax^2 + bx + c is (h, k), where h = -b/(2a) and k = y(h).
Using the given equation, a = -16, b = 125, and c = 147. First, find h:
h = -125/(2 * -16) = 3.90625
Next, find k by plugging h into the equation:
k = -16(3.90625)^2 + 125(3.90625) + 147 ≈ 441.2
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Help Please Thank you very much :)
Answer:
For n = 1, 2, 3,.....,
[tex] a(n) = \frac{10n(n + 1)}{2} + 1 = 5n(n + 1) + 1 [/tex]
[tex] = 5 {n}^{2} + 5n + 1[/tex]
a homeowner is creating a new garden in the shape of a 1/2 circle with a radius of 6 feet. he wants to cover the garden with a 3 inch layer of mulch. if mulch costs $3.50 per cubic foot, how much will the mulch cost the homeowner? round to the nearest dollar
The mulch will cost the homeowner $49.
How to find how much will the mulch cost the homeownerTo find the cost of the mulch, we need to first find the volume of mulch required to cover the garden.
Using the formula for a circle:
Area of a half circle = (1/2) * π * r^2
Plugging in the values, we get:
Area of half circle = (1/2) * π * 6^2 = 56.55 square feet
We need to find the volume of mulch required to cover the garden with a 3 inch layer.
Volume of mulch = Area of half circle * Height of mulch
Volume of mulch = 56.55 * 0.25 = 14.14 cubic feet (rounded to two decimal places)
Finally, we can find the cost of the mulch by multiplying the volume by the cost per cubic foot:
Cost of mulch = Volume of mulch * Cost per cubic foot
Cost of mulch = 14.14 * 3.50 = $49 (rounded to the nearest dollar)
Therefore, the mulch will cost the homeowner $49.
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For all values of α and β for which the expression is defined, cos(α+β) over sinβ=tanαcotβ+1cosαcotβ−sinαsinα+cosαtanβcotαcosβ+sinβcosβ−tanαsinβ
The expression cos(α+β)/sinβ can be simplified using trigonometric identities to give tanαcotβ+1/cosαcotβ−sinαsinα+cosαtanβcotαcosβ+sinβcosβ−tanαsinβ.
To simplify the expression cos(α+β)/sinβ, we first use the trigonometric identity cos(A+B) = cosAcosB - sinAsinB to obtain:
cos(α+β) = cosαcosβ - sinαsinβ
Substituting this into the numerator of the original expression, we have:
cosαcosβ - sinαsinβ ------------------- sinβ
We then use the identity cotθ = 1/tanθ to simplify the expression further. This gives: tanαcotβ + 1 --------------cosαcotβ - sinαsinβ/sinβ
We can then use the identities tanθ = sinθ/cosθ and cotθ = cosθ/sinθ to obtain:
sinαcosβ + cosαsinβ--------------------cosαcosβsinβ - sinαsinβsinβ
Simplifying this expression gives:
sin(α+β)---------cosαsinβ
Finally, we use the identities sin(A+B) = sinAcosB + cosAsinB and cos(A+B) = cosAcosB - sinAsinB to obtain:
sinαcosβ + cosαsinβ--------------------cosαcosβsinβ - sinαsinβsinβ
= sin(α+β)/(cosαsinβ)
Therefore, we have successfully simplified the expression cos(α+β)/sinβ to tanαcotβ+1/cosαcotβ−sinαsinα+cosαtanβcotαcosβ+sinβcosβ−tanαsinβ.
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find a formula for f(x) given that f is continuous and −2x5 x3 4x=∫x0f(t)dt.
The formula for f(x) is f(x) = -10x^4 + 3x^2 + 4.
How can we find the derivative of both sides of the equation?
We can find the derivative of both sides of the equation using the Fundamental Theorem of Calculus:
d/dx [−2x^5 + x^3 + 4x] = d/dx [∫_0^x f(t) dt]
-10x^4 + 3x^2 + 4 = f(x)
Therefore, the formula for f(x) is:
f(x) = -10x^4 + 3x^2 + 4
We can check that this formula satisfies the original equation by taking the definite integral:
∫_0^x f(t) dt = ∫_0^x (-10t^4 + 3t^2 + 4) dt = [-2t^5 + t^3 + 4t]_0^x = -2x^5 + x^3 + 4x
Thus, the formula for f(x) is f(x) = -10x^4 + 3x^2 + 4.
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Gas costs $3. 50 per gallon in Brielle's neighborhood. How much would it cost for a full tank of gas?
Given: B
is the midpoint of AC⎯⎯⎯⎯⎯.
Prove: AC=2AB
Place the steps in order to complete the proof.
a) B is the midpoint of segment AC (given)
b) AB+BC=AC (segment addition postulate)
c) AB+AB=AC (substitution)
d) AB=BC (definition of midpoint)
e) 2AB=AC (substitution)
The proof that AC=2AB when B is the midpoint of segment AC involves the use of the given statement, segment addition postulate, definition of midpoint, and substitution method.
Explanation:To prove that AC=2AB when B is the midpoint of segment AC, follow these steps:
B is the midpoint of segment AC (given) AB+BC=AC (segment addition postulate) AB=BC (definition of midpoint) AB+AB=AC (substitution) 2AB=AC (substitution)
Thus, by these steps, you can see that when B is the midpoint of AC, the length of segment AC is twice the length of segment AB.
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what is (28+58)-54+2=
please help
Answer: 34
I really hope that this helps
100 Points! PLEASE BE HONEST!!! Have some integrity :(
If f(x) = 9x+5 then what is f(4c+1) ?
[tex]f(4c+1)=9(4c+1)+5=36c+9+5=36c+14[/tex]
you can choose to add the common factor which is 2(18c+7)
This line has a y-intercept of -
Answer: C(2)
Step-by-step explanation: Count by 2's like 4,6,8
Answer:
Step-by-step explanation:
y-intercept is when x=0.
The rule here is y-x=3.
So when x=0, we get y=3.
SOLUTION: (D) 3
Prove that for all integers a,b and c, if a|bc, then a|b or a|c.
Thus, we have proved that for all integers a, b, and c, if a|bc, then a|b or a|c.
To prove that for all integers a, b, and c, if a|bc, then a|b or a|c, we need to use the definition of divisibility.
Assume that a|bc. This means that there exists an integer k such that bc = ak.
We can consider two cases:
Case 1: a and b are coprime.
In this case, a does not share any factors with b. Therefore, a cannot divide b. However, since a|bc and b and c share no factors, a must divide c. Hence, a|c.
Case 2: a and b have a common factor.
In this case, we can write a = dx and b = dy, where d is the greatest common divisor of a and b. Therefore, bc = dxy*c = ak = dxy*k.
Dividing both sides by dxy, we get c/k = a/dy.
Since a and d share no factors, d|c/k. Therefore, there exists an integer m such that c/k = dm. This means that c = dkm.
Since a = dx, we have a|dxk. Since a|bc = dxy*k, we have d|a and d|k. Therefore, we can write k = dh and a = dg, where h and g are integers.
Substituting these expressions into c = dkm, we get c = dg*dh*m. Since d|c and d|a, we have d|b and a|b.
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Find the work done by the force field F(x,y,z)=6xi+6yj+2k on a particle that moves along the helix r(t)=2cos(t)i+2sin(t)j+5tk,0≤t≤2π
The work done by the force field on the particle moving along the given helix is 60π units of work.
How to find work done?To find the work done by the force field F on the particle that moves along the helix r, we use the formula:
W = ∫ F · dr
where · denotes the dot product, and dr is the differential displacement vector along the path of the particle.
First, we need to calculate dr. Since the particle moves along the helix r, we can write:
dr = dx i + dy j + dz k
where dx, dy, and dz are the differentials of x, y, and z with respect to t, respectively. We have:
dx = -2sin(t) dt
dy = 2cos(t) dt
dz = 5 dt
Therefore, we can write:
dr = (-2sin(t) i + 2cos(t) j + 5k) dt
Next, we need to calculate F · dr. We have:
F · dr = (6x i + 6y j + 2k) · (-2sin(t) i + 2cos(t) j + 5k) dt
= -12sin(t) + 12cos(t) + 10 dt
Finally, we can integrate F · dr over the interval 0 ≤ t ≤ 2π to obtain the work done by the force field F on the particle that moves along the helix r:
W = ∫ F · dr = ∫ (-12sin(t) + 12cos(t) + 10) dt
= [-12cos(t) + 12sin(t) + 10t]0[tex]^(2π)[/tex]
= (-12cos(2π) + 12sin(2π) + 10(2π)) - (-12cos(0) + 12sin(0) + 10(0))
= 20π
Therefore, the work done by the force field F on the particle that moves along the helix r is 20π.
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