Answer:
y = 0.49x + 62.8
Step-by-step explanation:
The line of best fit regression equation can be modeled using a regression analysis calculator
However, since the answer choices are given, with a bit of intuitive and logical thinking we can arrive at the correct answer choice
Let's eliminate the last answer choice: y = −0.65x − 69.5
For all values of x > 0 the value of y(height) will be negative which is absurd
The second-last(3rd answer choice) can also be eliminated. At x = 10
y = 0.65(10) - 69.5 = - 6.5 - 69.5 = - 64. The y-value is negative for all shoesizes shown
First choice seems reasonable:
However because of the -0.49x factor the height decreases as shoe size increases. This is counter-intuitive. Taller women tend to have bigger feet
Therefore the only correct answer choice is the second one:
y = 0.49x + 62.8
which shows a positive correlation between x and y
Mrs. Ross the couselor, is helping plan a field at her middle school and is trying to decide what yard games to buy. She randomly surveyed 80 students at lunchtime anf asked about the yard game each one preferref. The results of the survey are shown in the table. Bean bag toss 14 checkers 16 connect 4 28 jenga 14 tic tac toe 8, based on the results in the table, which statement is true? A a student is more likely to prefer tic tac toe or connect 4 than checker or jenga. B a student is four times as likely to prefer connect 4 as tic tac toe. C a student is twice as likely to prefer tic tac toe as checkers. D a student is less likely to prefer checkers or bean bag toss than jenga or tic tac toe.
To determine which statement is true, we need to compare the number of students who prefer each game relative to the total number of students surveyed.
The total number of students surveyed is:
14 + 16 + 28 + 14 + 8 = 80
A) To find the probability of a student preferring tic tac toe or connect 4 versus checker or jenga, we add the number of students who prefer tic tac toe or connect 4:
28 + 8 = 36
And add the number of students who prefer checker or jenga:
14 + 16 + 14 = 44
Therefore, statement A is false.
B) To find the probability of a student preferring connect 4 versus tic tac toe, we divide the number of students who prefer connect 4 by the number of students who prefer tic tac toe:
28/8 = 3.5
Therefore, statement B is false.
C) To find the probability of a student preferring tic tac toe versus checkers, we divide the number of students who prefer tic tac toe by the number of students who prefer checkers:
8/16 = 0.5
Therefore, statement C is true.
D) To find the probability of a student preferring jenga or tic tac toe versus checkers or bean bag toss, we add the number of students who prefer jenga or tic tac toe:
28 + 8 = 36
And add the number of students who prefer checkers or bean bag toss:
14 + 16 = 30
Therefore, statement D is true.
Therefore, the correct answer is option D: a student is less likely to prefer checkers or bean bag toss than jenga or tic tac toe.
Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4.
After she rolls it 2,000 times, she finds that she rolled the number 2 a total of 187 times. Which of the following is true?
A. Joan has provided evidence that calls into question whether or not this is a fair die because the relative frequency of rolling a 2 is quite different than the theoretical probability even after repeating the experiment many times.
B. Joan has demonstrated that this is a fair die, since the relative frequency of rolling a 2 is nearly equal to the theoretical probability.
C. We cannot draw any conclusions from Joan's experience with this die because there is only a very weak link between the relative frequency of an event and the theoretical probability.
D. We cannot draw any conclusions from Joan's experience with this die without also knowing how many times the other numbers appeared.
The true statement is that Joan has provided evidence that calls into question whether or not this is a fair die because the relative frequency of rolling a 2 is quite different than the theoretical probability even after repeating the experiment many times. The answer is A.
The theoretical probability of rolling a 2 on a fair four-sided die is 1/4 or 0.25. If Joan rolled the die 2,000 times, we would expect her to roll a 2 approximately 500 times (0.25 x 2,000 = 500).
However, she only rolled a 2 187 times. The relative frequency of rolling a 2 is 187/2,000, which is 0.0935 or 9.35%. This is quite different from the expected theoretical probability of 25%, which suggests that the die may not be fair.
Joan's experience provides evidence that the die may not be fair. The relative frequency of rolling a 2 is significantly lower than the theoretical probability, indicating that the die may be biased.
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Rhonda has a USB drive that can hold
8
,
000
,
000
,
000
B
8,000,000,000 B8, comma, 000, comma, 000, comma, 000, start text, space, B, end text.
Choose the best approximation of the number of bytes that Rhonda's USB drive can hold.
The best approximation of the number of bytes that Rhonda's USB drive can hold is 8 x [tex]10^9[/tex] B.
What is Scientific Notation?Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.
Given:
We have Rhonda has a USB drive that can hold 8, 000, 000, 000 B.
In Scientific Notation the decimal point should be placed just after one number and the number of extra zeroes raised to power.
Here we have 9 zeroes after 8 then the Scientific Notation is
= 8, 000, 000, 000 B.
= 8 x [tex]10^9[/tex] B
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A high school student became dehydrated while recuperating from a virus. In the hospital he was given 120 cc of glucose intravenously at a drip rate of 1.02 cc per minute.
a. Make a table comparing the elapsed time with the amount of glucose given to the patient by calculating how much glucose is left in the bag over time. Use g for the number of ccs of glucose left in the bag and t for time in minutes.
NOTE: The x-axis is usually used to represent time.
b. Write an equation describing the relationship between the elapsed time and the amount of glucose remaining in bag.
c. Draw a graph. Discuss the meaning of the t-intercept and the g-intercept in this real-world situation.
d. What information from the table in part (a) and the graph in part (b) might be valuable to the doctor?
The equation describing the relationship between the elapsed time and the amount of glucose remaining in the bag is: g = 120 - 1.02t
What is an equation ?
In mathematics, an equation is a statement that shows the equality between two expressions containing variables. It is typically written as a combination of numbers, variables, and mathematical symbols, such as addition, subtraction, multiplication, and division.
Here is a table comparing the elapsed time with the amount of glucose given to the patient:
Time (minutes) Glucose remaining in bag (cc)
0 120
1 119.98
2 119.96
3 119.94
4 119.92
... ...
t 120 - 1.02t
The equation describing the relationship between the elapsed time and the amount of glucose remaining in the bag is: g = 120 - 1.02t
where g represents the amount of glucose remaining in the bag in cc and t represents the elapsed time in minutes.
Hence, The equation describing the relationship between the elapsed time and the amount of glucose remaining in the bag is: g = 120 - 1.02t
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Write an equation of the line that passes through the points (−4, −7) and (1, −7).
An equation of the line that passes through the points (−4, −7) and (1, −7) is y = -7.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.At data point (-4, -7), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-7) = (-7 - (-7))/(1 - (-4))(x - (-4))
y + 7 = (-7 + 7)/(1 + 4)(x + 4)
y + 7 = 0/5(x + 4)
y + 7 = 0
y = -7.
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Nicole has two bags of coins. The first bag contains 5 silver dollars, 4 quarters, and 6 dimes. The second bag contains 2 silver dollars, 3 quarters, and 2 dimes. Nicole is going to let her little brother, Jacob, randomly select and keep 1 coin from each bag. What is the probability that Jacob will choose a silver dollar from each bag?
First, we need to find the probability of Jacob choosing a silver dollar from the first bag and a silver dollar from the second bag.
The probability of choosing a silver dollar from the first bag is 5/15 = 1/3 since there are 5 silver dollars out of a total of 15 coins in the bag.
The probability of choosing a silver dollar from the second bag is 2/7 since there are 2 silver dollars out of a total of 7 coins in the bag.
To find the probability of both events happening (Jacob choosing a silver dollar from each bag), we multiply the probabilities:
(1/3) x (2/7) = 2/21
Therefore, the probability that Jacob will choose a silver dollar from each bag is 2/21.
Which of the following can be used to determine the proportion of data points that fall within a specified number of standard deviation from the mean?
a. The mode
b. percentiles
c. Chebyshev's Theorem
d. The empirical rule - assuming a normal distribusion
Chebyshev's Theorem can be used to determine the proportion of data points that fall within a specified number of standard deviation from the mean.
Chebyshev's Theorem is a mathematical theorem that can be used to determine the proportion of data points that fall within a specified number of standard deviation from the mean. It states that for any distribution, no matter what its shape, at least a certain proportion of values will fall within a certain number of standard deviations from the mean. This proportion can be calculated using the formula 1-1/k², where k is the number of standard deviations. For example, if k is 3, then at least 75% of all data points will fall within three standard deviations of the mean. This theorem is particularly useful for distributions that are not normally distributed, since it provides a way to estimate the proportion of data points that fall within a certain range, even if the distribution is not symmetrical. Chebyshev's Theorem is an important tool for data analysis and can be used in a wide variety of contexts.
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help i don't understand my math
Answer:
cant help if there is nothing to answer bud/gal.
Step-by-step explanation:
cant help if there is nothing to answer bud/gal.
determine the volume of the solid whose base is the region enclosed by the curve and the line . the cross sections perpendicular to the -axis are right isosceles triangles.
The volume of the solid whose base is the region enclosed by the curve and the line is calculated as V = ∫ A(x) dx.
This solid has a base that is defined by a curve and a line, and its cross sections perpendicular to the x-axis are right isosceles triangles. We will use mathematical techniques to find the volume of this solid.
To find the volume of this solid, we need to use calculus. First, we need to determine the equation of the curve that forms the base of the solid. Once we have the equation, we can find the limits of integration that define the boundaries of the base region.
Next, we need to find an expression for the area of a cross section of the solid. We are given that these cross sections are right isosceles triangles. This means that the base and height of each triangle are equal. Let's call this length "a". Then, the area of each cross section is given by
=> A(x) = (1/2) * a²
To find the volume of the solid, we need to integrate the area of each cross section over the range of x values that define the base region. We can write the volume as V = ∫ A(x) dx.
To perform the integration, we need to determine the limits of integration. We can do this by finding the points where the curve intersects the line that defines the base region. Let's call these points (x1, y1) and (x2, y2). Then, the limits of integration are x1 and x2.
Finally, we need to substitute the expression for A(x) into the integral and evaluate it. The final result will give us the volume of the solid.
In summary, to find the volume of this solid, we need to use calculus. We first determine the equation of the curve that forms the base, then find an expression for the area of a cross section, and integrate this expression over the limits of integration that define the base region.
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Q1. what is 6 to the -3rd power
SEPERATE QUESTION
Q2. what is -9 to the -2nd power
SEPERATE QUESTION
Q3. what is 3 to the -4th power
Answer:
1. is 216
2. 100000
3. 81
Step-by-step explanation:
The “power” of a number indicates how many times the base would be multiplied by itself to reach the correct value.
Simplify the expression: 4p + 2 (5p - 4)
Answer:
14p - 8Step-by-step explanation:
4p + 2 (5p - 4)
Expand:-
4p + 10p - 8Combine like terms (4p + 10p = 14p) :-
14p - 8-Hope this helps! :)
Answer:
2(7p-4)
Step-by-step explanation:
1. Find the 15th term in the sequence if a1= 3 and d= 4
2. Find Sn for the arithmetic series where a1= 5, an= 119, n= 20
3. Find Sn for the arithmetic series where a1= 12, d= 6, n= 15
4. Find the 6th term in the geometric sequence where a1= 2, a6= 64, r= 2
5. Find Sn for the geometric series where a1= 2 , r= 4, n= 6
Using the formula, we can conclude that the 15th term in the following sequence is 59.
What is Arithmetic Sequence?A progression or sequence of numbers known as an arithmetic sequence maintains a consistent difference between each succeeding term and its predecessor.
The common difference in that mathematical progression is the constant difference.
n: The method for determining the nth term is used to locate a particular term in an arithmetic series.
Step 1:
An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
Therefore, enter the values a = 2 and d = 3 into the formula to determine the nth term.
So, the formula is:
an = a + (n – 1)d
Now, insert the values as follows:
an = a + (n – 1)d
a15 = 3 + (15 – 1)4
a15 = 3 + (14)4
a15 = 3 + 56
a15 = 59
Therefore, using the formula, we can conclude that the 15th term in the following sequence is 59.
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Correct question:
Find the 15th term in the sequence if a1= 3 and d= 4
The table shows the median individual income for the citizens of a particular town since 2005. Find the average rate
of change from 2010 to 2020.
The average rate of change from 2020 to 2010 of the median individual income is 157.
What is average rate of change?The average rate at which one item is changing in relation to another is known as the average rate of change. An average rate of change function, put simply, is a calculation that divides the amount of change in one thing by the corresponding amount of change in another.
The average rate of change is given by the formula:
R = f(b) - f(a) / (b - a)
where, f(b) and f(a) are values of the function at b and a respectively.
Here, the value of the functions are:
f(b) = 31675
f(a) =30105
b = 2020
a = 2010
Substituting the values in the equation we have:
R = (31675 - 30105)/ (2020 - 2010)
R = 1570/10 = 157
Hence, the average rate of change from 2020 to 2010 of the median individual income is 157.
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Answer: 158
Step-by-step explanation: The average rate of change from 2020 to 2010 of the median individual income is 157.
What is average rate of change?
The average rate at which one item is changing in relation to another is known as the average rate of change. An average rate of change function, put simply, is a calculation that divides the amount of change in one thing by the corresponding amount of change in another.
The average rate of change is given by the formula:
R = f(b) - f(a) / (b - a)
where, f(b) and f(a) are values of the function at b and a respectively.
Here, the value of the functions are:
f(b) = 31675
f(a) =30105
b = 2020
a = 2010
Substituting the values in the equation we have:
R = (31675 - 30105)/ (2020 - 2010)
R = 1570/10 = 157
When I combine 2x and - 10x what should I get?
Answer:
-8x
Step-by-step explanation:
when you combine 2x and -10x,
2x - 10x = -8x
This means that the expression 2x and -10x are combined to form the expression -8x.
Which function represents exponential growth?
A) y = 8x
B) y = 0.5x^2
C) y = 3(1.5)^x
D) y = -3(0.5)^x
A function that represents exponential growth include the following: C) y = 3(1.5)^x.
How to determine an exponential growth rate?Mathematically, an equation which can be used to model an exponential growth rate is given by this mathematical expression:
A(t) = P(1 + r)^{t}
Where:
A(t) represents the future value.P represents the initial value.r represents the rate of change or growth rate.T represents the time.Based on the exponential functions provided above, we can reasonably infer and logically deduce that the required exponential growth rate function is given by;
y = 3(1.5)^x
1 + r = 1.5
r = 1.5 - 1
Rate of change, r = 0.5.
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a map measuring 21.6 cm by 9 cm is enlarged twice in the ratio 3:5 calculate the final dimensions of the map
Answer:
36cm and 15cm
Step-by-step explanation:
What is a ratio?A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
Divide the dimensions of the map by the given ratio.
3:5 = [tex]\frac{3}{5}[/tex]After the first reduction the dimensions of the new map are:
21.6 ÷ [tex]\frac{3}{5}[/tex] = 369 ÷ [tex]\frac{3}{5}[/tex] = 15Therefore, the new dimensions of the map are 36cm and 15cm.
The final dimensions of the map are 72 cm by 30 cm.
How to find the final dimensions ?If the map is enlarged twice in the ratio 3:5, this means that both the length and the width are multiplied by the same factor. Let the scale factor of the enlargement be x. Then, we have:
x = ( 5 / 3) x 2
x = 10 / 3
To find the final dimensions of the map, we multiply the original dimensions by the scale factor.
Final length = 21.6 cm x ( 10 / 3 ) = 72 cm
Final width = 9 cm x ( 10 / 3 ) = 30 cm
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HELP ME PLEASE ANYONE I NEED HELPP
Step-by-step explanation:
I don't know car stuff, but that looks like its asking you to use the formula:
F1 x r1 = F2 x r2
Therefore, it will be:
175N x 200mm = 160N x 20mm
I hope this helps :)
A binomial experiment consists of 10 trials. The probability of success on trial 3 is 0.34. What is the probability of success on trial 7?
0.85
0.34
0.32
0.56
0.23
0.43
The probability of success on the trial 7 for the given binomial experiment is 0.34.
Binomial experiment - what is it?An experiment utilizing a set number of independent trials with just two results is called a binomial experiment. There are two possible outcomes for these experiments: success and failure. Because of the nature of what is being tested, results in these studies can only ever be successes or failures.
Because there are only a limited number of outcomes that can occur during each trial of a binomial experiment, they are unique from other types of studies. Particularly, there can only ever be one of two outcomes in binomial experiments.
The probability of success and failure of a trial is same for every number of trials.
Given that,
n = 10 trials
Success = 0.34
Hence, the probability of success on the trial 7 for the given binomial experiment is 0.34.
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17.) passes through X(1,-4), parallel to YZ with Y(5, 2) and Z(-3,-5) helppp please
The equation of the line parallel to the line passing through the points Y(5, 2) and Z(-3,-5) will be y = 7/8x + 4.5.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the line is passes through X(1,-4), parallel to YZ with Y(5, 2) and Z(-3,-5).
The equation of the line will be calculated as:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -5 - 2 ) / ( -5 - 3 )
Slope = 7 / 8
The equation will be written as:-
y = 7/8x + c
The slope of the two parallel lines will be the same. The y-intercept of the parallel lines will be,
y = 7/8x + c
1 = (7/8 x -4 ) + c
c = 4.5
The equation will be:-
y = 7 / 8x + 4.5
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A shop is recording queiong times of its customers and produces cumalative frequency graph
how many customers qeued for more than 20 minutes
Find the median queing time
The number of customers who queued for more than 20 minutes was 11 customers .
The median queuing time was 11 minutes .
How to find the queuing time ?The number of customers who queued for more than 20 minutes would be found by the formula :
= Number of customers at 25 minutes - Number of customers at 20 minutes
= 100 - 89
= 11 customers
The median queuing time would be the queuing time at 50 customers which according to the cumulative frequency graph is 11 minutes .
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Yellow cab charges 1.75 flat rate in in addition to $0.75per mile. Leo has no more than $20 to spend on a ride. How many miles can Leo travel without exceeding his limit?
Show steps
Answer:
Step-by-step explanation:
Set x miles Leo can travel, and his cost have to be no more than $20, so
1.75+0.75x =20
0.75x = 20-1.75
0.75x = 18.25
x = 18.25/0.75 = 24.333 miles
Two numerical expressions are equivalent if______________________
Which of the following statements are true about the following expressions?
the expressions- 18-(6*2) or (18+6)*2
1. The two expressions are equivalent
2. The first expression is eight times as large asthe second expression
3. Both expressions are numerical expressions.
The given expressions are not equivalent. They are numerical expressions.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expressions are -18-(6 * 2) or (18 + 6)*2.
If the expressions are equivalent, then they will have the same values.
If they are not equivalent, then they will have different values.
-18-(6 * 2) = -18 - 12 = -30
(18 + 6)*2 = 24 * 2 = 48
Both the expressions are not equivalent.
Hence the expressions are not equivalent.
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25 points and will make the brainiest. Please answer each question as soon as possible. Thank you.
The sets of the domain and range of the relation are X = {- 4, - 3, 1, 0} and Y = {- 4, - 1, 0, 3, 4}.
How to determine the domain and range of a relation
In this problem we find a graphic representation of a relation, that is, a construction formed by two sets and its relationships. There is an input set called domain and an output set called range. Domain is represented by all values along the horizontal axis (x-axis) and range is represented by all values along the vertical axis (y-axis).
The points seen in the graph are now listed: (x₁, y₁) = (- 4, 0), (x₂, y₂) = (- 3, - 1), (x₃, y₃) = (1, - 4), (x₄, y₄) = (1, 4) and (x₅, y₅) = (0, 3). The set of the domain is {- 4, - 3, 1, 0} and the set of the range is {- 4, - 1, 0, 3, 4}.
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Point A is located at (-3, 7) on a
coordinate plane. Which point is located
8 units from Point A?
A. (-3, 8)
B. (8,7)
C. (−3, 1)
D. (-3,-1)
A point that is located 8 units from Point A include the following: D. (-3,-1).
What is a translation?In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
By translating the coordinate of point A vertically downward by 8 units, the coordinates of the image of point A' include the following:
(x, y) → (x, y - 8)
Coordinate of point A = (-3, 7) → Coordinate of point A' (-3, 7 - 8) = (-3, -1)
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Question Write an equation that you can use to find the value of x . Perimeter of square: 30 m
An equation that helped to find the value of x is 30 = 4x.
The value of x is 7.5mm.
What is the perimeter?A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.
Given:
A shape is a square.
And perimeter of the square is 30 mm.
And we know that the sides of the square are equal.
So, the perimeter of the square = 4 x The length of one side.
Substituting all the given values,
we get,
30 = 4x
x = 30/4
x = 7.5 mm
Therefore, x = 7.5 mm.
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Amount of water in a pool
which is greater 4/7 ×1/4 or 4/7×1/6
Answer:4/7*1/4
trust me >:)
write a function even count fr : int list -> int that returns the number of even integers found in the input list. the function is required to use (only) forward recursion (no other form of recursion). you may not use any library functions or any problems later in this set.
The answer of given question: That we are using the fact that True is treated as 1 and False as 0 in Python, so the expression (lst[0] % 2 == 0) will evaluate to 1 if the first element of the list is even, and 0 otherwise.
Here's an implementation of the even count function using forward recursion in Python:
python
def even_count_fr(lst: list[int]) -> int:
if not lst:
return 0
else:
return (lst[0] % 2 == 0) + even_count_fr(lst[1:])
This function takes a list of integers as input, and returns the number of even integers found in the list.
The base case for the recursion is when the list is empty, in which case the function returns 0. Otherwise, the function checks if the first element of the list is even, and adds 1 to the result if it is. The function then makes a recursive call to the same function with the tail of the list (i.e., all the elements except the first one), and adds the result of that call to the result from the previous step.
The equation (lst[0]% 2 == 0) will evaluate to 1 if the first entry of the list is even and 0 otherwise. This is because we are exploiting the Python fact that True is considered as 1 and False as 0, respectively.
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A head nurse borrowed 35 syringes from the intensive care unit (ICU). If this was 20% of the ICU's total supply, how many syringes did the ICU have in total?
The total number of syringes that the ICU had is given as follows:
175.
How to obtain the total number of syringes that the ICU had?The total number of syringes that the ICU had is obtained applying the proportions in the context of the problem.
20% of the total supply x is equivalent to 35 syringes, hence the equation is given as follows:
0.2x = 35
Solving the equation, the total number of syringes that the ICU had is given as follows:
x = 35/0.2
x = 175 syringes.
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The DNA molecule comes in the form of a double helix, meaning two helices that wrap around one another. Suppose a single one of the helices has a radius of 7 A (1 angstrom = 10-8 cm) and one full turn of the helix has a height of 33 A. Find the paremetrization r(t) of the helix. r(t) = (7 cos(t), a,b) (Use symbolic notation and fractions where needed.) a = b= Find the arc length L of one full turn of the helix.
The parameterization of the helix is:
[tex]r(t) = (7 cos(t), 7 sin(t), 33/(2*\pi ) * t)[/tex] & the arc length of one full turn of the helix is approximately 147.26 Å
where t is the parameter that varies from 0 to [tex]2\pi[/tex]
In this parameterization, the first two coordinates give the coordinates of a point on a circle of radius 7 that lies in the plane perpendicular to the helix axis, while the third coordinate gives the height of the point along the axis.
To find the arc length L of one full turn of the helix, we use the arc length formula:
[tex]L = ∫_0^(2π) ||r'(t)|| dt[/tex]
where r'(t) is the derivative of r(t) with respect to t, and || || denotes the Euclidean norm.
We have:
[tex]r'(t) = (-7 sin(t), 7 cos(t), 33/(2*pi))and||r'(t)|| = √[(-7 sin(t))^2 + (7 cos(t))^2 + (33/(2pi))^2] = 7√(2 + (33/(2pi))^2)So, we get:L = ∫_0^(2π) 7√(2 + (33/(2pi))^2) dt = 7√(2 + (33/(2pi))^2) * ∫_0^(2π) dt = 14π√(2 + (33/(2*pi))^2)[/tex]
(Note: the symbol "Å" represents angstrom, which is [tex]10^(-10)[/tex] meters, and it is used to express atomic distances.)
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