find the value of integral ∫ c ( x 2 y 2 z ) d s ∫c(x2 y2 z)ds , where c c is parmeterized by → r ( t ) = ⟨ 2 cos ( 2 t ) , 2 sin ( 2 t ) , 5 t ⟩ r→(t)=〈2cos(2t),2sin(2t),5t〉 for 0 ≤ t ≤ 4 0≤t≤4 .
Answers
The value of integral ∫ c ( x 2 y 2 z ) d s ∫c(x2 y2 z)ds is 156.864.
To evaluate the line integral ∫c(x^2 y^2 z)ds, we need to parameterise the curve C and then compute the integral along that curve.
The parameterization of C is given by → r ( t ) = ⟨ 2 cos ( 2 t ) , 2 sin ( 2 t ) , 5 t ⟩ r→(t)=〈2cos(2t),2sin(2t),5t〉 for 0 ≤ t ≤ 4 0≤t≤4.
To compute the line integral, we first need to get the unit tangent vector →T(t) of the curve C. The unit tangent vector is :
→T(t) = →r'(t)/|→r'(t)|
Taking the derivative of →r(t) gives:
→r'(t) = ⟨ -4 sin(2t), 4 cos(2t), 5 ⟩So, the magnitude of →r'(t) is:
|→r'(t)| = √( (-4 sin(2t))^2 + (4 cos(2t))^2 + 5^2 ) = √( 16 + 25 ) = √41
Therefore, the unit tangent vector is:
→T(t) = (1/√41) ⟨ -4 sin(2t), 4 cos(2t), 5 ⟩
Now, we can compute the line integral as follows:
∫c(x^2 y^2 z)ds = ∫0^4 (x^2 y^2 z) |→T(t)| dt
Substituting the parameterization and the unit tangent vector, we get:
∫c(x^2 y^2 z)ds = ∫0^4 (4 cos^2(2t) 4 sin^2(2t) 5t) (1/√41) dt
= (20/√41) ∫0^4 (16 cos^2(2t) sin^2(2t) t) dt
Using the identity sin(2θ) = 2sin(θ)cos(θ), we can simplify the integrand as follows:
16 cos^2(2t) sin^2(2t) = 4 sin^2(4t) = 2 (1 - cos(8t))
Substituting this back into the integral, we get:
∫c(x^2 y^2 z)ds = (20/√41) ∫0^4 [ 2 (1 - cos(8t)) t ] dt
Integrating by parts with u = t and dv = 1 - cos(8t), we get:
∫c(x^2 y^2 z)ds = (20/√41) [ t^2/2 - (1/8) sin(8t) ] |_0^4
= (20/√41) [ 8 - (1/8) sin(32) ]
≈ 156.864
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Related Questions
the proportion of college football players who have had at least one concussion is estimated to be 34% in the united states. we wanted to know if football players at our university were less likely to have suffered a concussion, so we surveyed a random sample of 100 past and present football players at our university. is this survey valid or not valid for testing the hypothesis that the proportion of college football players at our university with at least one concussion is less than the national average?
Answers
All of the criteria's are fulfilled the survey is valid.
We have the information from the question:
The proportion of college football players who have had at least one concussion is estimated to be 34% in the united states.
Then, 34% = 0.34
The sample size of the data is = 100
p: the ‘proportion’ of ‘college’
The required conditions for testing the hypothesis of population proportion are,
(i) The population is larger than the sample
(ii) np > 10
=> 100 × 0.34
=34
(iii) n(1-p) > 10
100 × (1 - 0.34)
=> 100 × 0.66
=66
iv)The ‘sample’ is drawn randomly from the population.
Since all of the above criteria's are fulfilled the survey is valid.
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5. Dylan walks into a video arcade with a pocketful of quarters. He spends them
at a rate of nine every half hour until he runs out. If the amount of quarters Dylan
has is graphed over time, which feature of the graph corresponds to Dylan's
initial amount of quarters, before he spends the first one?
The y-intercept
The slope
The x-intercept
The minimum value
Answers
Answer:
The y-intercept
Step-by-step explanation:
Have a good day :)
A triangular prism is 8 yards long. It has a triangular face with a base of 12 yards. The volume of the prism is 720 cubic yards. What is the height of its triangular face
Answers
The height of the triangular face is 15 yards.
To find the height of the triangular face, we will use the formula for the volume of a triangular prism:
Volume = (1/2) * Base * Height * Length.
We are given the following values:
- Volume (V) = 720 cubic yards
- Length (L) = 8 yards
- Base (B) = 12 yards
We need to find the height of the triangular face (H).
Let's plug in the given values into the formula and solve for H:
720 = (1/2) * 12 * H * 8
First, simplify the equation:
720 = 6 * H * 8
720 = 48 * H
Now, divide both sides by 48 to find the value of H:
H = 720 / 48
H = 15 yards.
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What is another example for data on a statistical question
Answers
a sample consists of the following data: 7, 11, 12, 18, 20, 22, 43. Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier
a. true
b. false
Answers
The statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.
Given data:
7, 11, 12, 18, 20, 22, 43.
To find out whether the last observation is an outlier or not, let's use the three standard deviation criterion.
That is, if a data value is more than three standard deviations from the mean, then it is considered an outlier.
The formula to find standard deviation is:
S.D = \sqrt{\frac{\sum_{i=1}^{N}(x_i-\bar{x})^2}{N-1}}
Where, N = sample size,
x = each value of the data set,
\bar{x} = mean of the data set
To find the mean of the given data set, add all the numbers and divide the sum by the number of terms:
Mean = $\frac{7+11+12+18+20+22+43}{7}$
= $\frac{133}{7}$
= 19
Now, calculate the standard deviation:
$(7-19)^2 + (11-19)^2 + (12-19)^2 + (18-19)^2 + (20-19)^2 + (22-19)^2 + (43-19)^2$= 1442S.D
= $\sqrt{\frac{1442}{7-1}}$
≈ 10.31
To determine whether the value of x = 43 is an outlier, we need to compare it with the mean and the standard deviation.
Therefore, compute the z-score for the last observation (x=43).Z-score = $\frac{x-\bar{x}}{S.D}$
= $\frac{43-19}{10.31}$
= 2.32
Since the absolute value of z-score > 3, the value of x = 43 is considered an outlier.
Therefore, the statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.
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What is the area of this trapezoid?
A rectangle with a length of 17 and a height of 4 has two right triangles on each side of it with long leg lengths of 5.
Answers
The area of the trepezium will be 80 sq. unit.
What precisely is a trepezium?
Trapezoids are made up of two parallel and two oblique sides. A Trapezium is another name for it. A trapezoid is a closed four-sided shape or figure with a space-filling perimeter. It is a 2D figurine rather than a 3D figure. A trapezoid's bases are the sides that are parallel to one another. Legs are non-parallel sides, often known as lateral sides. The space between its parallel sides determines its height.
A trepezium's area is equal to 1/2*(a+b)*h.
where h is the height or distance between two parallel lines
The lines a and b are parallel.
Now,
Given A rectangle with a length of 17 and a height of 4 has two right triangles on each side of it with long leg lengths of 5
then parallel sides of trepezium will be 17 and 17+3+3=23
because for the triangle base will be =√5²-4²
=3
and height of trepezium=4 unit
So, area of trepezium will be=1/2(23+17)*4
=40*2
=80 sq. unit
hence,
The area of the trepezium will be 80 sq. unit.
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Given that a minute hand travels through 360 degrees in an hour, how many degrees does it turn in only 23 minutes?
Answers
Answer:
138 degrees
Step-by-step explanation:
360 divided by 60 equals 6
every minute equals 6 degrees
23 * 6 equal 138 degrees
Write the number 11 as a fraction with the denominator of 15.
Answers
Answer:
11/15
there ya go!!
Step-by-step explanation:
Answer:
165/15
Step-by-step explanation:
11 times 15 equals 165
If you divide 165 by 15, you get the value of 11.
Paula's Pizza Parlor uses the following ingredients to make pizza.
Number of Pizzas Sauce (oz) Cheese (oz)
2 18 12
5
help
At this rate, how much sauce and cheese will Paula use to make 5 pizzas?
Paula will use 30 oz of sauce and 45 oz of cheese to make 5 pizzas.
Paula will use 35 oz of sauce and 24 oz of cheese to make 5 pizzas.
Paula will use 45 oz of sauce and 30 oz of cheese to make 5 pizzas.
Paula will use 90 oz of sauce and 60 oz of cheese to make 5 pizzas.
Answers
Paula will use 45 oz of sauce and 30 oz of cheese to make 5 pizzas, 3rd option.
How to find quantity of ingredients for 5 pizzas?To find this, you can use the proportion of ingredients used for 2 pizzas and scale it up to 5 pizzas.
For 2 pizzas, Paula uses 18 oz of sauce and 12 oz of cheese.
The proportion of sauce to cheese used is 18/12
To make 5 pizzas, you can use this proportion to find how much sauce and cheese is needed:
2 pizzas = 18 sauce
5 pizzas = 5 / 2 x 18 = 45 sauces.
For cheese required, Paula will use:
2 pizzas = 12 cheese
5 pizzas = 5 / 2 x 12 = 30 cheese.
So the total is 45 oz of sauce and 30 oz of cheese.
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neeeeed helppppppppppppppppppppppppp
Answers
Answer:
I think the first one would be 49 and then 61 hope it helps :)
Find the GCF of the two numbers, and rewrite the sum of the two numbers using the distributive property.
12 + 18
A) 4(2 + 3)
B) 4 + (2 + 3)
C) 6(2 + 3)
D) 6 + (2 + 3)
Answers
what is the rate of change for the function y= 5x+ 25
Answers
Answer:
5
Step-by-step explanation:
100% right!!
Answer:
5 or -5
Step-by-step explanation:
rate of change is the same thing as slope (or m)
Light travels at a speed of about 1.86×10^5 miles per second. Suppose a space ship is able to travel at the speed of light. If the distance around Earth along the Equator is about 2.48×10^4 miles, how many times could the space ship travel around the Earth in 1 second? Round to the nearest tenth if necessary.
Answers
Based on the speed that light travels and the distance around the Earth along the Equator, the number of times the space ship would travel in 1 second is 0.133 times
How to find the number of times the spaceship would travel around Earth?The number of times that the space ship would travel around Earth around the Equator, going at the speed of light is:
= Distance around the Earth along the Equator / Speed of light
Solving for the number of times around the Earth for the space ship gives:
= 2.48×10⁴ / 1.86×10⁵
= 24,800 / 186,000
= 0.133 times
In conclusion, going at the speed of light, the space ship would go around the Earth, along the equator, 0.133 times.
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how to find the number of solutions to a system of equations
Answers
Molly and Torry like to eat ice cream sandwiches. In one week, Molly ate 5 ice cream sandwiches, and Torry ate n ice cream sandwiches. They ate a total of 12 ice cream sandwiches all together
Answers
The solution allows us to determine the individual consumption of Molly and Torry, with Molly eating 5 ice cream sandwiches and Torry eating 7 ice cream sandwiches.
To explain further, let's assume Torry ate "n" ice cream sandwiches in one week. When we add Molly's consumption of 5 sandwiches to Torry's "n" sandwiches, the total number of sandwiches eaten by both of them is 5 + n. According to the given information, the combined total is 12 sandwiches.
We can express this relationship in an equation:
5 + n = 12
To find the value of "n," we subtract 5 from both sides of the equation:
n = 12 - 5
n = 7
Hence, Torry ate 7 ice cream sandwiches in one week. The solution allows us to determine the individual consumption of Molly and Torry, with Molly eating 5 ice cream sandwiches and Torry eating 7 ice cream sandwiches.
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The scale drawing of the tennis court shown below is drawn using a scale of 1 inch = 12 feet.
(image)
The net would have to be ________ to stretch from one side of the court to the other, as shown by the center line.
fill in the blank
A. 7.05 ft
B. 20.4 ft
C. 30 ft
D. 51 ft
Answers
The net would be 51 feet long to stretch from one side of the court to the other.
What are scaled drawings?Scale drawings are drawings that shows a diagram with another proportional dimensions
The scale ratio of the diagram is given as:
Scale = 1 inch = 12 feet
The length of the net is given as:
Length = 4.25 inches
So, the actual length of the net is:
\(Length=4.25*12\)
Evaluate the product
\(Length=51\)
Hence, the net would be 51 feet long, if stretched across the court
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An elevator can hold less than 2700 pounds of extra weight. If an average person weighs 150 pounds, what is the maximum number of people (p) that can be on the elevator at one time?
Answers
Answer:
18
Step-by-step explanation:
2700/150 = 18
Answer:
p<18
Step-by-step explanation:
90 minus 10x
ill give 25 points and brainiest
Answers
Answer:
80x
Step-by-step explanation:
There is no substitution for the variable so the expression is 80x
Can someone please help me????? Will mark Brianliest !!!!!!!!
Answers
Answer:
FGH is 63 degrees
Step-by-step explanation:
Activity 1: Try Me! Directions: Read and analyze the given activity. Answer and do what is needed for the following. A. Computing for the Mean of a Sample Find the mean of the following sets of numbers. Given Mean 3, 4, 9, 11, 5 7, 11, 10, 13, 5, 6 13, 3, 6, 8, 12, 9, 5 15, 11, 16, 15, 18, 20, 20 21, 23, 25, 19, 15, 26, 27, 29
Answers
The mean of the first set is 8.67
The mean of the second set is 8
The mean of the third set is 16.43
The mean of the fourth set is 23.13.
Compute for the sum of the given numbers in each set.
Divide the sum computed in step 1 by the total number of values in each set (count the values).
The resulting quotient is the mean of the respective set of numbers.
A. Computing for the Mean of a Sample
Given Mean 3, 4, 9, 11, 5
To find the mean of the given set, we need to compute the sum first.
3 + 4 + 9 + 11 + 5 = 32
There are five (5) values in the set, so we divide the sum by 5.32 ÷ 5 = 6.4
Thus, the mean of the first set is 6.4.7, 11, 10, 13, 5, 6
Sum = 52
Count = 6
Mean = 52 ÷ 6 = 8.67
The mean of the second set is 8.67.13, 3, 6, 8, 12, 9, 5
Sum = 56
Count = 7
Mean = 56 ÷ 7 = 8
The mean of the third set is 8.15, 11, 16, 15, 18, 20, 20
Sum = 115
Count = 7
Mean = 115 ÷ 7 = 16.43
The mean of the fourth set is 16.43.21, 23, 25, 19, 15, 26, 27, 29
Sum = 185
Count = 8
Mean = 185 ÷ 8 = 23.13
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Find the 11th term of the geometric sequence 1, 4, 16, ...
Answers
Answer:
a(11) = 4^10 = 1048576
Step-by-step explanation:
The first term of this geometric sequence, a(1), is 1, and the common ratio, r, is 4. Each new term is 4 times the previous term. Thus,
a(n) = 1*4^(n - 1), and
a(11) = 4^10 = 1048576
Answer:
The 11th term is 1048576
Step-by-step explanation:
Solve each of the follow
your answers:
| 2.5x=10
3. 2x=14
4. 3x=15
5. 7x=21
| 6.5x = 30
7. 9p=27
8. 6m=30
9. 3q=24
10, 8r=24
Answers
Step-by-step explanation:
5x=10 divide both sides by the coefficient of x and that will give you 2. Therefore, x=2
2x=14 divide both sides by the coefficient of x and that will give you 7. Therefore, x=7
3x=15 divide both sides by the coefficient of x and that will give you 3. Therefore, x=3
7x =21 divide both sides by the coefficient of x and that will give you 3. Therefore, x=3
5x=30 divide both sides by the coefficient of x and that will give you 6. Therefore, x=6
9p=27 divide both sides by the coefficient of p and that will give you 3. Therefore, p=3
6m=30 divide both sides by the coefficient of m and that will give you 5. Therefore, m=5
3q=24 divide both sides by the coefficient of q and that will give you 8. Therefore, q=8
8r=24 divide both sides by the coefficient of r and that will give you 3. Therefore, r=3
I will be glad to be corrected if I make any mistake
Find the area of the figure below composed of a parallelogram and one semicircle rounded to the nearest tenths place 
Answers
We have a parallelogram and a half of circle.
The area of parallelogram are: A=basis*height
The area of circle are: A=πr², where r is the radius (half of diameter). Thus the half circle have Area equals to:
Approaching π to 3,14
parallelogram:
b=26
h=13
A=13*26
A=338
Half circle:
r=12
A=(3,14*12²)/2
A=226,08
Total Area of the figure are:
A=338+226,08
A=564,08
What is the remainder when g(x)=2x-3 is divided by
2x^3-9x² + x +q
Answers
Answer:9x>6=76
Step-by-step explanation:9x>6=76
20 Points, Part A What percentage of the time margins are at least 0.6 second? Part B What is the most common margin of victory? (Screenshot)
Answers
Answer:
20%
0.5
Step-by-step explanation:
There are 20 margins, so you have to count how many are 6.0 or higher. There are 4 margins that fit this so you divide the 4 margins by 20, then multiply the quotient by 100. That's how you get 20%.
The most common time was 0.5.
What is 78/100 in standard form
Answers
Answer:
0.78 x 10^ 0
Step-by-step explanation:
If 3 varies inversely as x and y=2 when x=25, find x when y=40
Answers
Answer:
you get X= 1.25!!!!! :) have a great day
Step-by-step explanation:
a ladder leans against a wall so that its slope is 1.60. the top of the ladder is 8 vertical feet above the ground. what is the approximate horizontal distance from the base of the ladder to the wall? (assume that the positive direction points from the base of the ladder toward the wall.)
Answers
Answer: We can use the trigonometric function tangent to solve this problem. Let x be the horizontal distance from the base of the ladder to the wall. Then we have:
tan(1.60) = x / 8
Multiplying both sides by 8, we get:
x = 8 tan(1.60)
Using a calculator, we find:
x ≈ 8 × 1.518 = 12.14
Therefore, the approximate horizontal distance from the base of the ladder to the wall is 12.14 feet.
Step-by-step explanation:
In simple regression analysis, the standard error is ________ greater than the standard deviation of y values.
Answers
What is the slope of (-3,0) and (0,-6)
Answers
Answer:
\(m=-2\)
Step-by-step explanation:
Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)
Simply plug in your 2 coordinates into the slope formula to find slope m:
\(m=\frac{-6-0}{0-(-3)}\)
\(m=\frac{-6}{0+3}\)
\(m=\frac{-6}{3}\)
\(m=-2\)