Evaluate R C F · dr, where F(x, y, z) = 5xi − 5yj − 3zk and C is given by the vector function r(t) = hsin t, cost, ti, where 0 ≤ t ≤ π.
Answers
Answer:
\(\mathbf{ - \dfrac{3 \pi^2}{2}}\)
Step-by-step explanation:
Given that:
F(x, y, z) = 5xi - 5yj - 3zk
The objective is to evaluate the \(\int _c F \ dr .C\)
and C is given by the vector function r(t) = (sin t, cost, t) where 0 ≤ t ≤ π
\(F(r(t)) = 5 \ sint \ i - 5 \ cost \ j - 3t \ k\)
∴
\(\int_c F . \ dr = \int ^{\pi}_{0} ( 5 \ sint \ i - 5 cos t \ j - 3 t \ k ) ( cos \ t , - sin \ t , 1 ) \ dt\)
\(=\int ^{\pi}_{0} ( 5 \ sint \ cost+ 5 cos t \ sin t - 3 t) dt\)
\(=\int ^{\pi}_{0} ( 10 \ sint \ cost) \ dt -3 \int ^{\pi}_{0} \ dt\)
\(= \int ^{\pi}_{0} ( 10 \ sint \ cost) \ dt - 3 [\dfrac {t^2}{2}]^{\pi}_{0} \ \ dt\)
\(= 10 [\dfrac{sin^2 \ t}{2}]^{\pi}_{0} - \dfrac{3}{2}(\pi)^2\)
By dividing 2 with 10 and integrating \(= 10 [\dfrac{sin^2 \ t}{2}]^{\pi}_{0}\); we have:
\(=5(sin^2t -sin^2 0) -\dfrac{3 \pi^2}{2}\)
\(=5(0) -\dfrac{3 \pi^2}{2}\)
\(= 0 - \dfrac{3 \pi^2}{2}\)
\(\mathbf{= - \dfrac{3 \pi^2}{2}}\)
Related Questions
How many times can 1/5 go into nine
Answers
Answer:
1.8
Step-by-step explanation:
Which unit rate corresponds to the proportional relationship shown in the graph?
Answers
The required slope of the graph is 5/4.
What is Slope?The steepness or incline of a line is determined using the slope formula. The slope of the lines is determined using the x and y coordinates of the lines. It is the proportion of the y-change axis's to the x-change. axis's
How to find slope?The slope of a line is a measure of how steep the line is and it is also commonly referred to as the "rise over run". You can find the slope of a line using the following formula:
m = (y2 - y1) / (x2 - x1)
Where m is the slope, (x1, y1) and (x2, y2) are two points on the line. The formula calculates the change in the y-coordinate (the rise) divided by the change in the x-coordinate (the run) between the two points.
According to question:We have,
Two points
(0, 0) and (8, 10)
Slope = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
= (10 - 0)/(8 - 0)
= 10/8
= 5/4
Thus, required sloe is 5/4.
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I need to find the measure
Answers
Answer:
x = 147°
Step-by-step explanation:
To find x, we have to find the angle measures in the small triangle.
180 - 61 = 119° (sum of adjacent angles on straight line=180)
The other angle measure in the triangle is 28° because they are vertically opposite angles.
We subtract 119° and 28° to find the angle measure next to x.
180 - 119 - 28 = 33° (sum of angles in a triangle=180)
x = 180 - 33
= 147° (sum of adjacent angles on straight line=180)
Plz answer my questions
Answers
- 6 (1+3)=
Propiedad distributiva
Answers
-6•1=-6
-6•3=-18
-6+-18=-24
Please give brainliest!
What is the system of checks and balances designed to ensure?
Answers
Answer:
ensure that no single branch of government would have too much power
Step-by-step explanation:
Molly also buys a bag of 8 apples for 3.60.Write and solve an equation to find how much molly paid for each apple.
Answers
Answer:
$0.45
Step-by-step explanation:
We know that Molly paid $3.60 for 8 apples, that means that $3.60 is consisted of 8 equal prices (each price is equal to the cost of one apple). From here we can make an equation.
Let "a" be the price of one apple, then
8a = $3.60
8a / 8 = $3.60
a = $0.45
Now we know that Molly paid $0.45 for each apple in the bag.
Calc II Question
Find the volume of the solid obtained by rotating the region bonded bt the given curves about the specified line.
Y = In x
Y = 1
Y = 2
X = 0
About the Y axis
Answers
Work attached in image. Since the solid is being rotated about the y-axis, you would need to solve y=lnx in terms of x. The rest of the process is showed in the image.
Find a recurrence relation for the number of n-digit binary sequences with no pair of consecutive 1s. Be sure to include the initial conditions Solution an an-1+ an-2 Initial condition: a 2, a2 = 3
Answers
The two case given below are disjoint and cover all the cases for n length strings, hence the numbers add up to give \(a_{n} =a_{n-1}+a_{n-2}\).
In the given question we have to find a recurrence relation for the number of n-digit binary sequences with no pair of consecutive.
Be sure to include the initial conditions Solution an \(a_{n-1}+ a_{n-2}\) Initial condition: \(a_{1}=2,a_{2}=3\)
Clearly \(a_{1}\) = 2 (0,1) and \(a_{2}\) = 3 (00,10,01). Now for the case of n. Suppose we are given a string with no consecutive 1's. There are two cases:
Case 1: the given string starts with a 0. In this case the n-1 length string after the first bit can be any string without consecutive 1's of length n-1. Hence there are n-1 of those.
Case 2: the given string starts with a 1. In this case the second bit has to be a 0 since we don't want consecutive 1's. Not the last n-2 length string can be any string without consecutive 1's of length n-2. Hence there are \(a_{n-2}\) of those.
These two case are disjoint and cover all the cases for n length strings, hence the numbers add up to give \(a_{n} =a_{n-1}+a_{n-2}\).
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Larissa is picking out some movies to rent, and she is primarily interested in horror films and foreign films. She has narrowed down her selections to 19 horror films and 18 foreign films. Step 1 of 2 : How many different combinations of 3 movies can she rent?
Answers
Based on the number of horror films and the number of foreign films, the number of different combinations of 3 movies that Larissa is able to rent are
How many combinations can be rented?The total number of movies that Larissa has narrowed down are:
= 19 + 18
= 37 movies
The number of combinations of 3 movies that Larissa can select are:
= Total number of movies! / ( ( Total number of movies - Number of combinations)! x Number of combinations!)
= 37! / ( (37 - 3)! - 3!)
= 46,620 combinations
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Given îx)= 10-2x, find f(7).
o 4
o 3
o 7
o 56
Answers
Answer:
-4
Step-by-step explanation:
f(x) = 10-2x
Let x = 7
f(7) = 10-2(7)
=10 -14
= -4
Answer:
Given,\(f(x)=10-2x\)\(\rm \longmapsto \: f(x) = 10 - 2x\)
\(\rm \longmapsto \: f(7) = 10 - 2(7)=10-14=-4\)
What is the solution to the system of equations?
y = 2/3x+3
x=-2
Answers
Answer:
solution (-2, 5/3 ).
Step-by-step explanation:
Given : y = + 3 and x = –2.
To find : What is the solution to the system of equations.
Solution : We have given that y = + 3 ------equation (1)
and x = –2. ------equation (2)
On plugging the x = -2 in equation (1)
y = + 3
y = + 3 .
On simplification we get ,
y = .
Therefore, solution (-2, 5/3 ).
If 2/3 of the girls in class have brown eyes and 1/4 of the girls have blue eyes what fraction of the girls in class have neither blue or brown
Answers
Makayla and her children went into a grocery store that sells apples for $0.75 each
and peaches for $1.50 each. Makayla has $15 to spend and must buy no less than 12
apples and peaches altogether. If z represents the number of apples purchased and y
represents the number of peaches purchased, write and solve a system of inequalities
graphically and determine one possible solution.
Answers
The system of inequalities's point (4,8), where an is the number of apples and 8 is the number of peaches.
what is inequality ?A pair of expresses or values that is neither equal in mathematics is referred to as an inequality. Thus, inequity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and inequality are distinct things. Use the same equal symbol most frequently when two quantities are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two faces until only the variables are left, many straightforward inequalities can be solved. However, a variety of factors support inequality: Both sides' negative values are split or added. Exchange the left and the right.
given
The following will be the solution to the expressions:-
0.75a + 1.5y = 15
a + y ≥ 12
To determine the values of a and y, solve both equations.
0.75a + 1.5(12 - a) = 15
0.75a + 18 - 1.5a = 15
-0.75a = -18 + 15
-0.75a = -3
a = 4
y = 12 - 4 = 8
The system of inequalities's point (4,8), where an is the number of apples and 8 is the number of peaches.
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1.An equation of a line passing through the point ( 3, 0 ) with a slope of 1 is *
A y = x + 3
B y - x = 3
C y = x - 3
D y - 3 = x
2.The line y = 2x - 8 cuts the x -axis at the point R. What are the coordinates of R? *
A ( 4, 0)
B ( -4, 0)
C ( -8, 0)
D (0, 8)
Answers
1) if to substitute the given coordinates and slope into the common form of equation (it is y=s*x+i), then 0=3*1+i, ⇒ i= -3. The required equation is y=x-3.
C. y=x-3.
2) according to the condition coordinates of R are (x;0). Then it is possible to calculate the x-coordinate of R after substitution into the slope-interception form (it is y=s*x+i): 0=2x-8; ⇒ x=4. The coordinates of R are (4;0).
A. (4;0).
Doors for the small cabinets are 11.5 inches long. Doors for the large cabinets are 2.7 times as long as the doors for the small cabinets. How many large doors can be cut from a board that is 10 feet long?
Answers
Answer:So if you take the small cabinet door length which is 11.5 inches long and multiply by a factor of 2.3 you get the total length of the large cabinet doors, which is 26.45 inches
Step-by-step explanation:
Please PLEASE please!!! Any math experts can solve these I will give thanks and mark thank you!!!!
Answers
Answer:
8.
numerator: 3
denominator: 2
9.
numerator: 2
denominator: 2
10.
numerator: 2
denominator: 4
After adding the two equations to eliminate x you are left with 4y=-8. Solve for y: y =
Answers
Answer: -2
Step-by-step explanation:
4y/4 = -8/4
y = -2
Answer:
Step-by-step explanation:
Answer is -2
NO LINKS!! Each graph represents a relation. Determine the domain and range. 2ii
Answers
Answer:
7) Domain: (-∞, ∞)
Range: [-1, ∞)
8) Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.
[ or ] : Use square brackets to indicate that the endpoint is included.
Domain & Range
The domain is the set of all possible input values (x-values).
The range is the set of all possible output values (y-values).
Question 5From inspection of the graph, the line is continuous.
The arrows either end of the line indicate that the line continues indefinitely in those directions.
Therefore, the domain of the relation is unrestricted: (-∞, ∞)
From inspection of the graph, the minimum y-value is y = -1.
The end behavior of the relation is:
\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)
\(y \rightarrow + \infty, \textsf{as } x \rightarrow +\infty\)
Therefore, the range of the relation is restricted: [-1, ∞)
Question 6From inspection of the graph, the line is continuous.
The arrows either end of the line indicate that the line continues indefinitely in those directions.
Therefore, the domain of the relation is unrestricted: (-∞, ∞)
The end behavior of the function is:
\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)
\(y \rightarrow -\infty, \textsf{as } x \rightarrow +\infty\)
Therefore, the domain of the relation is unrestricted: (-∞, ∞)
answer quickly please
Answers
= .000444
4.44x10^-4
NO LINKS!! Use the cylinder shown to mark each statement as true or false. Rewrite and correct any false statements.
Answers
Problem 9
Answer: FalseReason:
The height of the cylinder is 2.5 ft. It's misleading because the cylinder is tipped onto its side, so it appears that 4 ft is the height. The height of any cylinder is always perpendicular to the circular base. It might help to rotate the paper so that the circular base is horizontal.
==============================================================
Problem 10
Answer: FalseReason:
The diameter of the base is 4 feet, which divides in half to 2 feet and it's the radius of the circle.
Area = pi*(radius)^2 = pi(2)^2 = 4pi
So the area expression should be either pi(2^2) or pi(4) or 4pi
==============================================================
Problem 11
Answer: TrueReason:
V = pi*r^2*h
V = 3.14*2^2*2.5
V = 31.4 cubic feet
This volume is approximate since pi = 3.14 is approximate.
5⁶ • 5 how do i simplify
Answers
The square below represents one whole.
Express the shaded area as a fraction, a decimal, and a percent of the whole.
Fraction:
Decimal:
Percent:
Answers
Answer:
Fraction: 9/10
Decimal: 0.9
Percent: 90%
help pls
What is the solution to this system of equations?
x = 12 − y
2x + 3y = 29
Answers
Answer:
Step-by-step explanation:
a line passes through the points (2,6) and (4,9) move an expression and a number
Answers
Answer:
General equation of line is y=mx+c where m is the slope
Slope of line parallel to x-axis is m=0
So y=(0)x+c⟹y=c
(−4,6) lies on our required line y=c
⟹6=0(−4)+c
⟹c=6
Equation of the line is y=6
Step-by-step explanation:
Can someone please help me I will mark u brilliant
Answers
Answer:
the first one
Step-by-step explanation:
The problem says that the plot must have a maximum of 44, which means the most right dot must be on the 44 mark. All the graphs fit this requirement (the dashes are in increments of 2) The problem says that it must have an upper quartile of 39, which means the line closest to the maximum dot must be on the 39 mark. Graphs 2 and 3 do not meet this requirement, so they are eliminated. The last requirement is the median of 25. The median is represented by the middle line in the middle of the boxes. Graph 4 does not fit this requirement, so it is eliminated. Thus, only the first graph follows all 3 requirements.
Is 5/6 larger or 2/3? Pls help.........
Answers
Answer:
yes 5/6 is bigger
Step-by-step explanation:
Bargain Rental Car offers rental cars in an off-airport location near a major tourist destination in California. Management would like to better understand the variable and fixed portions of it car washing costs. The company operates its own car wash facility in which each rental car that is returned is thoroughly cleaned before being released for rental to another customer. Management believes that the variable portion of its car washing costs relates to the number of rental returns. Accordingly, the following data have been compiled:
Month Rental Returns Car Wash Costs
January 2,300 $ 10,200
February 2,500 $ 12,700
March 2,700 $ 11,000
April 2,900 $ 13,100
May 3,600 $ 15,400
June 4,900 $ 21,700
July 5,400 $ 21,400
August 5,300 $ 20,200
September 4,600 $ 22,000
October 3,800 $ 18,700
November 2,100 $ 9,900
December 2,500 $ 11,400
2. Using least-squares regression, estimate the variable cost per rental return and the monthly fixed cost incurred to wash cars. What is the R2 rounded to the nearest whole percentage? (Round Fixed cost to the nearest whole dollar amount and the Variable cost per unit to 2 decimal places.)
Answers
Answer:
Variable cost $3.79 ; fixed cost = $2185.47
Step-by-step explanation:
Given the data :
Rental return(x) :
2300
2500
2700
2900
3600
4900
5400
5300
4600
3800
2100
2500
Car wash cost :
10200
12700
11000
13100
15400
21700
21400
20200
22000
18700
9900
11400
Using the online regression calculator :
The obtained regression equation is :
ŷ = 3.79X + 2185.47
Comparing the obtained result with the general form of the equation:
y = mx + c
Where m = gradient or slope whose value gives the variation in cost per rental return (x)
c = intercept, which is constant or fixed, it is the value where the regression line crosses the y axis, hence, it corresponds to the fixed cost.
Hence,
The variable cost per rental return(m)
mx = 3.79x
m = $3.79
The fixed cost :
c = $2185.47
Suppose you are interested in testing a new teaching method. You know that the
population of students has μ = 50 and o= 15. You expose your class of 25 students to a new
teaching method and administer a test. The mean test scores achieved by the students in you
class is M = 55. Compute the z-score associated with M = 55.
Answers
The z-score related to the mean test scores achieved by the students is 0.33.
What is described as normal distribution?The normal distribution, also established as the Gaussian distribution, is just a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far from the mean. The normal distribution is graphically illustrated as a "bell curve."For the given question;
mean population; μ = 50.
standard deviation; σ = 15
Test score; x = 55.
The z-score is estimated as;
z = (x - μ)/σ
Put the values;
z = (55 - 50)/15
z = 0.33
Thus, the z-score related to the mean test scores achieved by the students is 0.33.
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A full container of juice holds 64 fluid ounces. How many 7 fluid ounces servings of juice in a full container?
Answers
Answer:
× = , . ℍ, - , .