Evaluate and input the result of the following integral.
∫ Fdr= ?
c
F=
Answers
Answer:
∫ F dr= 1
c
Step-by-step explanation:
The correct question is -
Given - [tex]F = < \frac{sec^{2} x}{y} , - \frac{tan x}{y^{2} }>[/tex] and C : (0, 1) to [tex](\frac{\pi }{4} , 1)[/tex]
To find - Evaluate and input the result of the following integral.
Proof -
We know that,
dr = dx i + dy j
F = < F1, F2 >
Now, we know
[tex]d(\frac{tanx}{y }) = \frac{d}{dx}(\frac{tanx}{y}) + \frac{d}{dy}(\frac{tanx}{y})[/tex]
So,
[tex]\frac{d}{dx}(\frac{tanx}{y}) =\frac{1}{y} \frac{d}{dx}({tanx}) \\\\ = \frac{sec^{2} x}{y} \\\frac{d}{dy}(\frac{tanx}{y}) = tanx \frac{d}{dy}(y^{-1}) \\ = -\frac{tanx}{y^{2} }[/tex]
Now,
We can see that,
[tex]d(\frac{tanx}{y }) = \frac{sec^{2} x}{y} dx - (\frac{tanx}{y^{2} })dy[/tex]
So,
[tex]\int\limits^{}_C {F. dr} = \int\limits^{}_C d(\frac{tanx}{y} )\\= [\frac{tanx}{y} ]\limits^{(\frac{\pi }{4} ,1)}_{(0,1)}\\= [\frac{tanx}{y} ]\limits^{}_{(\frac{\pi }{4} ,1)} - [\frac{tanx}{y} ]\limits^{}_{(0,1)}\\= \frac{tan(\frac{\pi }{4} )}{1} - \frac{tan 0}{1}\\= 1 - 0\\= 1[/tex]
∴ we get
∫ F dr= 1
c
Related Questions
This is the first year Janis is playing softball. She has been practicing her batting. On her last swing the bat made an arc with a radius of 49 inches and swept
through 283 of rotation. Assuming the arc is circular, what is the distance the tip of the bat travels to the nearest inch?
Answers
Answer:
2*pi*49*283/360=242 (to the nearest inch)
the distance the tip of the bat travels 242 inches.
giving out brainliest answer please help me out asap !! it’s due today
Answers
Answer:
180=3x+7x+10
simplify
180=10x+10
subtract 10 from both sides
170=10x
divide both sides by 10
x=17
Inscribed angles: find the value of each variable. The dot represents the center
Answers
Answer:
4
Step-by-step explanation:
Each triangular face of the following solid figure is congruent. If the area of each face is 12 square inches, what is the
surface area of the entire figure?
Answers
Answer:
the surface area is 48in^2 because there are 4 faces and you have to find the surface are in which you must multiply 12 by 4.
Step-by-step explanation:
A picture frame measures 5 inches wide and 7 inches long. What is the perimeter of the frame?
Answers
Remember finding perimeter is always adding, so add 5 two times for the sides do the shape, do the same for 7, then you get your answer. Hope this helps!
Which expression is equivalent to (see the picture)
A. 20x-21y +14
B. 20x + 11y + 14
C. 20x - 11y + 6
D. 20x + 21y +6
Answers
Answer:
A
Step-by-step explanation:
[tex]\frac{1}{5} (150x-80y+50-50x-25y+20)[/tex]
step 1 apply the 1/5 to everything that inside of the parenthesis
[tex]\frac{150x}{5} =30x\\\\\frac{-80y}{5} =-16y\\\\\frac{50}{5} =10\\\\\frac{-50x}{5} =-10x\\\\\frac{-25y}{5} =-5y\\\\\frac{20}{5} =4[/tex]
we now have 30x - 16y + 10 - 10x - 5y + 4
Step 2 combine like terms
30x - 10x = 20x
-16y - 5y = - 21y
10 + 4 = 14
we're left with 20x - 21y + 14 Which corresponds with answer choice A
Answer:
20x-21y+14
Step-by-step explanation:
1/5(150x-80y+50-50x-25y+20) is equal to 1/5(150x) + 1/5(-80y) + 1/5(50) + 1/5 (-50x) + 1/5(-25y) + 1/5(20)
So if we simplify, we would have 30x + (-16y) + 10 + (-10x) + (-5y) + 4, or 30x -16y + 10 -10x -5y + 4
When organizing the values by variable, the equation would look like this -
30x - 10x -16y -5y + 10 + 4
Combining like terms will result in 20x -21y + 14.
Hope this helps!
what are the answers for these two questions? please also tell me HOW you got that answer
Answers
9. Multiply the money he has by the portion he spent:
75 x 3/5 = (75 x3)/5 = 225/5 = 45
He spent $45
10. First rewrite 4 1/8 as an improper fraction
33/8
Now multiply by 1/3:
33/8 x 1/3 = (33 x1) /(8 x 3) = 33/24 = 1 3/8
She spent 1 3/8 hours studying math.
The area of a triangle is 30 square feet. If
the base is 4 feet, then what is the height?
Answers
Explanation:
Area of a triangle= 1/2base x height
Plug in information
30=1/2 x 4 x h
Solve 1/2 x 4 = 2
30= 2 x h
Divide both side by two
30/2=2 x h/2
Solve:
15= h
Does anyone know how to find the volume of cylinders, cones and shapes? Any good videos/tips?
Answers
volumes of cone: V= TT ×R2 × H ÷ 3
Answer:
I believe for a cylinder the volume is the base times the height.
Step-by-step explanation:
this is just from my own head
Helpppp pleaseeee please pretty please NO LINKS OR I WILL REPORT YOU please give an explanation I will mark brainliest
Answers
Answer:
A: 88 square inches
Step-by-step explanation:
trust me
PLEASE HELP ME I CAN'T FAIL THIS, JUST 2 QUESTIONS!!
What is the volume of the composite figure if both the height and the diameter of the cylinder are 3.5 feet? Give the exact answer and approximate to two decimal places.
Find the height in centimeters of a square pyramid with a volume of 455cm3 and a base edge length equal to the height. Give the approximate answer rounded to 2 decimal places.
PLEASE SHOW YOUR WORK
Answers
im a boy im in 7th grade 13 years old and single i need some help
Answers
single too and 13 I can't help bc I ain't smart
Two trains leave New York at the same time. One travels south 50 miles per hour and the other traveled east at 40 miles per hour. How far apart are they at the end of THREE HOURS?
Answers
Answer:
192 miles
Step-by-step explanation:
This is a right triangle problem
One leg of the triangle is
50 * 3 = 150
The other leg is
40 * 3 = 120
the distance is the hypotenuse
c^2 = 150^2 + 120^2
c^2 = 22500 + 14400
c^2 = 36900
Take the square root of both sides
c = 192.093727123
c ≈ 192 miles
Answer:
30 miles apart
Step-by-step explanation:
Im not sure if this is the corect answer to this but this is what i think what i did was get 50 x 3 and 40 x 3 since they starded at the same times and finished after 3 hours so multiply your numbers by 3 so...
50 x 3=150
40 x 3=120
150-120=30 miles apart
A sample of restaurants in a city shows that the average cost of an appetizer is $6.32 with a standard deviation of $0.47. A brand new restaurant wants to get noticed by offering appetizers for a much lower price. To determine the lower price, should the formula use a z-value that is greater than or less than -1?
a.
Greater than -1
c.
Greater than 1
b.
Less than -1
d.
Either way, it doesn’t matter
Answers
Answer:
D
Step-by-step explanation:
Is the corrext answer hope it helps
By using a z-value less than -1, we can find a price that is significantly lower than the average cost, and therefore more likely to attract customers.
Option B is the correct answer.
What is a standard deviation?Standard deviation is a measure of the amount of variability or spread in a set of data.
It is calculated as the square root of the variance and is often denoted by the symbol σ (sigma) for a population and s for a sample.
We have,
The z-value formula is used to determine the number of standard deviations a data point is from the mean.
To determine the lower price of appetizers, we want to find a price that is significantly lower than the average cost.
Since the new restaurant wants to offer appetizers for a much lower price, we should use a z-value that is less than -1, which indicates a price that is more than one standard deviation below the mean.
Recall that the z-value formula is:
z = (x - μ) / σ
where x is the value of interest, μ is the mean, and σ is the standard deviation.
Thus,
By using a z-value less than -1, we can find a price that is significantly lower than the average cost, and therefore more likely to attract customers.
Learn more about standard deviation here:
https://brainly.com/question/13905583
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ms. irwin teaches four periods of weight training. she required each student in thr class to record the maximum amount of weight lifted for the squat. based upon the data listed below, which period had the greatest mean score?
period 1 : 100, 100, 125, 125, 130, 130
period 2 : 90, 125, 125, 130, 135, 135
period 3 : 90, 90, 100, 125, 125, 125
period 4: 90, 90 , 90, 100, 100, 125
a. period 1
b. period 2
c. period 3
d. period 4
Answers
Answer:
a
Step-by-step explanation:
Please mark brainliest
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Answers
Answer:
A. (-4,5) is the answer to describe the set
What is the difference of -9 + 2i and 4 - 6i?
Answers
Answer:
-13-4i
Step-by-step explanation:
The new number 200 is 400 less than the original number what is the approximate per percent change
Answers
Answer:
200+400=600
400/600=2/3=66.6%
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Point P is plotted on the coordinate grid. If point S is 12 units to the left of point P, what are the coordinates of point S? 10 NAG -12-10-864 -20 32 2 4 6 8 10 12 TP -6 -S 10 - 12 (6.-16) (-6.-16) o(-6,-4) (6,4)
Answers
Answer:
(-6, -4)
Step-by-step explanation:
Original coordinates: (6, -4)
POINT S IS 12 UNITS TO THE LEFT OF POINT P.
There are multiple ways to solve this, but I will explain the easiest way.
We can subtract 12 from the x-coordinate.
This because the x-axis runs RIGHT and LEFT.
The y-axis runs UP and DOWN.
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A Biology teacher wants to see if there is any difference in the abilities of students enrolled in biology today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago 81 85 σ 14.5 8.5 n 81 36 The point estimate for the difference between the means of the two populations is
Answers
Answer:
The point estimate for the difference between the means of the two populations is x1`-x2`= 81-85=-4 where x1` is the mean of the of the first population and x2` is the mean of the second population.
Step-by-step explanation:
The data given is
Today Five Years Ago
X` 81 85
σ 14.5 8.5
n 81 36
The point estimate for the difference between the means of the two populations is x1`-x2`= 81-85=-4 where x1` is the mean of the of the first population and x2` is the mean of the second population.
The test statistics that will be used is
Z= x1-x2/ √σ₁²/ n₁ + σ₂²/n₂
Z= 81- 85/ √14.5² /81 + 8.5² /36
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Can someone help me with question 1 and 2 please
Answers
there’s 180 degrees in a triangle
70 + 70 = 140
180 - 140= 40
A= 40
question 2)
there’s only one line of symmetry, down the middle
Helppppppppppp!!!!! Please
Answers
Answer:
The answer is C.
Step-by-step explanation:
angle 5 and 4 makes a line which is 180 and since angle 5 equals 57 , 180-57=123.
Which of the following is the solution to 9/x+ 4 54 ?
O A. x5-10 and x32
O B. x2-10 or x22
O c. xs-10 or x2 2
O D. x22
Answers
Im guessing its c. I dont really know if i'm wrong im sorry
Amy knits 1/10 of a scarf in 4/5 of an hour. What fraction of scarf can Amy knit in 1 hour
Answers
Answer:
Amy can knit [tex]\frac{1}{8}[/tex] of a scarf in 1 hour.
Step-by-step explanation:
This question can be solved by proportions, using a rule of three.
We have that:
1/10 of a scarf - 4/5 of an hour
x of a scarf - 1 hours.
Applying cross multiplication:
[tex]\frac{4x}{5} = \frac{1}{10}[/tex]
[tex]x = \frac{5}{10*4} = \frac{5}{40} = \frac{1}{8}[/tex]
Amy can knit [tex]\frac{1}{8}[/tex] of a scarf in 1 hour.
Modal 9 10 11 14 19 22 27 29 21 18 11 6
Answers
Answer:
modal is 11. it's the correct answer
Need help pls help will gift extra points if help plz explain how you soved it
Answers
Answer:
both 125° and the 5x+30 are congruent to eachother. therefore you can go
5x+30=125
subtract 30 from both sides.
5x=95
then divide both sides by 5
x=19
what is the value of 2(4x + 3) when x=3
Answers
Answer: 30
Step-by-step explanation:
Im pretty sure its that! Have a good day. Do not press the link for the other people its fake :)
Which of the following represents the area of a rectangle whose length is 3x + 5 and whose width is. x – 2?.
A.) 3x^2 + x – 10
B.) 3x^2 – 10
C.) 3x^2 – 11x – 10
D.) 3x^2 – x – 10
Answers
Area = l x w
Area = (3x+5)(x-2)
Area = 3x² - 6x + 5x - 10
Area = 3x² - x - 10
the correct answer is option D.
Determine whether the underlined numerical value is a parameter or a statistic. Explain your reasoning. for a certain movie 64.3% of the 112 members of the audience were females
Answers
Answer:
The given numerical value is a Parameter.
Step-by-step explanation:
Given - For a certain movie 64.3% of the 112 members of the audience were females.
To find - Determine whether the underlined numerical value is a parameter or a statistic.
Proof -
Given that, 64.3% of the 112 members of the audience were females.
Now,
64.3% of 112 = [tex]\frac{64.3}{100}*112[/tex] = 72.016
Since it is not a perfect number
And Human can not be in fraction
So,
The given numerical value is a Parameter.
It is 186 miles from Sergio's house to his parents' house.
Twice a year, he drives to visit them.
Then he drives home.
How many miles does he drive on the two round-trips?
ANSWER CHOICES-
372 miles
424 miles
724 miles
744 miles
Answers
Answer:
Step-by-step explanation:
He drives double the distance from his house to his parents house.
Answer:
answer: 744
Step-by-step explanation:
He drives 744 because 186 × 4 = 744 because its 186 to go there then 186 to go back then 186 to go there then 186 to go back so that adds up to 744 Hope that helps!