This question is missing some parts. Here is the complete question.
Consider the oriented path which is a straight line segment L running from (0,0) to (16,16).
(a) Calculate the line inetrgal of the vector field F = (3x-y)i + xj along line L using the parameterization B(t) = (2t,2t), 0 ≤ t ≤ 8.
Enter an exact answer.
[tex]\int\limits_L {F} .\, dr =[/tex]
(b) Consider the line integral of the vector field F = (3x-y)i + xj along L using the parameterization C(t) = [tex](\frac{t^{2}-256}{48} ,\frac{t^{2}-256}{48} )[/tex], 16 ≤ t ≤ 32.
The line integral calculated in (a) is ____________ the line integral of the parameterization given in (b).
Answer: (a) [tex]\int\limits_L {F} .\, dr =[/tex] 384
(b) the same as
Step-by-step explanation: Line Integral is the integral of a function along a curve. It has many applications in Engineering and Physics.
It is calculated as the following:
[tex]\int\limits_C {F}. \, dr = \int\limits^a_b {F(r(t)) . r'(t)} \, dt[/tex]
in which (.) is the dot product and r(t) is the given line.
In this question:
(a) F = (3x-y)i + xj
r(t) = B(t) = (2t,2t)
interval [0,8] are the limits of the integral
To calculate the line integral, first substitute the values of x and y for 2t and 2t, respectively or
F(B(t)) = 3(2t)-2ti + 2tj
F(B(t)) = 4ti + 2tj
Second, first derivative of B(t):
B'(t) = (2,2)
Then, dot product between F(B(t)) and B'(t):
F(B(t))·B'(t) = 4t(2) + 8t(2)
F(B(t))·B'(t) = 12t
Now, line integral will be:
[tex]\int\limits_C {F}. \, dr = \int\limits^8_0 {12t} \, dt[/tex]
[tex]\int\limits_L {F}. \, dr = 6t^{2}[/tex]
[tex]\int\limits_L {F.} \, dr = 6(8)^{2} - 0[/tex]
[tex]\int\limits_L {F}. \, dr = 384[/tex]
Line integral for the conditions in (a) is 384
(b) same function but parameterization is C(t) = [tex](\frac{t^{2}-256}{48}, \frac{t^{2}-256}{48} )[/tex]:
F(C(t)) = [tex]\frac{t^{2}-256}{16}-\frac{t^{2}-256}{48}i+ \frac{t^{2}-256}{48}j[/tex]
F(C(t)) = [tex]\frac{2t^{2}-512}{48}i+ \frac{t^{2}-256}{48} j[/tex]
C'(t) = [tex](\frac{t}{24}, \frac{t}{24} )[/tex]
[tex]\int\limits_L {F}. \, dr = \int\limits {(\frac{t}{24})(\frac{2t^{2}-512}{48})+ (\frac{t}{24} )(\frac{t^{2}-256}{48}) } \, dt[/tex]
[tex]\int\limits_L {F} .\, dr = \int\limits^a_b {\frac{t^{3}}{384}- \frac{768t}{1152} } \, dt[/tex]
[tex]\int\limits_L {F}. \, dr = \frac{t^{4}}{1536} - \frac{768t^{2}}{2304}[/tex]
Limits are 16 and 32, so line integral will be:
[tex]\int\limits_L {F} \, dr = 384[/tex]
With the same function but different parameterization, line integral is the same.
how many $10 bills are equal to a $1000 bill?
100 ten dollar bills are equal to 1000.If you divide 1000 by 10 you get 100.
How many $10 bills are equal to a $1000 bill?$10 × $100 = $1,000 .The answer is a hundred 1 ten five cents.S: 10, 20, 30, 40, 50, 60, 70, 80, 81, 82, 83, 84, 85.The $1,000 banknote is still recognised as legal tender despite having been phased out for more than 50 years. This implies that any $1,000 banknote you come across is worth at least its face value, or $1,000. $10 and $20 bills can be obtained through Citibank, Capital One, Bank of America, Chase, and PNC.1,000 is 10 hundreds.To learn more about $10 bills refer
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In the number 37,278, how many times greater is the 7 in the thousand place
Answer:
100
Step-by-step explanation:
7000 to 70
7000/70 = 100
a room contains 156.1m of air . if the room is 8.31m long and 5.72m wide . use tabe to calculate it height
Answer:
height=3.28m
Step-by-step explanation:
air means volume of room
let the height of room be x.
so, volume of room= 156.1 m³
8.31*5.72*x=156.1m³
x =3.28m
Please help me, thank you!
Answer:
10*g-4
Step-by-step explanation:
By the way * is multiplicaton
I need help with the three of them with a step by step example please
Answer:
4
Step-by-step explanation:
Help me please i need this now
Giving extra points
Correct answer
Answer:
Step-by-step explanation:
(A) and (B)
If zeina has seven times as many books as ali if zeina gave ali 15 books they would eash have the same number of books how many books did each have
Answer:
Zeina had 35 books and Ali had 5 books
Step-by-step explanation:
Equations
We know Zeina has seven times as many books as Ali. If we call
x = Number of books Ali has
Then Zeina has
7x = Number of books Zeina has
We also know if Zeina gave Ali 15 books, they would have the same number of books, thus:
x + 15 = 7x - 15
Adding 15:
x + 15 +15 = 7x
Subtracting x:
15 +15 = 7x - x
Operating:
30 = 6x
Dividing by 6:
x = 30 / 6
x =5
7x = 35
Thus Zeina had 35 books and Ali had 5 books
Given are the functions f(x) = x ^ 2 and g(x) = (x - 2) ^ 2 + 1 How can the graph of g(x) be obtained from the graph of f(x) ?
Answer:
c because it's the opposite
Please show me the steps to solve this problem
This is a pre-algebra problem. I'll go through the steps with you. If you don't get it, don't be afraid to ask!
Step One - Cross Multiply
These are fractions, but that doesn't mean you have to add them. Fractions are just the numerator divided by the denominator. So to 'remove' the 9, multiply both sides by 9. To 'remove' the 6, multiply both sides by 6. (We multiply both sides of the equation by the same number because we need to make each side the same). Note that when you multiply both sides by 9 or 6, you have to multiply the whole part.
(2x+1)×6 = (1-1)×9
Distribute.
12x+6 = 9-9
Step Two - Solve the Equation
So we are left with this equation after cross multiplying:
12x+6 = 9-9
First, we can start by subtracting 9 from 9, because those are the same types of numbers.
12x+6 = 0
Now, we have to 'remove' the 6. We can do that by subtracting each side by 6.
(12x+6)-6 = 0-6
12x = -6
Now we are left this this.
We need to 'remove' the 12 now, so we can isolate the x. Since 12 is multiplied to x, we divide each side by 12.
(12x)÷12 = -6÷12
We get x = -1/2
x = -1/2 or -0.5
Hope this helped!
A pipe is 24 feet long. It needs to be cut into pieces that are each 3/4 feet long. How many pieces can be made from the pipe?
Which shows two possible values for a number represented by the point?
0
1
7 and 3
AN
27 and 1
2
2 and 2
O 2 and 2
Answer:
b
Step-by-step explanation:
Drag each number to the correct location on the table. Not all numbers will be used.
Jacob performed an experiment with a weighted die, numbered 1 to 6. He rolled the die 125 times and recorded the results. Complete the table below.
24
22
0.176
18
0.232
37
0.048
0.104
Answer:
Complete Table:
Result of Roll ------ Frequency ------- Experimental Probability
1 --------------------------- 22 ------------------- 0.176
2 --------------------------- 13 ------------------- 0.104
3 --------------------------- 18 ------------------- 0.144
4 --------------------------- 29 ------------------- 0.232
5 --------------------------- 37 ------------------- 0.296
6 --------------------------- 6 ------------------- 0.048
Step-by-step explanation:
Required: Complete the table
The table is divided into 3:
1. Result of Roll
2. Frequency (F)
3. Experimental Probability (P)
The relationship between (2) and (3) is:
[tex]P = \frac{F}{N}[/tex]
Where
N = Number of Rolls
N = 125
For Roll of Result = 2
Frequency = 13
The probability is calculated as thus:
[tex]P = \frac{13}{125}[/tex]
[tex]P = 0.104[/tex]
For Roll of Result = 3
Probability = 0.144
The Frequency is calculated as thus:
[tex]0.144 = \frac{F}{125}[/tex]
[tex]F = 0.144 * 125[/tex]
[tex]F = 18[/tex]
For Roll of Result = 4
Frequency = 29
The probability is calculated as thus:
[tex]P = \frac{29}{125}[/tex]
[tex]P = 0.232[/tex]
For Roll of Result = 5
Probability = 0.296
The Frequency is calculated as thus:
[tex]0.296 = \frac{F}{125}[/tex]
[tex]F = 0.296* 125[/tex]
[tex]F = 37[/tex]
For Roll of Result = 6
Frequency = 6
The probability is calculated as thus:
[tex]P = \frac{6}{125}[/tex]
[tex]P = 0.048[/tex]
For Roll of Result = 1.
To get the frequency; we subtract the sum of frequencies of roll of results 2 to 6 from the total number of rolls.
In other words:
Frequency of 1 = Total Rolls - (Frequency of 2 + Frequency of 3 + Frequency of 4 + Frequency of 5 + Frequency of 6)
Frequency of 1 = 125 - (13 + 18 + 29 + 37 +6)
Frequency of 1 = 125 - 103
Frequency of 1 = 22
The probability is calculated as thus:
[tex]P = \frac{F}{N}[/tex]
[tex]P = \frac{22}{125}[/tex]
[tex]P = 0.176[/tex]
What is the solution for the system of equations that has a sum of 1 and
differece of 9?
Answer 9
Step-by-step explanation:
Need help asap i hate these type of questions but i know it isnt to hard
Answer:
A,C,D are correct
Kennedy has 8 feet of ribbon. She wants to cut the ribbon into smaller pieces to make bows, but first she needs to figure out how many inches of ribbon she has. Kennedy knows 12 inches = 1 foot. How many inches of ribbon does she have?
Answer:
She has 96 inches of ribbon.
Step-by-step explanation:
12 times 8 = 96.
Answer:
so 12 inches = 1 foot
she has 8 feet so,
let x be the amount of ribbon she has
12*8=x
Step-by-step explanation:
12*8=96
she has 96 inches of ribbon
Zoe is starting her own snow plowing business. Zoe has calculated that she needs to earn $550 per week to support her family. If she knows she will only be able to work 40 hours per week, what is the minimum amount of dollars per hour that she will need to charge her customers?
What is -(3x - 12) = 9 x -4
Answer:
X = 1.3
Step-by-step explanation:
What strategies do you use to make a ratio table?
Is finding the value for the variable the only solution to real-world problems? Explain.
Answer:
The answer is "No. In many real-world scenarios, the variable is a value that is compared to other quantities. The value for the variable is used to find the quantities it is compared to".
Step-by-step explanation:
I WILL GIVE BRAINIEST Enter the data to create a histogram and use the drop-down menus to complete the statements.
The scale on the graph is ?
The interval with the highest frequency is ?
Answer:
1. 0-7
2. 2-3
Step-by-step explanation:
got it right on edgu.
Answer:
The scale on the graph is
✔ 0–7
.
The interval with the highest frequency is
✔ 2–3
.
Step-by-step explanation:
15 rounded to the nearest hundredth
Step-by-step explanation:
ummmmmmmm how does that work
Help me out hereeeeeeeeeee
Answer:
The gravitational attraction between them would decrease.
Select whether the function is discrete or continuous.
Function: The number of basketballs manufactured per day
Answer:
Continuous
Step-by-step explanation:
The library is to be given 7 books as a gift. The books will be selected from a list of 15 titles. If each book selected must have a different title, how many possible selections are there?
can earn coins
Pedro is making a graph to represent how each chocolate purchased costs $3. Pedro says that the line
will pass through the origin (0,0) because if you buy o chocolates, it will cost 0 dollars. Does Pedro's logic
make sense?
Answer:
No Pedro's logic does not make any sense
Step-by-step explanation:
It depends on how it is graph.
PLZ HURRY I WILL GIVE BRAINLIEST (50 points)
A person weighs a different amount on other surfaces in space than they do on Earth because the gravitational pull of each surface is different than that of Earth. The table and graph show the weights of objects on Earth, Mars, and the Moon.
Weight on Earth and Mars
Weight on Earth, e
90 pounds
120 pounds
160 pounds
Weight on Mars, a
36 pounds
48 pounds
64 pounds
Weight on Earth and Moon
A graph has weight on earth (pounds) on the x-axis, and weight on moon (pounds) on the y-axis. A line goes through points (60, 10) and (120, 20).
If a person weighs 240 pounds on Earth, what would be the difference in weight of the same person on Mars and on the Moon (based on the table and graph)?
The person weighs 56 pounds more on Mars than on the Moon.
The person weighs 56 pounds more on the Moon than on Mars.
The person weighs 560 pounds more on Mars than on the Moon.
The person weighs 560 pounds more on the Moon than on Mars.
this is on edge2020
Answer:
The answer is A The person weighs 56 pounds more on Mars than on the Moon.
Step-by-step explanation:
Answer:
the first answer
Step-by-step explanation:
did it on edge
(GIVING BRAINLIEST!!)
Two magnets push away from each other and do not attract. What do we know to be true and what type of force is being demonstrated? Write 2 or more sentences to support your answer :)
Answer: it could be a mangintic force.. Because if two magnets a.k.a the north and south pole magnets are brought together they will push each other away instead of sticking.
Hope this helps
Answer:
They are repeling because they are both negitively charged
Step-by-step explanation:
please mark brainelist
(4c + 7) + (8c + 8)
(adding and subtracting polynomials)
Answer:
12c + 15
Step-by-step explanation:
Combine like terms
Which statement describes the congruent triangles?
∆WXZ=∆YZX
∆WXZ=∆YXZ
∆WXZ=∆XYZ
∆WXZ=∆ZYX
Answer:
A) WXZ=YZX
Step-by-step explanation:
WXZ=YZK
The straight line L has equation y = 2x - 5
Find an equation of the straight line perpendicular to L which passes through (-2, 3).
Answer:
slope of perpendicular line - m = -1/2
passing through (-2,3)
thus,
y-3 = -1/2 (x+2)
or y = -1/2x +2
An equation of the straight line perpendicular to [tex]\boldsymbol{y=2x-5}[/tex] which passes through [tex]\boldsymbol{(-2,3)}[/tex] is [tex]\boldsymbol{x+2y-4=0}[/tex]
An equation of a straight line is [tex]\boldsymbol{y=2x-5}[/tex]
Compare this equation with the form [tex]\boldsymbol{y=mx+b}[/tex] where [tex]\boldsymbol{m,b}[/tex] denote slope and [tex]\boldsymbol{y-}[/tex]intercept respectively.
So,
[tex]\boldsymbol{m=2}[/tex]
As the slopes of two perpendicular lines are negative reciprocals of each other, slope of a required line is equal to [tex]n=\frac{-1}{2}[/tex]
Take [tex](x_1,y_1)=(-2,3)[/tex]
Equation of the required line is [tex]\boldsymbol{y-y_1=n(x-x_1)}[/tex]
[tex]y-3=\frac{-1}{2}(x+2)[/tex]
[tex]2y-6=-1(x+2)[/tex]
[tex]x+2y-4=0[/tex]
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