a. Parameterize C₁ by
[tex](x(t),y(t)) = (1-t)(-13,-7) + t(0,6) = (-13+13t,-7+13t)[/tex]
with 0 ≤ t ≤ 1. Then both dx = 13 dt and dy = 13 dt, so that the line integral along C₁ is
[tex]\displaystyle \int_C y^2\,dx + x\,dy = \int_0^1 (-7+13t)^2(13\, dt) + (-13+13t)(13\,dt)[/tex]
[tex]\displaystyle \int_C y^2\,dx + x\,dy = 13 \int_0^1 (169t^2 - 169t + 36) \, dt[/tex]
[tex]\displaystyle \int_C y^2\,dx + x\,dy = 13 \left(\frac{169}3-\frac{169}2+36\right) = \boxed{\frac{611}6}[/tex]
b. Parameterize C₂ by
[tex](x(t),y(t)) = (36-t^2,t)[/tex]
with -7 ≤ t ≤ 6. Then dx = -2t dt and dy = dt, so the line integral is
[tex]\displaystyle \int_C y^2\,dx + x\,dy = \int_{-7}^6 t^2(-2t\,dt) + (36-t^2)\,dt[/tex]
[tex]\displaystyle \int_C y^2\,dx + x\,dy = \int_{-7}^6 (36-t^2-2t^3) \, dt[/tex]
[tex]\displaystyle \int_C y^2\,dx + x\,dy = \left(36\cdot6-\frac{6^3}3-\frac{6^4}2\right) - \left(36\cdot(-7)-\frac{(-7)^3}3-\frac{(-7)^4}2\right) = \boxed{\frac{5005}6}[/tex]
Let C1 and C2 be two smooth parameterized curves that start at P0 and end at Q0 ≠ P0, but do not otherwise intersect. If the line integral of the function f(x, y, z) along C1 is equal to 43.1 and the line integral of f(x, y, z) along C2 is −15.9, what is the line integral around the closed loop formed by first following C1 from P0 to Q0, followed by the curve from Q0 to P0 along C2, but moving in the opposite direction? Incorrect: Your answer is incorrect.
We're given that
[tex]\displaystyle \int_{C_1} f(x,y,z) \,ds = 43.1[/tex]
and
[tex]\displaystyle \int_{C_2} f(x,y,z) \,ds = -15.9[/tex]
The closed loop formed by joining C₁ and C₂ is then C₁ U (-C₂), which is to say we follow C₁ normally, then traverse C₂ in the opposite direction. Then
[tex]\displaystyle \int_{C_1 \cup (-C_2)} f(x,y,z) \,ds = \int_{C_1} f(x,y,z) \,ds + \int_{-C_2} f(x,y,z) \,ds[/tex]
[tex]\displaystyle \int_{C_1 \cup (-C_2)} f(x,y,z) \,ds = \int_{C_1} f(x,y,z) \,ds - \int_{C_2} f(x,y,z) \,ds[/tex]
[tex]\displaystyle \int_{C_1 \cup (-C_2)} f(x,y,z) \,ds = 43.1 - (-15.9) = \boxed{59}[/tex]
geomtry plz help 10 points
Answer:
22.3<x<27.6
Step-by-step explanation:
X=greater than a number but less than another
22.3<27.6
Knowing that we can place 27.6 to the right of x and 22.3 to the left.
Hope this helps :)
Answer:
[tex]4.3<x<50.9[/tex]
Step-by-step explanation:
To find our Inequality sentence we have to add the largest number with the smaller much
[tex]27.6+23.3=50.9[/tex]
To find the second part of our inequality sentence we have to subtract the larger number from the smaller number
[tex]27.6-23.3=4.3[/tex]
Our inequality sentence is [tex]4.3<x<50.9[/tex]
Brainliest please
a toll box has 10 screw drivers and 6 wrenches Bella puts 8 more wrenches in the tool box how many more wrenches are in the toolbox
Write an equation perpendicular to x-4y=20 that passes through the point (2,-5)
Answer:
x – 4y = 20
Step-by-step explanation:
Put the line above in Slope Intercept Form
You can do that by solving for y
y = (1/4)x - 5
The slope, m above is 1/4
The perpendicular will a negative inverse slope m = -4
In Slope Intercept Form your perpendicular line starts below
y = -4x + b
Use the coordinates of the given point on the line (2, -5) to insert and solve for b
-5 = -4(2) + b
-5 = - 8 + b
Add 8 to both sides of the equation
-5 + 8 = b
3 = b
Finally your perpendicular line
y = -4x + 3
I hope this helps
Check my arithmetic
Answer:
×4y=20
Step-by-step explanation:
mark me as brainlist please
Suppose that you take 1000 simple random samples from a population and that, for each sample, you obtain a 95% confidence interval for an unknown parameter. Approximately how many of those confidence intervals will contain the value of the unknown parameter?
Using the interpretation of a confidence interval, it is found that approximately 950 of those confidence intervals will contain the value of the unknown parameter.
A x% confidence interval means that we are x% confident that the population mean is in the interval.
Out of a large number of intervals, approximately x% will contain the value of the unknown parameter.In this problem:
95% confidence interval.1000 samples.0.95 x 1000 = 950
Hence, approximately 950 of those confidence intervals will contain the value of the unknown parameter.
A similar problem is given at https://brainly.com/question/24303674
what is the change from 3 to -8?
Answer:
-11
Step-by-step explanation:
3 - 11 = -8
help pls :))))))))))))
Answer:
yes, the triangle are congruent by SAS
Latisha works x hours each day. Demetrius works 1 more hour each day than Latisha. Which expressions both calculate the number of hours Demetrius works in a 5-day work week? 5 x + 1 and 5 ( x + 1 ) 5 x plus 1 and 5 times open paren x plus 1 close paren ( x + 1 ) × 5 and 5 × x + 1 open paren x plus 1 close paren times 5 and 5 × x + 1 5 ( x + 1 ) and 5 x + 5 5 times open paren x plus 1 close paren and 5 x plus 5 ( x + 1 ) × 5 and 5 + ( x × 1 )
The number of hours worked by both Latisha and Demetrius is; 5x + 5(x+1)
According to the question:
We are required to generate an expression that can be used to calculate the number of hours used to work by Latisha and Demetrius.Since Latisha works x hours per day; In 5 days she works 5x hours.Demetrius works 1 more hour each day than Latisha; In 5 days; she must have worked; 5(x +1) hours.The sum of both of them gives; 5x + 5(x +1).
Read more:
https://brainly.com/question/16989990
which expression represents the product of 3 and 1 1/4 n 1.8
•ω• Hewo fren!
☆☆●◉✿ Answer:✿◉●☆☆
3•1 1/4•1.8= 6 3/4
☆☆●◉✿Step-by-step explanation:✿◉●☆☆
Let’s start of with 3•1 1/4~
3 times 1 and 1/4 is 3 3/4
Now let’s multiply 3 3/4 • 1.8
1.8 is also 1 8/10, simplified: 1 4/5.
3 3/4 • 1 4/5 = 6 3/4
THERE IS YOUR ANSWER! >o<
HOPE I HELPED! ∧∧
→⇒brainliest please? ∑(OΔO )♥♥︎
What is the slope of the line that passes through the points
(−5,−7) and (4,−1)? Write your answer in simplest form.
9514 1404 393
Answer:
2/3
Step-by-step explanation:
The slope is found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-1 -(-7))/(4 -(-5)) = 6/9 = 2/3
The slope of the line is 2/3.
_____
The attached graph shows the equation of the line in point-slope form.
Which value of x is a solution of the inequality?
3x−3≥9
Answer:
It's probably X since X doesn't have a written number for it it equals 1.
Step-by-step explanation:
25Y^2/5y-4 + 16/4-5y
Answer:
5Y2y-5y
Step-by-step explanation:
5
Y
2
y
−
5
y
f x and r are inversely proportional and x = 9 when r = 72, then what is x when r = 40?
Answer:
16.2
Step-by-step explanation:
r = k/x
when x = 9 and r = 72 ,72 = k/9
k = 72*9
When r = 40 ,
x = k/r
x = 72*9/40 = 16.2
Can someone please answer this question? Someone answered and they deleted their answer, so I need someone else to help me!
Please do not delete your answer, steal the points, or send links, I really need some help!
Check the picture below.
now, notice the triangles made, 3 right triangles with legs of 5 and 4 each.
looking at quadrilateral (1), from the leg 5 units long, we have a line with a run of -1 and a rise of 3, from the leg 4 units long, we have a line with a run of 4 and a rise of -1.
Now, quadrilaterals (2) and (4) display the same lengths and rise and runs, which means they're all congruent, quadrilateral (3) has no equal.
so 1 ≅ 2 and 1 ≅ 4.
A store has apples on sale for $3.00 for 2 pounds. If an apple is approximately 5 ounces, how many apples can you buy for $12.00? Complete the explanation
Answer:
you can buy 6 pounds of apples
Step-by-step explanation:
evaluate 6^2 - (9 divided by x) when x = 3
Answer:
33
Step-by-step explanation:
A partnership begins its first year with the following capital balances:
Alexander, Capital . . . . . . . . . . . . . . . . . . . . . . . . $ 90,000
Bertrand, Capital . . . . . . . . . . . . . . . . . . . . . . . . . 100,000
Coloma, Capital . . . . . . . . . . . . . . . . . . . . . . . . . . 160,000
The articles of partnership stipulate that profits and losses be assigned in the following manner:
∙ Each partner is allocated an interest equal to 5 percent of the beginning capital balance.
∙ Bertrand is allocated compensation of $45,000 per year.
∙ Any remaining profits and losses are allocated on a 3:3:4 basis, respectively.
∙ Each partner is allowed to withdraw up to $25,000 cash per year.
Assuming that the net income is $115,000 and that each partner withdraws the maximum amount
allowed, what is the balance in Coloma’s capital account at the end of the year?
a. $143,000
b. $135,000
c. $168,000
d. $164,000
Based on the information given the balance in Coloma’s capital account at the end of the year is: d. $164,000.
First step is to calculate the interest on capital for each partner
Alexander=$90,000×5%=$4,500
Bertrand=$100,000×5%=$5,000
Coloma=$160,000×5%=$8,000
Second step is to calculate Coloma capital and drawing
Coloma capital =$160,000 + (5% x $160,000)
Coloma capital=$160,000+ $8,000
Coloma capital=$168,000
Coloma drawing=$168,000-$25,000
Coloma drawing=$143,000
Third step is to calculate Coloma share of profit
Share of profit=$115,000-$45,000-$4,500-$5,000-$8,000
Share of profit=$52,500
Coloma profit=4/(3+3+4)×$52,500
Coloma profit=4/10×$52,500
Coloma profit=4/(3+3+4)×$52,500
Coloma profit=$21,000
Fourth step is to calculate balance in Coloma’s capital account
Coloma’s capital account balance=$143,000+$21,000
Coloma’s capital account balance=$164,000
Inconclusion the balance in Coloma’s capital account at the end of the year is: d. $164,000.
Learn more here:https://brainly.com/question/21270829
5.You are driving at a constant speed of 20 m/s when you suddenly hit a patch large oil slick. You slam on the brakes and eventually skid to a complete stop. The skid marks are 40 meters long. Calculate the coefficient of kinetic friction between the oil-covered road
and the car tires.
The coefficient of kinetic friction between the oil-covered road
and the car tires. is 0.51
To solve this question, we would consider one of the equations of motion.
v² = u² + 2as, where
v = final velocity, which is also equal to 0
u = initial velocity, which is 20m/s
s = skid marks, which is 40 meters long
a = acceleration, which is unknown
0² = 20² + 2*a*40
0 = 400 + 80a
80a = -400
a = -400/80
a = -5 m/s
Also, it is known that acceleration a = (mu)g, where mu is the coefficient of kinetic friction and g is the acceleration due to gravity.
-5 = mu * 9.8
mu = -5/9.8
mu = 0.51
learn more about equations of motion here https://brainly.com/question/16878713
y-3=1/2(x-7)
PLS HELP ME OUT GUYS
Answer:
X = -1
Step-by-step explanation:
y - 3 = 1/2 (x - 7)
x would equal -1.
The graph of the linear function is shown on the coordinate grid. What is the equation of this line?
Answer:
we know that it is 0.6 km
so we convert into meters
and then get 600 m
Hope that helps
Answer:
ok thank u ig
Step-by-step explanation:
determine the slope and y intercept and write the equation in slope intercept form
Answer: slope is 2 and the y-intercept is 1 intercept form is y=2x+1
Step-by-step explanation:
Hey help please math I need help good luck I’ll I’ve point
Answer:
180 degrees
Step-by-step explanation:
180 degrees would flip the triangle halfway through a full circle. B is A upside down rotated halfway through a full circle.
Jasmine wants to make more cleaning solution
Answer:
here
Step-by-step explanation:
Method 1 Method 1 of 3: Making Liquid Cleaners
Mix equal parts water and vinegar in a spray bottle. Use distilled white vinegar and, if possible, distilled or filtered water.
Add lemon juice to disinfect surfaces. Mix one part lemon juice, one part white vinegar and two parts water in a spray bottle.
Add dish soap for persistent stains on carpet. ...
Tackle tough stains and grime with undiluted vinegar. ...
how is 7 square root 2 is equal to 49?
Answer:
Square root is how many times your multiply the number by itself. So 7 square root 2 is 7x7 which is 49.
30 liters in 2 minutes = liters per minute
Answer:
0.06 would be the answer.
Step-by-step explanation:
Answer:
15 liters per minute
Step-by-step explanation:
30/2=15
Write two numbers that multiply to −33 and add to 8
Answer:
-3 and 11
Step-by-step explanation:
I need help with this problem no where on Brainly
Answer:
blue graph
Step-by-step explanation:
that graph looks similar to e^x
so f(-x) will be similar to e^-x
so it will be a reflection over y axis
see the picture below
Pre college need help
Answer:
C
Step-by-step explanation:
What is the position of B on the number line below?
Write your answer as a fraction or mixed number
Step-by-step explanation:
B = 1 4/5
because 1 is completely to the left, and from the distance between 1 and 2 B is at the end of the 4th of 5 sub-segments.
and 1 4/5 would be also 9/5, because B includes the 5 sub-segments (of 5) between 0 and 1. and then the 4 of 5 sub-segments between 1 and 2. so that are 9 sub-segments in total.
and each sub-segment represents 1 out of 5 (= 1/5) parts of each number interval.
therefore, we have 9×1/5 = 9/5.