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]
Which of the following is the graph of f(x) = |x|?
Graph 1
Graph 2
Graph 3
Graph 4
Answer:
i think its the second graph
Step-by-step explanation:
A recipe for pasta dough says, “Use 150 grams of flour per large egg.”
How much flour is needed if 6 large eggs are used?
How many eggs are needed if 450 grams of flour are used?
Answer:
1. 900 grams
2. 3 eggs
Step-by-step explanation:
1. 150 x 6 = 900
2. 450 / 150 = 3
Answer:
900 grams of flour are needed if six eggs are used. 3 eggs are needed if 450 grams of flour are used.
Step-by-step explanation:
First, multiply the number of large eggs by grams per large egg: 150×6=900
Next, divide the number of grams of flour by grams per large egg: 450/150=3
Mike burns 392 calories when he walks 4 miles how many calories does he burn when he walks 1 mile?
Answer:
Step-by-step explanation:
If mike burns 392 calories when he walks 4 miles then we just need to divide
/ =
Mike burns 98 calories when he walks 1 mile.
What is unitary method?"It is a method of finding the value of a single unit and based on that value, we can find the required value."
For given example,
Mike burns 392 calories when he walks 4 miles.
This means, 4 miles = 392 calories
By using unitary method we find the number of calories he burns when he walks 1 mile.
4 miles = 392 calories
So, 1 mile = 392/4 calories
1 mile = 98 calories
Therefore, Mike burns 98 calories when he walks 1 mile.
Learn more about the unitary method here:
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I NEED HELP PLSSSSSS
Answer:
130 is the answer I Think
Kenrick mows lawns on Sundays. Last
week it took him 5 hours to finish.
This week it took only 5 hours. How
many times longer did it take last
week than this week?
Answer:
0 hours.
Step-by-step explanation:
He finished at the same time than Kenrick finished last week. So, he/she did not delay in mowing the lawn. Hoped this helped.
Find the domain of the function
Answer:
Here you go :)
Step-by-step explanation:
solve pls brainliest
Answer:
for the first one it 2
3
12
Mr. Morton sold
bird houses to stores he started the week with 60 he sold 10 to one store and divided the rest between five other stores how many bird houses he’s so to each of the other five stores
Answer:
10
Step-by-step explanation:
b. A square has an area of 9 cm2 what is its side length?
Answer:
81 cm
Step-by-step explanation:
A square is equal an all sides so 9cm to the second power is 81 cm
SOmeone help me i'm stuck on thia question
Answer:
17
Step-by-step explanation:
...........................
Answer:
i think its c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
because -100,-57/8,6
the absolute value of -6 is 6 and
-8 7/8 is 8×(-8)+7=-64+7/8=-57/8 because when negative plus positive we subtract and we take the sign of the larger number
Are the following polynomial sets open or closed? 6. (x ^ 2 + x - 4) - (x ^ 2 + x + 8) 7 (2 - x)(1 + 3x) 8. (5b - 3c)(7b - 3c)
Answer:
=5880b2x4−6048bcx4+1512c2x4−3920b2x3+4032bcx3−1008c2x3+33320b2x2−34272bcx2+8568c2x2−82320b2x+84672bcx−21168c2x−31360b2+32256bc−8064c2+6x2+6x−24
Step-by-step explanation:
Calculations with Percent - Item 35698
Question 7
Asha bought 60 fruit baskets.
25% of the fruit baskets have 12 pieces of fruit in each basket.
The remaining 75% of the baskets have 15 pieces of fruits in each basket.
Complete the model.
25%
75%
Number of baskets with 12 piece of
fruit:
Number of baskets with 15 pieces of fruit:
60 fruit baskets
The number of baskets with 12 piece of fruit is 15.
The number of baskets with 15 pieces of fruit is 45.
Percentage is the fraction out of a number expressed as a number out of hundred. The sign used to represent percentages is %.
In order to determine the number of baskets that have 12 pieces of fruits and 15 pieces of fruits, multiply the given percentages by the total number of fruit baskets.
Number of baskets with 12 piece of fruit: 25% x 60 = 0.25 x 60 = 15
Number of baskets with 15 pieces of fruit: 75% x 60 = 0.75 x 60 = 45
To learn more about percentages, please check: https://brainly.com/question/92258
Find the equation for the linear function based upon this table. y = mx + b
y -6 -2 2 6 10
x -4 -2 0 2 4
Answer:
y = 2x + 2
Step-by-step explanation:
for each rise of 4 in y
there is a run of 2 in x
m = rise/run
m = 4/2
m = 2
when x = 0, y = 2
therefor the y-intercept, b = 2
y = mx + b
y = 2x + 2
A department store marked down all of its summer clothing 23%. The following week the remaining items were marked down again
15% off the sale price. When Jorge bought two tank tops on sale, he presented a coupon that gave him an additional 20% off. What
percent of the original price did Jorge save?
Answer:
58%
Step-by-step explanation:
An office manager has 10,000$ to spend on new equipment
300 divided by 72 equals (300 divided by 7) + (300 divided by 2) = 2,100 + 600 = 2,700
Please Help! it's simple!
Answer:
28.27
circumference of finding a circle divided by two.
[tex](2\pi \:r {}^{2} ) \div 2[/tex]
(2×3.14×9)/2
56.55/2
28.27
Need help with this quick plz??
Answer:10 or someones else’s answer this not my best
Step-by-step explanation:
PLEASE SHOW YOUR WORK!!!
Solve for y: 3^3 + 14 y- (25y - 13) = y + 7y - 9y
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3^3+14*y-(25*y-13)-(y+7*y-9*y)=0
Equation at the end of step 1
((3³ + 14y) - (25y - 13)) - -y = 0
Pull out like factors :
40 - 10y = -10 • (y - 4)
Equation at the end of step3:
-10 • (y - 4) = 0
STEP4:
Equations which are never true:
Solve : -10 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
Solve : y-4 = 0
Add 4 to both sides of the equation :
y = 4
[tex]y = 4[/tex]How many equal parts are there in this image
Answer:
6
It's kind of blury, so I can't really see it.
Answer:
4
Step-by-step explanation:
If Noah has 527,300,000 and Margho has 106,570,000. How much do they have in all?
Can someone help me pls?
Answer:
633,870,000
Step-by-step explanation:
Add it together either on a calculator of a sheet of paper.
draw a diagram for this fraction
7/2
Answer:
You can't draw a diagram for a improper
fraction
5) Which has more people? A car that is
full or a car that is full?
Answer:
a car that is full
Step-by-step explanation:
Answer:
mm definitely a car that is full
Step-by-step explanation:
Please help me
The variables x and y are proportional. Use the values to find the constant of proportionality. Then write an equation that relates x and y. Write any fractions in the simplest form.
When y=45 , x=40 .
y=kx
20=k(12)
k= 20/12 = 5/3
y= (5/3)x
y = 5x/3 or
3y=5x
The sum of two numbers is eight one number is four less than the other find the numbers
Step-by-step explanation:
the numbers : x, y
x + y = 8
x = y - 4
we use the second equation in the first :
y - 4 + y = 8
2y - 4 = 8
2y = 12
y = 6
x = y - 4 = 6 - 4 = 2
Answer: The answer is 6 and 2
Step-by-step explanation:
X is first number, Y is second
x + x - 4 = 8
2x = 12
x = 6
Y = x - 4
Y = 6 - 4
Y = 2
x = 6
Y = 2
Catering the concord theater serves punch during intermission. If each of 200 people think 1 c of punch, how many gallons of punch should be prepared?
please help and show me the answer thank you
Answer:
they will need 2 gallons of punch
Describe an example in which two variables are strongly correlated, but changes in one do not cause changes in the other.
Just because 2 things are related doesn't mean they will both be changed when one thing happens. For example steak and candy, just because they are both food doesn't mean they taste the same or interact with each other.
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 45% salt and Solution B is
95% salt. She wants to obtain 60 ounces of a mixture that is 85% salt. How many ounces of each solution should she use?
we know A is 45% salt, so the amount of salt in A is (45/100)*A or 0.45A.
likewise we know that B is 95% salt, so the salt amount in it is (95/100)*B or 0.95B.
[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{oz of }}{amount}\\ \cline{2-4}&\\ A&x&0.45&0.45x\\ B&y&0.95&0.95y\\ \cline{2-4}&\\ mixture&60&0.85&51 \end{array}~\hfill \begin{cases} x+y=60\\ 0.45x+0.95y=51\\[-0.5em] \hrulefill\\ y = 60 -x \end{cases}[/tex]
[tex]\stackrel{\textit{substituting on the 2nd equation}}{0.45x+0.95(60-x) = 51}\implies 0.45x+57-0.95x=51 \\\\\\ 0.45x-0.95x=-6\implies -0.5x=-6\implies x = \cfrac{-6}{-0.5} \\\\\\ \boxed{x = 12}~\hfill \stackrel{\textit{we know that}}{y = 60 -x}\implies \boxed{y=48}[/tex]
According to this diagram, what is sin 23°?
67°
13
5
Сл
23°
90°
12
O A.
13
5
12
O B.
B. 13
12
13
O c.
c.13
O D.
D.
5
13
O E.
13
12
5
OF.
Using relations in a right triangle, it is found that the sine of 23 degrees is given by:
D. 5/13.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.Looking at the graph, the side opposite to the angle of 23º is of 5, while the hypotenuse is of 13, hence the sine is given by:
sin(23º) = 5/13.
Which means that option D is correct.
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Barack is saving up his money to buy a television that costs $395.50. Right now he has $85.00 and can save $29.00 each week. How many weeks will it take for Barack to have enough money to buy the television?
Answer:
11 weeks
Step-by-step explanation:
Its easy
