Answers
Applying the steps, the result of the line integral is 99.
The curve is:
[tex]f(x,y,z) = xy i + 9y^2 j[/tex]
The vector field is:
[tex]r(t) = (x(t), y(t)) = (16t^6, t^4)[/tex]
Applying the vector field at the curve, we have that:
[tex]f(t) = (16t^{10}, 9t^8)[/tex]
The derivative of the vector field is:
[tex]r^{\prime}(t) = (96t^5, 4t^3)[/tex]
The dot product of the vector field along the curve with the derivative is:
[tex]f(t)r^{\prime}(t) = (16t^{10}, 9t^8)(96t^5, 4t^3) = 1536t^{15} + 36t^{11}[/tex]
Hence, the line integral is:
[tex]I = \int_{0}^{1} (1536t^{15} + 36t^{11}) dt[/tex]
[tex]I = 96t^{16} + 3t^{12}|_{t = 0}^{t = 1}[/tex]
[tex]I = 96 + 3[/tex]
[tex]I = 99[/tex]
A similar problem is given at https://brainly.com/question/12666512
Related Questions
Can you help me with this ?:)
With explanation step-step Thanks
Answers
Part A
The given angle is 4pi/3. Multiply it by the factor 180/pi to convert from radians to degree mode.
Note how the given angle has pi in the numerator, while the conversion factor has pi in the denominator. The two pi terms will cancel.
(4pi/3)*(180/pi)
(4/3)*(180/1)
(4*180)/(3*1)
720/3
240
The angle 4pi/3 radians is equivalent to 240 degrees. This 240 degree angle is in quadrant 3. Any angle in this quadrant is between 180 degrees and 270 degrees, excluding both endpoints. This is the bottom left quadrant, aka the southwest quadrant.
Answer: Quadrant 3===========================================================
Part B
To find the reference angle, we'll subtract off pi. This only works for angles in quadrant 3. This is because the first pi radians, aka 180 degrees, is taken up by the first two upper quadrants. The remaining bit in the third quadrant is all we care about to find the reference angle.
reference angle = (given angle in quadrant 3) - pi
reference angle = (4pi/3) - pi
reference angle = (4pi/3) - (3pi/3)
reference angle = (4pi - 3pi)/3
reference angle = pi/3
Answer: pi/3 radians===========================================================
Part C
Use a calculator or a reference table to find that
tan(4pi/3) = tan(pi/3) = sqrt(3)
Alternatively, you can compute the sine and cosine values first
sin(pi/3) = sqrt(3)/2cos(pi/3) = 1/2Dividing the two items in the order mentioned will get us the tangent value
tan = sin/cos
tan(pi/3) = sin(pi/3) divide cos(pi/3)
tan(pi/3) = sqrt(3)/2 divide 1/2
tan(pi/3) = sqrt(3)
In the jump from the second to last step, to the last step, the denominators '2' cancel out when dividing.
Answer: sqrt(3)
There are 10 circles and 2 triangles. What is the
simplest ratio of triangle to circle
Answers
5 being the circles, 1 being the triangles
Answer:
1:5
Step-by-step explanation:
put no. of triangles over no. circles because it asks triangles to circles
2/10
1/5........simplify
Which one is the correct answer ? Find the amplitude , period. Phase shift asymptotes domain range Use the fact that cos(x)=0 will be an asymptote
Answers
Answer:
3. is your correct answer ok
Han earns $33.00 for babysitting 4 hours. At this rate, how much will he earn if he babysits for 1 hour?
Answers
Answer: $8.25
Step-by-step explanation: 33 divided by 4 (find unit rate)
Answer: $8.25
Step-by-step explanation:
Simply divide $33.00 by 4. 33/4 = 8.25
A certain star has a luminosity that is 5.9 times greater than that of our sun and a radius that is 2.8 times greater than the sun. What is the temperature of this star relative to the sun?
Answers
Answer:
16.5
Step-by-step explanation:
times the numberthen u will get your answer
HIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
Answers
Answer:
The x-intercept is a point on the x-axis where the line crosses the x-axis and you can easily find it at point (-7, 0) because the line crosses the x-axis there.
Similarly, the y-intercept is a point on the y-axis where the line crosses the y-axis and you can easily find it at point (0, 2) because the line crosses the y-axis there.
Please solve these algebraic questions? THANKS
Answers
Step-by-step explanation:
Note: I'm only providing solutions for Problem 9.
9. Simplify the following by collecting like terms:
Combining like terms involve performing the required mathematical operations (using the PEMDAS rule). The terms must have the same degree (or exponents).
a) 3a + 7a
Add the coefficients of both terms.
3a + 7a = 10a
b) 4n + 3nAdd the coefficients of both terms.
4n + 3n = 7n
c) 12y - 4ySubtract the coefficient of both terms.
12y - 4y = 8y
d) 5x + 2x + 4xAdd the coefficients of all terms.
5x + 2x + 4x = 11x
e) 6ab - 2ab - baThe last term, "ba," can be rewritten as, "ab." Remember that with algebraic expressions such as "ab," it essentially involves multiplication of both variables within the same term. Thus, ab = a × b. The variables ab also have a numerical coefficient of 1: 1a × 1b.
Now, we can perform the subtraction on all terms:
6ab - 2ab - ab = 3ab.
f) 7mn + 2mn - 2mnSubtract 2mn from 2mn, which leaves you with 7mn:
7mn + 2mn - 2mn = 7mn
g) 4y - 3y + 8For this algebraic expression, you could only combine the terms with the same variable and degree. Therefore, you'll have to subtract 3y from 4y, leaving the constant, 8, unaffected.
4y - 3y + 8 = y + 8
h) 7x + 5 - 4x
Similar to question g, only combine the terms with the same degree and variable, leaving the constant unaffected.
7x + 5 - 4x = 3x + 5
i) 6xy + xy + 4y
You could only combine the terms with the same set of variables and degree, which are the first two terms on this given question. You cannot combine the last term, 4y, into the other terms.
6xy + xy + 4y = 7xy + 4y
j) 5ab + 3 + 7ba
Using the same reasoning as in question e: the last term, 7ba, can be rewritten as 7ab, for which you could combine with the first term, 5ab.
5ab + 3 + 7ba = 12ab + 3
k) 2 - 5m - mCombine the like terms, which are the second and the last term.
2 - 5m - m = 2 - 6m
l) 4 - 2x + x
Combine the like terms, which are the second and the last term.
4 - 2x + x = 4 - x
An elliptically shaped garden is surrounded by a wood walkway. The garden is 15 meters long and 8 meters wide. The walkway is 2.5 meters wide. Find the standard equation describing the ellipse formed by the walkway.
Answers
Answer:
x^2/b^2 + y^2/a^a = 1
Step-by-step explanation:
I believe that is the answer, also theanswerme answered this question. :)
if line 1 has a slope of -4 and line 2 has a slope of 1/4, they are parallel
True
O False
Answers
The lines have different slopes
It is false.
Find the area of grass
Answers
Answer:
125m²Step-by-step explanation:
find the area of the green rectangle and remove the area of the yellow rectangle
(12 - 2) * (16 - 2) - (6 * 2.5) =
10 * 14 - 15 =
140 - 15 = 125m²
ok. 4. 62 decreased by 2 7 co 8 anolo 5. 14 increased by 14
Answers
Answer: Arachidonic acid (AA, sometimes ARA) is a polyunsaturated omega-6 fatty acid 20:4(ω-6), or 20:4(5,8,11,14).
Step-by-step explanation: It is structurally related to the saturated arachidic acid found in cupuaçu butter.[3] Its name derives from the New Latin word arachis (peanut), but it is important to note that peanut oil does not contain any arachidonic acid.[4]
Guided Practice
Write the equation of the parabola in vertex form. The vertex is (3, 2) and the parabola passes through the point (0, 38). Create a rough sketch of the graph to use as a visual aid.
A.
y = 4(x + 3)2 + 2
B.
y = (x + 3)2 + 2
C.
y = 19(x − 2)2 + 3
D.
y = 4(x − 3)2 + 2
Answers
Answer:
D.
y = 4(x − 3)^2 + 2
Step-by-step explanation:
A. y = 4(x + 3)^2 + 2 = ( − 3 , 2 )
B. y = (x + 3)^2 + 2 = ( − 3 , 2 )
C. y = 19(x − 2)^2 + 3 = ( 2 , 3 )
D. y = 4(x − 3)^2 + 2 = ( 3 , 2 )
3^12*(2^x)^2 = 6^12 then x equals to..?
Answers
Answer:
x=6
Step-by-step explanation:
Item 4 Evaluate. [(1 1/4−3/4)⋅(−2/3)3]÷(−4) What is the value of the expression? Enter your answer as a simplified fraction in the box.
Answers
Answer:
1/27
Step-by-step explanation: I took the quiz and the right answer is 1/27
The value of the given expression would be 0.25 which is simplified by using the PEMDAS rule in the expression.
What is PEMDAS rule?The Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction rule is abbreviated as PEMDAS. This rule is used to answer the problem correctly and properly.
The given expression would be below as:
⇒ [(1 1/4−3/4)⋅(−2/3)3]÷(−4)
Using the PEMDAS rule in the above expression,
⇒ [(5/4−3/4)⋅(−2/3)3]÷(−4)
Apply the subtraction operation,
⇒ [(2/4)⋅(−6/3)]÷(−4)
Reduce the fractions, and we get
⇒ [(1/2)⋅(−2)]÷(−4)
Cancel out the terms of 2 to each other
⇒ (−1)÷(−4)
Cancel out the negative sign to each other
⇒ 1 / 4
Apply the division operation to get
⇒ 0.25
Therefore, the value of the given expression would be 0.25 which is evaluated.
To learn more about the Algebra link is given below.
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PLEASE HELP WITH THIS ONE QUESTION
Answers
Answer:
D. -3
Step-by-step explanation:
g(x) moved 3 units to the right
Complete the table for the value of each digit in 123.
Answers
Answer:
1,2,3,4,5,6,7,8,9,10
2,4,6,8,10,12,14,16,18,20
3,6,9,12,15,18,21,24,27,30
Step-by-step explanation:
Help help help help help help
Answers
Answer:
b
gnzjfzjgzjxjgzfjsngdjgsjfzgjskzjtztjsgjd5uduajai
Alguém me ajuda pfv rápido
Answers
Answer:
9.72
Step-by-step explanation:
1.8 x 1.8 x 3 = 9.72
it is predicted that by 2050 there will be 10^10 people living on earth. approximatrly will be 10^12 trees. how many trees for each person?
Answers
Interesting question. Does that mean near the end of humanity?
Solution 1:
10^10 = 1,000,000,000
10^12 = 100,000,000,000
100,000,000,000/1,000,000,000 = 100 trees per person
Solution 2:
10^12 / 10^10 --- 10^10 / 10^10
10^2/1 = 10^2 = 100 trees per person
Please take a look at the picture.
Answers
Answer:
A and B
Step-by-step explanation:
a) -x+0+(-x)=0
Combine like terms.
-2x+0=0
Subtract 0 from both sides.
-2x=0
Divide both sides by -2.
x=0
b) -x-(-x)=0
Remove parentheses.
-x+x=0
Combine like terms.
0=0
Hope this helps :)
Which situation can be represented by this inequality 135 ≤ 10r + 15
Answers
[tex]135\leq 10r +15\\\\\implies 120 \leq 10r\\\\\implies 12 \leq r \\\\\implies r \geq 12 \\\\\text{Interval,}~~ [12,\infty)[/tex]
A tortoise is walking in the desert. It walks 5.12 meters in 2 minutes. What is its speed?
Answers
Answer:
2.61 meters per minute
Step-by-step explanation:
All you have to do is divide by 2!
The speed of the tortoise is 2.56 meters per minute.
What is speed?Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.
Given, A tortoise is walking in the desert.
It walks 5.12 meters in 2 minutes.
The speed meter per minute;
5.12/2
= 2.56 meters per minute.
Therefore, 2.56 meters per minute is the speed of the tortoise.
To learn more about the speed;
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1.02 = _____ hundredths
Answers
102 hundredths
102/100
0.7619047619 as a fraction?
which one
1. 1/16
2. 16/21
3. 2
4. 4
Answers
Answer:
16/21
Step-by-step explanation:
Mr. Williams bought a plot of land for $ 40 000. The value of the land appreciated by 7% each year.
Answers
Answer:
no
Step-by-step explanation:
Andre ran a 100 meter race in 12 seconds. What was his average speed as he ran?
Answers
his average speed as he ran: V = S/t = 100/12 = 25/3 (m/s)
ok done. Thank to me :>
Speed is the time rate at which an object is moving along a path. 25/3 is the average speed as he ran
What is Speed?Speed is the time rate at which an object is moving along a path.
Speed =Distance/Time
His average speed as he ran:
V = S/t
Hundred by twelve.
= 100/12
Divide numerator and denominator by four.
Twenty five by three.
Average speed= 25/3 (m/s)
Hence if Andre ran a 100 meter race in 12 seconds. 25/3 is the average speed as he ran
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City planners are planning to build a new community pool. They agree that the pool will be rectangular in shape, but the proposed dimensions changed. At the most recent meeting, it was determined that the width would remain at 11.6 meters but that the length would increase by 3.7 meters. So, the pool would now cover an area of 205.85 square meters.
Which equation can be used to determine the original length of the pool, l?
205.85=2(l+15.3)
205.85=11.6(l+3.7)
205.85=3.7(l+11.6)
Answers
The equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)
Let l be the original length of the pool.
Since the length of the pool is increased by 3.7 m, the new length L = l + 3.7.
Also, the area of the pool A = 205.85 square meter and it is a rectangle with width, W = 11.6 meters,
So, A = LW
Substituting the values of the variables into the equation, we have
A = LW
205.85 = (l + 3.7)11.6
So, the equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)
Learn more:
https://brainly.com/question/12932084
Answer:
Step-by-step explanation
205.85=11.6(l+3.7)
We are flying at 30 000 feet.
Our speed is 500 miles per hour.
Our total flight time will be 10 hours and 20 minutes.
Mark knows the distance from London to Cancun is 4944 miles. He asks his daughter to check the information given by the pilot. She knows this formula for speed.
s = dt
s = speed (miles per hour) d = distance (miles)
t = time (hours)
Evaluate the information given by the pilot.
Show calculations to support your answer.
Answers
Answer:
Step-by-step explanation:
500 mph with a flight time of 10 hours and 20 minutes [(20 min)*(1 h/60 min) = 0.333 hr]
Distance = Speed * Time
Time = 10.333 hours
Distance = (500 miles/hr)*(10.333 hrs) = 5166.5 miles
The pilot's numbers indicate a distance of 5167 miles, compared to Mark's number of 4944 miles. That is a 4.3% reduction from the pilot's numbers. Not too bad, so we might question 1) Mark's knowledge, or 2) the impact that the approach and landing speeds have of the total miles flow.
My preference would be to trust the pilot's data. I don't know where Mark got his math education.
Henry can run 2.5 miles in 1/4 of an hour if he maintains the same pace how many miles can Henry run in 1 1/2 hours
Answers
Answer:
Since Henry runs 2.5 miles every 15 minutes, he runs 5 miles in 30 minutes, 7.5 miles in 45 minutes, and 10 miles every 60 minutes.
explanation: just trust me
Answer:
60 minutes
Step-by-step explanation:
I hope this would help
Sara earns $12.75 per hour at her job. She works 18 hours each week. While at work, she parks her car in a garage that charges $10.50 every 3 hours.
After paying for parking, how much does Sara earn each week?
A.$198.00
B.$229.50
C.$166.50
D.$261.00
Answers
She earns $229.50 each week, since 12.75•18 is 229.50. If the garage charges $10.50 every 3 hours, and she works 18 hours, she would have to pay $63 for parking. 229.50 - 63 = $166.50 each week.
9514 1404 393
Answer:
C. $166.50
Step-by-step explanation:
The rate Sara pays for parking is ...
$10.50/(3 hours) = $3.50 /hour
So, Sara's net pay, after paying for parking, is ...
$12.75/hour - 3.50/hour = $9.25 /hour
If she works 18 hours per week, her net earnings are ...
(18 h)($9.25/h) = $166.50 . . . . weekly earnings