Suppose that the Celsius temperature at the point (x, y) in the xy-plane is T(x, y) = x sin 2y and that distance in the xy-plane is measured in meters. A particle is moving clockwise around the circle of radius 1 m centered at the origin at the constant rate of 2 m/sec.How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point?

Answers

Answer 1

Missing information:

How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point

[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]

Answer:

[tex]Rate = 0.935042^\circ /cm[/tex]

Step-by-step explanation:

Given

[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]

[tex]T(x,y) =x\sin2y[/tex]

[tex]r = 1m[/tex]

[tex]v = 2m/s[/tex]

Express the given point P as a unit tangent vector:

[tex]P = (\frac{1}{2}, \frac{\sqrt 3}{2})[/tex]

[tex]u = \frac{\sqrt 3}{2}i - \frac{1}{2}j[/tex]

Next, find the gradient of P and T using: [tex]\triangle T = \nabla T * u[/tex]

Where

[tex]\nabla T|_{(\frac{1}{2}, \frac{\sqrt 3}{2})} = (sin \sqrt 3)i + (cos \sqrt 3)j[/tex]

So: the gradient becomes:

[tex]\triangle T = \nabla T * u[/tex]

[tex]\triangle T = [(sin \sqrt 3)i + (cos \sqrt 3)j] * [\frac{\sqrt 3}{2}i - \frac{1}{2}j][/tex]

By vector multiplication, we have:

[tex]\triangle T = (sin \sqrt 3)* \frac{\sqrt 3}{2} - (cos \sqrt 3) \frac{1}{2}[/tex]

[tex]\triangle T = 0.9870 * 0.8660 - (-0.1606 * 0.5)[/tex]

[tex]\triangle T = 0.9870 * 0.8660 +0.1606 * 0.5[/tex]

[tex]\triangle T = 0.935042[/tex]

Hence, the rate is:

[tex]Rate = \triangle T = 0.935042^\circ /cm[/tex]


Related Questions

Sue has taken four exams so far in her History course. Her scores are 84.0, 78.2, 93, and 87.5. What is the average of these scores?

Answers

Answer: 85.7

Step-by-step explanation:

Write the reciprocal of each mixed number.
1 1/6

Answers

Answer:

The reciprocal of mixed number is 6/11

What is the value of the underlined digit? Write your answer as a fraction. 0.812? 2 is underline number?

Answers

9514 1404 393

Answer:

  1/500

Step-by-step explanation:

The value of the digit is found by setting the other digits to zero:

  0.002

This is 2 thousandths, or 2/1000. The fraction can be reduced to 1/500.

Answer:

the answer is 1/500

Step-by-step explanation:

:)))

hey i need helpppppol

Answers

Answer:

Option : C

Step-by-step explanation:

Hope it helps you!

Can y’all help me on question eight?!

Answers

Answer:

50

Step-by-step explanation:

PEMDAS

3(2)+24/2+2(3+7)

Pemdas

3(2)+24/2+2(10)

PeMDas

6+24/2+20

6+12+20

PemdAs

38

3*2 = 6
6+ 24 = 30
30/2 = 15
15+2 = 17
Now 3+7 is 10 so 17*10 = 170

ANSWER: 170

A submarine was 20 feet below sea level. If it ascends (goes up) 30 feet,
what is its new position?
50 feet above sea level
O 10 feet below sea level
O 50 feet below sea level
O 10 feet above sea level

Answers

Answer:

10 ft above sea level

Step-by-step explanation:

20 below goes up by 30 then it would be -20 -10 0 10

Please help i need the right answer fast will give brainliest​ if its correct answer

Answers

Answer:

8 X 5 = $40

Step-by-step explanation:

I need halo on the last one quickly please

Answers

I don’t know this either

the figure below shows a semicircular arch tunnel

Answers

Answer:

312.5

Step-by-step explanation:

Find the perimeter of the trapezoid.
16
7
5
4
20
Plz plz help

Answers

Answer:

48

Step-by-step explanation:

7+16+5+20=48

a rectangular prism that has a length of 13 ft of 2 ft and do with of 4 ft What is its volume in cubic feet ​

Answers

Answer:

104 ft³

Step-by-step explanation:

to find the volume of a rectangular prism you do

width x height x length or 13x2x4

13x2=26

26x4=104

so the volume of the rectangular prism is

104 ft³

have a great day :D

The answer the number 2

Answers

Answer:

69

Step-by-step explanation:

On a survey, 7 students reported how many minutes it takes them to travel to school. Here are their responses.
8,5,3,15,6,16,5
Find the mean travel time for these students.
If necessary, round your answer to the nearest tenth.

Answers

answers is




explaining

Answer:

8

Step-by-step explanation:

The mean of the minutes reported is 8. The mean is the average, or the sum of the data divided by the total number of data.

PLEASE HELP WILL GIVE BRAINLEIST!!! What type of angles are ∠4 and ∠8?

Answers

Answer:

Corresponding Angles

Step-by-step explanation:

They are both in the same positions but just on different lines meaning they are corresponding :)

The angle 4 and angle 8 are corresponding angles because line b and line c are parallel to each other and intersected by a line a option (D) is correct.

What is an angle?

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

As we can see in the figure, the line b and line c are parallel to each other and intersected by a line a.

The angles 1, 2, 3, 4, 5, 6, 7, and 8 formed.

The angles 1 and 4, angle 2 and 3 are vertically opposite angles.

Similarly, 5&8 and 6&7 are vertically opposite angles.

The angle 4 and angle 8 are corresponding angles.

Thus, the angle 4 and angle 8 are corresponding angles because line b and line c are parallel to each other and intersected by a line a option (D) is correct.

Learn more about the angle here:

brainly.com/question/7116550

#SPJ2

Please help me with math

Answers

iDisk dijo en la casa que se lo pase bien a mi madre que me pase la prueba y yo no me estaba por el verde y ni me siguió porque yo le voy a decir que no me puedes decir si me estaba llamando para allá porque me voy chao a mi I’m going to kill you

Answer:

These are the answers. Hope this helps!

Step-by-step explanation:

need help with these 2 questions

Answers

Answer:

I worked really hard on this problem, I had to manually edit with my editing tool for 15 minutes lol.

Find the missing lengths leave your answers as radicals in simplest form

Answers

Step-by-step explanation:

w = 4

y = 4√2

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you .

w would be 4
y would be 5.6

what amount of money can we obtain using the coins we have

Answers

Answer:

bitcoin

Step-by-step explanation:

Answer:

Step-by-step explanation:

2. The size of garage after a 12% decrease is 150 square feet. What was the original
size of the garage? Round to the nearest whole feet.

Answers

Answer:

168ft^2

Step-by-step explanation:

150 · 0.12 = 18.

150 + 18= 168

Find the volume of the given solid. Bounded by the cylinder y2 + z2 = 16 and the planes x = 2y, x = 0, z = 0 in the first octant

Answers

Answer:

[tex]\mathbf{ \dfrac{128}{3}}[/tex]

Step-by-step explanation:

Given that:

[tex]y^2 + z^2 = 16; \\ \\ where; \ x = 2y , x =0, z= 0[/tex]

[tex]Replace \ z = 0 \ \text{in the given equation ;} y^2+z^2=16[/tex]

[tex]Then;[/tex]

[tex]y^2 = 16 \\ \\ y = \sqrt{16} \\ \\ y = \pm 4[/tex]

[tex]\text{So; in 1st octant \ limits of y }= 0 \to 4 \ \text{and for x }= 0 \to 2y[/tex]

[tex]\text{Volume of solid: (V) = }\int ^{4}_{y=0} \int ^{2y}_{x=0} \sqrt{16-y^2} \ dxdy \\ \\ = \int^4_{y=0} \sqrt{16 -y^2} \ (x)^{2y} _o \ dy \\ \\ = \int^4_{y=0}\sqrt{16 -y^2} (2y -0) \ dy \\ \\ V = \int^{4}_{y=0} \ 2y \sqrt{16 - y^2} \ dy[/tex]

[tex]Now, let:\\\\ 16 - y^2 = u \\ \\ -2ydy = du \\ \\ 2ydy = -du \\ \\ Hence, when \ y = 0; u = 16 \\ \\ and \\ \\ when \ y = 4 \ then \ u = 0[/tex]

[tex]V = \int ^4 _{y=0} \ 2y \sqrt{16 -y^2 } \ dy \\ \\ = \int ^0_{16} - \sqrt{u}\ du \\ \\ = - \int^0_{16} \ u^{^{\dfrac{1}{2}}} \ du \\ \\ = \Bigg [\dfrac{u^{^{\dfrac{1}{2}+1}}}{\dfrac{1}{2}+1 } \Bigg]^0_{16} \\ \\ =\Bigg[ -\dfrac{u^{\dfrac{3}{2}}}{\dfrac{3}{2}}^0_{16} \Bigg] \\ \\[/tex]

[tex]= - \dfrac{2}{3}\Big( u^{\dfrac{3}{2}}\Big)^0_{16} \\ \\ = - \dfrac{2}{3} \Big(0^{^\dfrac{3}{2}}}- 16^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(0 - (4^2)^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(-(4)^{3}}\Big )[/tex]

[tex]= - \dfrac{2}{3} \Big(64\Big )[/tex]

[tex]\mathbf{V = \dfrac{128}{3}}[/tex]

Usa graph peper. Plot the points on a coordinate plane. In which quadrant
is cech point located?
2 A (3,7) B (2.0) C (8-1), D (0 -6) E (-3, 5) and F (-6, 7)

Answers

Answer:

Point A: quadrant 1

Point B: either quadrant 1 or 4

Point C: quadrant 4

Point D: either quadrant 3 or 4  

Point E: quadrant 2

Point F: quadrant 2

Step-by-step explanation:

Heeeeeeeelp meeeeeee

Answers

Answer:

(-8+1)

Step-by-step explanation:

need help ASAP plz and I've got more if anyone wants to help​

Answers

Answer:

1/4+1/4+1/4+1/4+1/4+1/4= 1.5

3/10x2/3= 0.2

2/4x2/3= 0.33333333333  (just put 0.3 with a line on top of the 3)

6 divided by 1/2 = 12/1 or 12

9 divided by 1/3 = 27/1 or 27

2/5 divided by 3/4 = 8/15

1/2 divided by 2/3 = 3/4

Need help with this, the answer is 61 but I need the work for it.

Answers

Answer:

61

Step-by-step explanation:

Arc AC = 180

Arc DC = 58

Arc AC = Arc AD + Arc DC

180 = Arc AD + 58

122 = Arc DC

Tangent Chord Angle = 1/2Intercepted Arc

Angle DBA = 1/2 Arc DC

Angle DBA = 1/2 (122)

Angle DBA = 61

HELP PLSSSS I BEG UUUU PLSSS

Answers

Answer: Thursday

Step-by-step explanation:

I hope this helps

Answer: Thursday

Step-by-step explanation:

It's Thursday because any number below 0 is a negative number but, as Thursday is 3° above 0, it is positive.

Hope this helps :)

Find the surface area of the figure

a. 150 square cm
b. 228.4 square cm
c. 78.4 square cm
d. 210 square cm

Answers

Answer:

c

Step-by-step explanation:

In a game involving a standard deck of 52 playing cards, an individual randomly draws 6 cards without
replacement. Let Y be the number of aces drawn.
What type of variable is Y?

Answers

Answer: Neither

Step-by-step explanation:

Thomas lives more than 0.55 km and less than 0.75 km from his school.
Thomas lives from his school?
A. 0.06 km
B 0.50 km
c. 0.60 km
D. 1.30 km
Which choice could be the distance Thomas lives from his school?

Answers

I think the answer is C. Not sure, sorry if it’s wrong

What is the ratio in simplest form 20: 10

Answers

Answer:

2:1 is the simplest form

Step-by-step explanation:

major arc BRA is 3/2 the length of minor arc BSA. the length of major arc BRA is 6pi centimeters. what is the radius of the circle?

Answers

9514 1404 393

Answer:

  5 cm

Step-by-step explanation:

The given arcs have the ratio ...

  BRA : BSA = (3/2) : 1 = 3 : 2

Then BRA is 3/(3+2) = 0.6 of the total circumference of the circle.

  0.6(2πr) = 6π . . . . . BRA is 6π long

  r = 6π/(1.2π) . . . . . . divide by the coefficient of r

  r = 5 . . . . centimeters

Other Questions
Mike walked 5/8 of the way to school before it started raining. How many percent of the trip did he get before it rained? Which of the following examples has a unit rate of 25 feetper second? Select all that apply.A) 100 feet in 4 secondsB) 150 feet in 10 secondsC) 225 feet in 9 secondsD) 275 feet in 11 secondsE) 100 feet in 5 seconds Why Deciduous forests are also called temperate forests. 10. A girl read a book that had 1,259 pages. She read 75 pages on the first day. She then read 45 pagesper day until she finished the book. Write an equation that could be used to find the number of days, d,it took her to read the book.I Take the role of a young person working in a factory in the North in the mid-1800s. Write a letter in which you tell a friend what you like and dislike about your job. 6. What are the four levels that anything can be understood on? Why does Reinhart bring up theselevels in regards to bread? What do you think goes through Fortunato's mind after he realizes what has happened to him? Why doesn't he try to reason with Montresor? Use what you know about Fortunato to write a monologue, retelling the last part of the story from his point of view. "Your first morning in your new office, you reflect on what type of manager and leader you hope to be. Which of the following best reflects what you believe about employees and how they can best be led? Select an option from the choices below and click Submit. Employees are more loyal and productive if they feel that their leader is admirable, caring, and ethical. Employees behavior can be shaped and motivated, not only by rewarding good behavior but also by penalizing bad behavior. Employees need to be discouraged from bad behavior. They work harder when they know that failure has consequences." Help plzzzzzzzzzzzzzzzzz Factor 6 x2 - 17 x + 5. (3x - 1)(2x - 5) (3x - 5)(2x - 1) (2x - 1)(3x + 5) A triangle has a base of 10 inches and a height of 4.5 inches. What is the area of the triangle in square inches? A right rectangular prism has a length of 3 1/3 yards, a width of 2 1/2 yards, and a height of 4 1/3 yards. What is the volume of the prism?Answer choices:A: 10 1/6 cubic yardsB: 24 1/18 cubic yards.C: 35 1/2 cubic yards.D: 36 1/9 cubic yards. lumination Corporation operates one central plant that has two divisions, the Flashlight Division and the Night Light Division. The following data apply to the coming budget year: Budgeted costs of operating the plant for 2000 to 3000 hours: Fixed operating costs per year $480,000 Variable operating costs $800 per hour Budgeted long-run usage per year: Flashlight Division 1500 hours Night Light Division 600 hours Practical capacity 3000 hours Assume that practical capacity is used to calculate the allocation rates.Actual usage for the year by the Flashlight Division was 1500 hours and by the Night Light Division was 800 hours. If a single-rate cost-allocation method is used, what amount of cost will be allocated to the Flashlight Division? Assume actual usage is used to allocate operating costs.a. $1,850,000b. $1,200,000c. $2,050,000d. $1,537,500 Brandi has equal numbers of hip-hop songs and country songs loaded on her personal music player. She has it set to play songs on a random shuffle. Suppose Brandl is designing a simulation that could be used to estimate the probability that the next three songs to play are all hip-hop songs Which simulation design could Brandi use to estimate the probability? A. Coin Let heads (H) = hip-hop Let tails (T) = country Toss coin three times. Repeat B. Random digits Let 0.1phop Let 2.3.4.5.6 = country Select two random digits Repeat C. Number cube Let 1 = hip-hop Let 2 = country Roll cube three times Repeat D. Nurbe cube let 1 = hip-hop let 2 = country Roll cube four times. Report Prob(Total time in process > t) = EXP(-t/T) T = (1/(Rp - Ri)) = (1 / Rs) R = min(Ri, Rp) u=R/Rp Dominic runs an appliance repair shop and sells replacement parts for appliances to walk in customers. Customer take an average of 5 minutes. It is a single phase system with 1 server. The coefficient of arrivals and the coefficient of processing times is 1.0. If Dominic's utilization were 80%, how many would be standing in line waiting to be served? A life guard is sitting on a platform, looking down at a swimmer in the water. If the lifeguards line of sight is 8 feet above the ground and the angle of depression is 18 degrees, how far away is the swimmer from the lifeguard? Round to the nearest tenth please would you be so kind and help me with problems four through 12? You buy a pair of shoes for $40, at check out you are also charged 8% sales tax. What is the total cost of your shoes PLEASE NO LINKS! PLEASE, PLEASE, PLEASE!Is this an example of indirect or direct characterization? Justify your answer. "That night, she slept with the letter under her cheek." List six consecutive numbers