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

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

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

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 :)

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.

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:

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:

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

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

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

Answers

Answer:

bitcoin

Step-by-step explanation:

Answer:

Step-by-step explanation:

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

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:

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

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

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

What is the ratio in simplest form 20: 10

Answers

Answer:

2:1 is the simplest form

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

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:

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]

I need halo on the last one quickly please

Answers

I don’t know this either

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:

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:

:)))

the figure below shows a semicircular arch tunnel

Answers

Answer:

312.5

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

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:

hey i need helpppppol

Answers

Answer:

Option : C

Step-by-step explanation:

Hope it helps you!

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

The answer the number 2

Answers

Answer:

69

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.

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