1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SOVA2 [1]
2 years ago
8

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?
Mathematics
1 answer:
liraira [26]2 years ago
3 0

Missing information:

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

P = (\frac{1}{2}, \frac{\sqrt 3}{2})

Answer:

Rate = 0.935042^\circ /cm

Step-by-step explanation:

Given

P = (\frac{1}{2}, \frac{\sqrt 3}{2})

T(x,y) =x\sin2y

r = 1m

v = 2m/s

Express the given point P as a unit tangent vector:

P = (\frac{1}{2}, \frac{\sqrt 3}{2})

u = \frac{\sqrt 3}{2}i - \frac{1}{2}j

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

Where

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

So: the gradient becomes:

\triangle T = \nabla T * u

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

By vector multiplication, we have:

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

\triangle T = 0.9870 * 0.8660 - (-0.1606 * 0.5)

\triangle T = 0.9870 * 0.8660 +0.1606 * 0.5

\triangle T = 0.935042

Hence, the rate is:

Rate = \triangle T = 0.935042^\circ /cm

You might be interested in
You roll a fair 6-sided die. what is the probability rolling greater than 4
Readme [11.4K]

Answer:

1/3

Step-by-step explanation:

There are 6 possible outcomes when you roll this die: 1,2,3,4,5 and 6. Of these, only 5 and 6 are greater than 4, which is 2 successful outcomes. Probability is successful outcomes/total outcomes = 2/6 = 1/3. Hope this helps!

6 0
3 years ago
Math questions plz help 10-11b
evablogger [386]
Question number 10 is the same as the previous questions add them up and make them equal to 180 degrees, and then solve for the x variable.

For the second part of the question, simply plug in the value of x for each expression for R and S.






6 0
3 years ago
1. Write 33% as a fraction.
Olegator [25]

Answer:

33/100

62%

0.77

0.4

9/10

8 0
2 years ago
Read 2 more answers
-(9x+12)-4x <br> Simplify <br> Need an answer ASAP
Burka [1]
-13x-12. remove the parenthesis them add the like terms.
6 0
3 years ago
Read 2 more answers
Write an equation In slope intercept form for the line that is parallel to the given line and that passes through the given poin
ludmilkaskok [199]

The equation of the parallel line in slope-intercept form is;

y = \frac{5}{2} x - \frac{25}{2}

Step-by-step explanation:

Let us revise some facts about parallel lines

The equations of two parallel lines have:

  • Same slopes
  • Different y-intercept

The slope-intercept form of the equation of a line is y = m x + b, where m is the slope of the line and b is the y-intercept

The given line has equation 5x - 2y = 10

Put it in the form of y = m x + b to find its slope

∵ 5x - 2y = 10

- Subtract 5x from both sides

∴ -2y = 10 - 5x

- Divide to sides by -2

∴ y = -5 + \frac{5}{2} x

∴ y =  \frac{5}{2} x - 5

- The value of m is the coefficient of x

∴ m = \frac{5}{2}

∴ The slope of the given line is \frac{5}{2}

∵ Parallel lines have same slopes

∴ The slope of the parallel line is m = \frac{5}{2}

- Substitute the value of m in the form of the equation

∴ The equation of the parallel line is y = \frac{5}{2} x + b

To find b substitute x and y in the equation by the coordinates of any point lies on the line

∵ The parallel line passes through point (3 , -5)

- Substitute x and y by the coordinates of the point (3 , -5)

∵ x = 3 and y = -5

∴ -5 = \frac{5}{2} (3) + b

∴ -5 = \frac{15}{2} + b

- Subtract \frac{15}{2} from both sides

∴ b = \frac{-25}{2}

∴ The equation of the parallel line is y = \frac{5}{2} x + \frac{-25}{2}

∴ The equation of the parallel line is y = \frac{5}{2} x - \frac{25}{2}

The equation of the parallel line in slope-intercept form is;

y = \frac{5}{2} x - \frac{25}{2}

Learn more:

You can learn more about the equations of parallel lines in brainly.com/question/8628615

#LearnwithBrainly

5 0
3 years ago
Other questions:
  • Which relationship is always correct for the angles p, q, and r of triangle ABC?
    14·1 answer
  • What is 22-8 over -7 - -9​
    14·1 answer
  • What’s the answer to 3/4 +5/8
    7·1 answer
  • What is the distance between P(12, 4) and Q(-8, 2)
    9·2 answers
  • What is a binomial? followed with an example?
    10·2 answers
  • #2) Solve for side BC, to the nearest whole number. *<br> 1 point<br> 105°<br> A<br> 15
    15·2 answers
  • How do i work this problem sin(2cos^-1 1/11)
    9·1 answer
  • Your classmate is unsure about how to use side lengths to determine the type of triangle. How would you
    7·2 answers
  • A sailboat travels at an average speed of 8 km/h. How many kilometers are traveled in 20 h at that speed?
    5·1 answer
  • Find the solution set of the inequality
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!