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3 years ago

Exercise 7.8.29. [S] Flying twice as far.

Mathematics

1 answer:

dalvyx [7]3 years ago

3 0

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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

liraira [26]

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:

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

3 0

2 years ago

THE property of two rational numbers is -28/81. If one of them is -2/3, then find the other.

KiRa [710]

The answer is:
(-28/81)/(-2/3) = -84/(-162) = 42/81

Work
Think of this simple question:
Two number when multiplied together give 15. If one number is 5, then the other is (15/5)=3.

4 0

3 years ago

HELP ASAP

SIZIF [17.4K]

Answer:

bcd= congruent property abstracted by -cdb

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

I need help with review #1-5

Ratling [72]

I earned 5 for x and 12 for y but I'm not sure about the «y»

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3 years ago

The population of California is approximately 3.8 x 10^7, and the population of Nebraska is approximately 1.9 x 10^6. Which stat

REY [17]

Answer:

YES

Step-by-step explanation:

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3 years ago