Please help me with this urgent

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

What is the formula to u-5=-4(w-1)

erastovalidia [21]

Answer: u = -4w + 9

Step-by-step explanation:

u - 5 = -4(w - 1)

u - 5 = -4w + 4

+5 +5

u = -4w + 9

3 0

3 years ago

A box of pencils is 5 1/4 inches wide. Seven pencils, laid side by side, take up 2 5/8 inches of the width. How many inches of t

Andre45 [30]

Answer: Width of box is not taken up by pencils = $2\dfrac58\text{ inches}$

Width of each pencil $=\dfrac38\text{ inches}$

Step-by-step explanation:

Given: Width of pencil box = $5\dfrac14\text{ inches}=\dfrac{21}{4}\text{ inches}$

Width of seven pencils = $2\dfrac58\text{ inches}=\dfrac{16+5}{8}\text{ inches}=\dfrac{21}{8}\text{ inches}$

Width of box is not taken up by pencils = Width of pencil box - Width of seven pencils

$\left \{ {{y=2} \atop {x=2}} \right. \dfrac{21}{4}-\dfrac{21}{8}\\\\=\dfrac{21\times2-21}{8}\\\\=\dfrac{21}{8}\text{ inches}=2\dfrac58\text{ inches}$

Width of box is not taken up by pencils = $2\dfrac58\text{ inches}$

Width of each pencil = (Width of seven pencils ) ÷ 7

$=\dfrac{21}{8}\div7\\\\=\dfrac{21}{8}\times\dfrac17\\\\=\dfrac38\text{ inches}$

Width of each pencil $=\dfrac38\text{ inches}$

3 0

2 years ago

Read 2 more answers

How do you write this quadratic equation using substitution

Arlecino [84]

Answer:

u^2 +7u -8=0 where u = 3x+2

Step-by-step explanation:

(3x+2)^2 + 7(3x+2) - 8=0

Let 3x+2 = u

u^2 +7u -8=0

7 0

3 years ago

Read 2 more answers

Somebody answer !!!!!

Rainbow [258]

Answer:

D)

Step-by-step explanation:

First we have to subtract 5 from both sides

$\sqrt{x-6} +5=12\\\\\sqrt{x-6}+5-5=12-5\\\\\sqrt{x-6}=7$

Now, square both sides

$(\sqrt{x-6})^{2}=7^{2}$

x - 6 = 49

Now, add 6 to both sides

x - 6 +6 = 49 + 6

x = 55

8 0

3 years ago