Find the slope of the line that passes through (2, 5) and (2,2 ) WORTH 20 POINTS

Find the following: F(x, y, z) = e^(xy) sin z j + y tan^−1(x/z)k Exercise Find the curl and the divergence of the vector field.

natulia [17]

$\vec F(x,y,z)=e^{xy}\sin z\,\vec\jmath+y\tan^{-1}\dfrac xz\,\vec k$

Divergence is easier to compute:

$\mathrm{div}\vec F=\dfrac{\partial(e^{xy}\sin z)}{\partial y}+\dfrac{\partial\left(y\tan^{-1}\frac xz\right)}{\partial z}$

$\mathrm{div}\vec F=xe^{xy}\sin z-\dfrac{xy}{x^2+z^2}$

Curl is a bit more tedious. Denote by $D_t$ the differential operator, namely the derivative with respect to the variable $t$ . Then

$\mathrm{curl}\vec F=\begin{vmatrix}\vec\imath&\vec\jmath&\vec k\\D_x&D_y&D_z\\0&e^{xy}\sin z&y\tan^{-1}\frac xz\end{vmatrix}$

$\mathrm{curl}\vec F=\left(D_y\left[y\tan^{-1}\dfrac xz\right]-D_z\left[e^{xy}\sin z\right]\right)\,\vec\imath-D_x\left[y\tan^{-1}\dfrac xz\right]\,\vec\jmath+D_x\left[e^{xy}\sin z}\right]\,\vec k$

$\mathrm{curl}\vec F=\left(\tan^{-1}\dfrac xz-e^{xy}\cos z\right)\,\vec\imath-\dfrac{yz}{x^2+z^2}\,\vec\jmath+ye^{xy}\sin z\,\vec k$

5 0

3 years ago

If you were moving at 14mph for 8 miles, how long would it take you to travel the 8 miles?

Rainbow [258]

Answer

34 minutes

Step-by-step explanation:

3 0

2 years ago

I need some help with this:)I'll apreciate the answers.

Travka [436]

Part A: The discounted monthly fee is $22.49 (original cost of $29.99 multiplied by 75%, the amount the customer would pay since 25% is discounted.) Since you would also pay $44.99 for setup, your equation is $44.99+$22.49m Part B: Add 1.08 (108%; the customer pays 100% of the cost plus 8% more for tax) to your equation for the sales tax. 1.08(44.99+22.49m) Part C: Plug in 4 for m (m represents months). 1.08(44.99+22.49•4) 1.08(44.99+89.96) 1.08(134.95) $145.75 Hope that helps. Let me know if you need more assistance :)

7 0

3 years ago

A small pizza at Little Italy pizzeria costs $9.25, and each topping is an additional $0.50. So the cost of ordering a pizza can

Vera_Pavlovna [14]

Answer:

Graph the equation is shown below.

Step-by-step explanation:

The linear equation representing the relation between cost of ordering a pizza and the number of additional toppings is:

$y=0.50x+9.25$