She spent $6.12 on the muffins for her and her friends, and she has $8.36 left on her gift card. By multiplying 6 by $1.02, you get the amount she spent, and by subtracting $14.48 by $6.12, I find how much she has left on her gift card.

8 0

3 years ago

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

A color printer prints 34 pages in 12 minutes. How many pages does it print per minutes?

RSB [31]

Answer:

almost 3 per minute but not just about there yet

Step-by-step explanation:

34/12 = 2.8333333333~

6 0

3 years ago

Read 2 more answers

Gary learned that the value of his car depreciates by 15% percent per year. Which of the following functions best describes the

Sever21 [200]

For this case we have that the original value of the car is:
m dollars
For the following year we have the value is:
((100-15) / (100)) m
Rewriting we have:
((85) / (100)) m
0.85m
Answer:
the value of his car the year after the car is worth m dollars is:
B.f (m) = 0.85m

5 0

3 years ago