I would say it is A because if you subtract <em>p,</em> the original price by $2.50, you would get <em>d, </em>the discounted price. Look at B u see that you're adding the discount which doesn't make sense. Looking at C, the discounted price of different prices can't always be the same. And finally, D, the discounted price is greater than the original. Also, if you subtract you would get different discounts.

6 0

3 years ago

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyi + 5zj + 7yk

REY [17]

By Stokes' theorem,

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

where $S$ is the surface with $C$ as its boundary. The curl is

$\nabla\times\vec F(x,y,z)=2\,\vec\imath-x\,\vec k$

Parameterize $S$ by

$\vec\sigma(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(8-u\cos v)\,\vec k$

with $0\le u\le9$ and $0\le v\le2\pi$ . Then take the normal vector to $S$ to be

$\vec\sigma_u\times\vec\sigma_v=u\,\vec\imath+u\,\vec k$

Then the line integral is equal to the surface integral,

$\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9(2\,\vec\imath-u\cos v\,\vec k)\cdot(u\,\vec\imath+u\,\vec k)\,\mathrm du\,\mathrm dv$

$\displaystyle=\int_0^{2\pi}\int_0^9(2u-u^2\cos v)\,\mathrm du\,\mathrm dv=\boxed{162\pi}$

7 0

3 years ago

To find the quotient of 726.02 and 1,000, move the decimal point in 762.02___Places to the ____

To find the quotient of 726.02 and 1,000, move the decimal point in 762.02_Places to the __