The product of 2x-3 and x+4 can be expressed as

In right triangle DEF, ∠E is a right angle, m∠D=26∘, and DF=4.5.

SVEN [57.7K]

The measurement of EF is EF=5.9

7 0

3 years ago

Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x

Serggg [28]

I assume $C$ has counterclockwise orientation when viewed from above.

By Stokes' theorem,

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

so we first compute the curl:

$\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k$

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

Then parameterize $S$ by

$\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k$

where the $z$ -component is obtained from

$1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v$

with $0\le u\le\dfrac\pi2$ and $0\le v\le\dfrac\pi2$ .

Take the normal vector to $S$ to be

$\vec r_v\times\vec r_u=2\cos u\cos v\sin^2v\,\vec\imath+\sin u\sin v\sin(2v)\,\vec\jmath+\cos v\sin v\,\vec k$

Then the line integral is equal in value to the surface integral,

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

$=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{\pi/2}\int_0^{\pi/2}\cos v\sin^2v(\cos u+2\cos^2v\sin u+\sin(2u)\sin v)\,\mathrm du\,\mathrm dv=\boxed{-\frac{17}{20}}$

6 0

3 years ago

How can you quickly calculate 20 percent of any bill amount?

il63 [147K]

The answer is C an example is 20% of $20 is 4, so you would lose the zero and double the 2 to get 4

8 0

3 years ago

Read 2 more answers

URGENT kaser needs $155 to pay for a new mouth piece for her saxophone she has $35 already and save $15 a week that she earns wa

yulyashka [42]

Answer:

A) she needs to earn $120 for her mouth piece

B) it will taker kaser 8 weeks to get enough money for the mouthpiece

Step-by-step explanation:

whats a segment tool? no idea but i can help solve this so you can attempt that part

explaining

so kaser needs $155, she already has $35 and gains $15 a week. i will be assisting you with how to solve for how much she has when she starts saving and how long until she saves it all

process A

155-35 = 120

answer A

she needs to earn $120 for her mouth piece

process B

120 divided by 15 = 8

answer B

it will taker kaser 8 weeks to get enough money for the mouthpiece

8 0

3 years ago

Please help check if this is correct?

Likurg_2 [28]

Answer:

50 is correct

Step-by-step explanation:

did my math but I know you need it quick so sorry for brief answer

4 0

3 years ago