Find the area and perimeter of parallelogram.

Christian is a professional chef for a restaurant who also runs a small catering business. Christian did not have enough withhel

diamong [38]

Answer:

He should pay his paychecks in time.

4 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

Andy is solving a quadratic equation using completing the square. If a step in the process results in = (x – 6)2, could the orig

Zarrin [17]

<span>Yes, the equation can be solved by factoring. Using the given equation, take the square root of both sides. Both 169 and 9 are perfect squares, so the left side becomes plus or minus 13/3, which is rational. Six plus 13/3 is a rational number, and 6 minus 13/3 is also a rational number. If the solutions of a quadratic equation are rational, then the equation is factorable. </span>

7 0

3 years ago

Read 2 more answers

17/39 + 11/12 −( 5/12 + 4 /39 )

Nana76 [90]

Answer:

.83333333 or 5/6

Step-by-step explanation:

Make common denominator

204/468 + 429/468 = 633/468 - (195/468 + 48/468)

Simplify: 633/468 - 243/468

390/468 can be further broken down to 5/6 if you divide by a common factor which is 78.

8 0

3 years ago

Read 2 more answers

What is the volume of a sphere with a diameter of 15 cm? Round the answer to the nearest whole number.

AveGali [126]

Answer:

1767 cm³

Step-by-step explanation:

We can use volume V = 4/3 π r³

We have diameter of 15 cm. To get radius, we need to divide diameter by 2.

r = 7.5 cm

So now plug in r = 7.5 then calculate V:

V = 4/3 π ( 7.5 )³

V = 4/3 π * 421.875 ≈ 1767.145 ≈ 1767

Hope this helps.

8 0

3 years ago