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3 years ago

Color in equations what to color in 1+2+3+4=10 What cubes to color in?

Mathematics

2 answers:

noname [10]3 years ago

5 0

Please explain what the question is more clearly please.

Leni [432]3 years ago

4 0

Can you explain more

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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

2) A product originally costs $125. If the product goes on sale for 20% off, and then goes on sale for an additional 30% off, wh

alukav5142 [94]

To do these, always convert the percents to decimals, so you can subtract it from 1. Remember, 1 is the whole. When you subtract the part that's taken off, you are left with what you have to pay. If you have 20% off of $100, then you are paying for 80% of $100. **of means to multiply** so you would multiply: 0.8X100, which would be $80.

First, multiply 125x0.8

Multiply that answer by 0.7

You should get B. $70

3) multiple 22.90x0.93

You should get D

7 0

3 years ago

Read 2 more answers

A square pyramid has a base

ozzi

Answer:

V≈25.06m³

Step-by-step explanation:

Unit Conversion:

a≈5.03m

h≈2.97m

Solution