All categories

2 years ago

The painter made— or quart of purple paint

Mathematics

1 answer:

Andreas93 [3]2 years ago

3 0

Answer:

32 oz

Step-by-step explanation:

Im assumin you mean how many oz

You might be interested in

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

You take a three-question true or false quiz. You guess on all the questions. What is the probability that you will get a perfec

prisoha [69]

It would be 1/8. 2 to the third is 8, and all three answers correct is one option.

4 0

3 years ago

Read 2 more answers

What is the square root of pie

givi [52]

3.14 is the square root of pie.

3 0

3 years ago

Read 2 more answers

Helpppppp pleaseeeeeee

NeX [460]

Answer: b)

Step-by-step explanation:

You can rule out A) and C), because you have to find area (no adding.)

To do this problem, you can individually multiply the estimated hieght and

width by 3 and then multiply together.

This is because there are 3 walls that each are 9 3/4 tall and 14 1/4 wide. To find total height and width, multiply by 3. Then find total area (lxw)

9 3/4 rounds to 10

14 1/4 rounds to 14

= 3 (10) x 3 (14)

D) is incorrect because you have to multiply each number by 3. (Or you can multiply by 6)

It is B)

4 0

2 years ago

Answer this and get 50 points.

stealth61 [152]

Answer:

I drew more points as uploaded picture.

We have, arc BD + 210 + 90 = 360 deg

(sum of all arcs on circle)

=> arc BD = 360 - 210 - 90 = 60 deg

Here we have angle CBD = (1/2) x arc CD = (1/2) x 90 = 45 deg

(property of angle on circle)

=> angle ABD = angle ABC - angle CBD = 180 - CBD = 180 - 45 = 135 deg

( A, B, C lie on same line => ABC = 180 deg)

Otherwise, we have:

angle BDA = (1/2) x arc BD = (1/2) x 60 = 30 deg

We have: x + angle BDA + angle ABD = 180 deg

(sum of all angles in a triangle)

=> x = 180 - angle BDA - angle ABD

=> x = 180 -135 - 30

=> x = 15 deg

Hope this helps!

7 0

3 years ago

Read 2 more answers