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2 years ago

A hot cocoa canister (can) is a cylinder with a height of 24.5 cm and a radius of

Mathematics

1 answer:

Masteriza [31]2 years ago

8 0

Its 159.25 because u just times 24.5 x 6.5

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Which expression is equivalent to 5−4/4−3 ? −64 −1/64 1/64 64

Anton [14]

Its 64 hope you get a good grade

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3 years ago

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Triangle jkl is similar to triangle mno what is the perimeter of triangle Mno

Alja [10]

This cannot be solved unless you provide the picture for further answering.

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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,

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

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

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

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3 years ago

Jamie has a bag containing purple, pink, yellow, and blue marbles. There are a total of 40 marbles in the bag. Jamie randomly se

Ad libitum [116K]

Answer:

1 pink marble

Step-by-step explanation:

If Jamie selected 10 times the pink marble in a total of 420 tries, we can assume that the proportion of pink marble in the total number of marbles is:

10 / 420 = 1/42

So to predict a good number of pink marbles in the total 40 marbles, we just need to multiply the 40 marbles by the proportion found above:

pink marble = 40 * (1/42) = 0.9524

As this number needs to be a whole number, a good assumption is that there is 1 pink marble in the 40 marbles.

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2 years ago

Ted likes to run long distances. He can run 20 km in 95 minutes.He wants to know how many kilometers he will go if he runs the s

gladu [14]

You just have to cross multiply. 20 x 285 = 5700. 5700 / 95 = 60.

He will run 60km

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3 years ago

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