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3 years ago

7

Isaac has 21 green marbles and 7 blue .He wants to place them in identical groups without any marbles left over.What is the grea

test number of groups Isaac can make

1 answer:

dybincka [34]3 years ago

8 0

Answer:

7 groups

Step-by-step explanation:

Each group would have 1 blue marble and 3 green marbles

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avanturin [10]

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3 years ago

G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =

Svetach [21]

Presumably you should be doing this using calculus methods, namely computing the surface integral along $\mathbf r(u,v)$ .

But since $\mathbf r(u,v)$ describes a sphere, we can simply recall that the surface area of a sphere of radius $a$ is $4\pi a^2$ .

In calculus terms, we would first find an expression for the surface element, which is given by

$\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k$
$\dfrac{\partial\mathbf r}{\partial v}=-a\sin u\sin v\,\mathbf i+a\sin u\cos v\,\mathbf j$
$\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k$
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So the area of the surface is

$\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=\pi}\int_{v=0}^{v=2\pi}a^2\sin u\,\mathrm dv\,\mathrm du=2\pi a^2\int_{u=0}^{u=\pi}\sin u$
$=-2\pi a^2(\cos\pi-\cos 0)$
$=-2\pi a^2(-1-1)$
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as expected.

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3 years ago

John rode 4 kilometers on his bike his sister sally rode 3400 meters on her bike who rode the farthest and how much farther did

emmasim [6.3K]

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4 years ago

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dimaraw [331]

Everything about number one is because it's a half of circle so its area = 1/2 ¶r^2 and its perimeter = ¶r

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3 years ago

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Stella [2.4K]

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Step-by-step explanation:

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3 years ago