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4 years ago

(32)2/5 RADICAL NOTATION

1 answer:

6 0

Hint: $\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}$

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Hi guys, can anyone help me with this triple integral? Many thanks:)

Crank

Another triple integral. We're integrating over the interior of the sphere

$x^2+y^2+z^2=2^2$

Let's do the outer integral over z. z stays within the sphere so it goes from -2 to 2.

For the middle integral we have

$y^2=4-x^2-z^2$

x is the inner integral so at this point we conservatively say its zero. That means y goes from $-\sqrt{4-z^2}$ and $+\sqrt{4-z^2}$

Similarly the inner integral x goes between $\pm-\sqrt{4-y^2-z^2}$

So we rewrite the integral

$\displaystyle \int_{-2}^{2} \int_{-\sqrt{4-z^2}}^{\sqrt{4-z^2}} \int_{-\sqrt{4-y^2-z^2}}^{\sqrt{4-y^2-z^2}} (x^2+xy+y^2)dx \; dy \; dz$

Let's work on the inner one,

$\displaystyle\int_{-\sqrt{4-y^2-z^2}}^{\sqrt{4-y^2-z^2}} (x^2+xy+y^2)dz$

There's no z in the integrand, so we treat it as a constant.

$=(x^2+xy+y^2)z \bigg|_{z=-\sqrt{4-y^2-z^2}}^{z=\sqrt{4-y^2-z^2}}$

So the middle integral is

$\displaystyle\int_{-\sqrt{4-z^2}}^{\sqrt{4-z^2}}2(x^2+xy+y^2)\sqrt{4-y^2-z^2} \ dy$

I gotta go so I'll stop here, sorry.

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3 years ago

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I need help qucikly whats the answer??

Anni [7]

Answer:

Step-by-step explanation:

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What is the rule for this input-output table?

andrew11 [14]

9514 1404 393

Answer:

y = 4x + 3

Step-by-step explanation:

The output of 3 at x = 0 tells you the y-intercept is 3.

The change of 4 from 3 to 7 for an input change of 1 from 0 to 1 tells you the slope is 4/1 = 4. Then the slope-intercept form of the equation is ...

y = mx + b . . . . . m = slope, b = y-intercept

y = 4x + 3

_____

It is pretty conventional to use y for the output variable and x for the input variable. Your rule could be ...

output = 4 × input + 3

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3 years ago

A cube is sliced by an angled plane as shown. Which of the following plane figures represents the cross section?

forsale [732]

Answer:

The rectangle

which should be the second option

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Multiply 2x(x2 + 5).

Irina18 [472]

Distributive property

2x^3 + 10x

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