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pashok25 [27]
3 years ago
10

One month, Ruby worked 6 hours more than isaac, and Svethlana worked 4 times as many hours as Ruby. Together they worked 126 hou

rs. How many hours did each person work?
Mathematics
1 answer:
stepladder [879]3 years ago
4 0
63.............................................
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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.

7 0
2 years ago
Read 2 more answers
Greg builds a new pond which has a volume of 7.35 m3. What is the width of the pond?
arsen [322]
The pong will be at 3.5 m
5 0
3 years ago
Consider the polynomial P(x)=x⁴+3x³-28x²-36x+144. Write the equation of P in factored form.
garik1379 [7]

Answer:

P(x)=(x-2)(x-4)(x+3)(x+6)

Step-by-step explanation:

Given: P(x)=x⁴+3x³-28x²-36x+144

It is a polynomial with degree 4.

It should maximum four factor.

Hit and trial error method.

Put x = 2 into P(x)

P(2)=2⁴+3×2³-28×2²-36×2+144

P(2) = 0

So, x-2 would be factor of P(x)

Now divide x⁴+3x³-28x²-36x+144 by x-2 to get another factors

(x^4+3x^3-28x^2-36x+144)\div (x-2) = x^3+5x^2-18x-72

P(x)=(x-2)(x^3+5x^2-18x-72)

Put x = 4

P(4) = 0

now divide x^3+5x^2-18x-72 by x-4

(x^3+5x^2-18x-72)\div (x-4) = x^2+9x+18

P(x)=(x-2)(x-4)(x^2+9x+18)

Now factor x^2+9x+18

\Rightarrow x^2+9x+18

\Rightarrow (x+6)(x+3)

Complete factor of P(x)

P(x)=(x-2)(x-4)(x+3)(x+6)

7 0
2 years ago
What is the value of x? Assume that the line is tangent to the cirlce.
Vanyuwa [196]
It’s definitely not D or A but the closest one would be C, that’s what I would put. So the answer might be C.90
4 0
3 years ago
Read 2 more answers
Hannah buys 3 pack of 36 exposure film and 2 packs of 24 exposure film.She uses 8 rolls of film.How many rolls does she have lef
xeze [42]
3 times 36= 108
2 times 24= 48
108+48= 156
156-8=148 rolls
3 0
3 years ago
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