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guajiro [1.7K]
3 years ago
13

Please help, I'm in trouble for not doing my homework, this is missing btw. First correct answer gets brainlist!!!!!

Mathematics
1 answer:
e-lub [12.9K]3 years ago
6 0

Answer:

I think the answer is A........

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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
3 years ago
Read 2 more answers
2 3/4 - 1 1/8=?
Airida [17]
Basically you need to make the denominator (whats on the bottom) the same, lets take the first one for example


2 3/4, lets put this all over 4 for the same denominator.

2=8/4, and then add this to 3/4 to get 11/4.

the second part will work the same way,

start by making 1 into 8/8. add this to 1/8 to get 9/8


now we have to add 11/4 and 9/8. to do this, you have to find the smallest multiple between the two (for example: between 6 and 4 it would be 12, since 4*3= 12, and 2*6=12)

now, the smallest common multiple between 4 and 8 would just be 8


11/4= 22/8, since you multiply the bottom and top by the same amount so it still equals 11/4, but your denominator will now be 8.


now you can subtract. 22/8- 9/8= 13/8


final answer: 13/8


try the rest yourself since this is important for later math, hoped this helped :)


3 0
2 years ago
Read 2 more answers
one days discharge at its mouth, 3 trillion gallons, could supply all of country A’s household for 5 months. how much water an a
serious [3.7K]

let's use engineering notation for the sake of brevity.

1 trillion is 1,000,000,000,000, or just 1E12, twelve zeros.

1 million is then 1E6, six zeros.

we know the discharge for one day is 3E12 gallons, and that'd do just fine for country A for 5 months.  How many gallons in 1 month only?

\bf \begin{array}{ccll} gallons&months\\ \cline{1-2} 3E12&5\\ x&1 \end{array}\implies \cfrac{3E12}{x}=\cfrac{5}{1}\implies 3E12=5x \\\\\\ \cfrac{3E12}{5}=x\implies 6E11=x\implies 600000000000=x

if there are 200million inhabitants in A, namely 200E6 or 2E8 inhabitants, how many gallons per inhabitant from all those 6E11 gallons?

\bf \begin{array}{ccll} gallons&households\\ \cline{1-2} 6E11&2E8\\ x&1 \end{array}\implies \cfrac{6E11}{x}=\cfrac{2E8}{1}\implies 6E11=2E8x \\\\\\ \cfrac{6E11}{2E8}=x\implies \cfrac{600000000000}{200000000}=x\implies 3000=x

5 0
3 years ago
Write the equation in vertex form and then find the vertex, focus, and directrix of a parabola with equation x=y^2+18y-2
kakasveta [241]

Answer:

Part 1) The vertex is the point (-83,-9)

Part 2) The focus is the point (-82.75,-9)

Part 3) The directrix is x=-83.25

Step-by-step explanation:

step 1

Find the vertex

we know that

The equation of a horizontal parabola in the standard form is equal to

(y - k)^{2}=4p(x - h)

where

p≠ 0.

(h,k) is the vertex

(h + p, k) is the focus

x=h-p is the directrix

In this problem we have

x=y^{2} +18y-2

Convert to standard form

x+2=y^{2} +18y

x+2+81=y^{2} +18y+81

x+83=(y+9)^{2}

so

This is a horizontal parabola open to the right

(h,k) is the point (-83,-9)

so

The vertex is the point (-83,-9)

step 2

we have

x+83=(y+9)^{2}

<em>Find the value of p</em>

4p=1

p=1/4

<em>Find the focus</em>

(h + p, k) is the focus

substitute

(-83+1/4,-9)

The focus is the point (-82.75,-9)

step 3

Find the directrix

The directrix of a horizontal parabola is

x=h-p

substitute

x=-83-1/4

x=-83.25

6 0
3 years ago
The following tree diagram shows the possible outcomes for the experiment.
Bingel [31]

Answer:

It should be 1/2 because they both have the same amount of wins and loses.

4 0
3 years ago
Read 2 more answers
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