Question

I have two questions!!!

Answer 1

HEllo!

Answer 2

It seems to have just gotten better but until now it was not loading properly!

Answer 3

@pitamar

Answer 4

dude I'm almost done

Answer 5

Ok, have you read the website I sent you about variation?

Answer 6

I was reading it yes

Answer 7

let me go back and finish

Answer 8

ok I"ll read and talk to you about this

Answer 9

Ok =)

Answer 10

Leave the specific question aside for a moment. Tell me, if x varies directly with y, what does it mean?

Answer 11

Well I would think that it meant that they were constricted together

Answer 12

but the website says .... increases, y increases by the same factor. In other words, y and x always have the same ratio:

Answer 13

Ok, think about it this way. Say I made a machine that makes you bigger. I used it and made your whole body twice as big than it is now.
How big is your arm now compared to before?

Answer 14

Twice as big as before!

Answer 15

Right, that's because there is a proportion between your arm size and your body size.
If I make your body 3 times as big, then the arm will get 3 times as big too.
But that doesn't mean they are equal, the arm is always smaller than your body, but there is a proportional relation.

Answer 16

Now, what makes it possible is the fact that your arm will always take a fixed part of your body size.
Let's try to think about something easier to compute. Say we're talking about your house instead. Say your room is 1/5 of the house.
It doesn't matter if I make the house bigger or smaller, your room will grow or shrink with the 'same factor' as the house and it will always be 1/5 of the entire house.

Answer 17

see what I mean?

Answer 18

ok gotcha

Answer 19

yes it makes sense

Answer 20

so what are you thinking now?

Answer 21

And it stopped working again! yay!
Anyway, direct proportion means there is a constant ratio between two variables. Like your house size and your room size.
It is the same as saying:
$$
\frac{x}{y} = k
$$Which becomes:
$$
x = k \cdot y
$$
So since we are told here that x and y are in direct proportion then they have to fulfill this form.
We don't know the that constant ratio \(k\). but that's why we're also told that \(x=4\) means \(y=-16\)
So we plug in:
$$
x = k \cdot y \implies 4 = k \cdot (-16)
$$And we have to solve for 'k'. Can you do it?

Answer 22

ok dude im good

Answer 23

You mean you finished this question?

Answer 24

yes

Answer 25

ok good =)

Answer 26

I got 1/4 is that right?

Answer 27

i did what u said

Answer 28

let's see. if we have
$$
4 = k \cdot (-16)
$$In order to find k we have to divide both sides by -16. so we get:
$$
\frac{4}{-16} = k
$$what does that simplify to?

Answer 29

oh its actually -1/4

Answer 30

Yes. and plugging back in the original equation:
$$
x = k \cdot y \implies x = -\frac{1}{4} \cdot y
$$

Answer 31

so that would D unless when you y*-1/4 it turned it postive

Answer 32

the equation is $$ x = - \frac{1}{4} y$$ because it describes the direction proportional relation between x and y. no matter what x or y are.

Answer 33

i think it wouldnt -/+=-

Answer 34

ok gotcha last one

Answer 35

but that actually made a lot of sense

Answer 36

This equation shows us that when y = -16 then indeed x = 4, that is how we got it. if y wasn't negative, say y = 8, then we'd get:
$$
x = - \frac{1}{4} \cdot 8\\
x = -2
$$So x could become negative. but the relation is still of the same form.

Answer 37

ok good I"ll keep that

Answer 38

=)

Answer 39

from just doing this I am thinking it would be C right off the bat

Answer 40

I'm gonna think for a sec though

Answer 41

Leave the question aside for a moment again. Now off-the-record, what 'x varies inversely with y' means?

Answer 42

I'm thinking it means that they are alike by the same ratio.

Answer 43

x and y that is

Answer 44

well, you can read it on the website I sent you.
If 'x varies directly with y' means:
$$ \frac{x}{y} = k $$ Then 'x varies inversely with y' means:
$$x \cdot y = k$$

Answer 45

hmm alright

Answer 46

If you compare the two forms then you see that in 'direct variation' we have ratio, so if x got twice as big, then so does y in order to keep the same ratio.
But here we have their product being constant. So if x got twice as big, then y has to get twice as small(!)
Now big and small are not exactly mathematically accurate words, but to understand what it means we can just play with it.
Say we are told:
$$
x \cdot y = 5
$$So for x = 1, y has to be 5:
$$
1 \cdot y= 5 \implies y = \frac{5}{1} = 5
$$But if we say x=2... then:
$$
2 \cdot y = 5 \implies \frac{5}{2} = 2.5
$$So you can see that multiplying x by 2 caused y to divide by 2. That is inverse variation.

Answer 47

oh ok gotcha

Answer 48

We can form our equation a little and say:
$$ x \cdot y = k \implies x = \frac{k}{y} $$Right?

Answer 49

But if we go back to the question, we have: 'x varies inversely with the cube of y'. so x doesn't vary inversely with y, but with its cube! so what is the cube of y? it would be \(y^3\)
And x varies inversely with that! Which means x and \(y^3\) have a constant product. So:
$$
x \cdot (y^3) = k \implies x = \frac{k}{y^3}
$$

Answer 50

ok i gotcha

Answer 51

Good =)

Answer 52

that makes sense

Answer 53

ok i got something for you too see how good at math you really are its easy ok

Answer 54

its not any of my work at all

Answer 55

I put this little quiz for you together are you ready?

Answer 56

well sounds interesting, but I don't claim to be good at math. Let's just say that it is one of those things where 'good' is a very relative term...

Answer 57

there easy

Answer 58

Well I have to go and eat, is it something you can post and I'll see afterwards?

Answer 59

I can post them ok then you can answer them k

Answer 60

Ok, i'll be back later =)

Answer 61

1.

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2.

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3.

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4.

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5.

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6.

Answer 67

7.

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8.

Answer 69

9.

Answer 70

10.

Answer 71

11.

Answer 72

12.

Answer 73

13.

Answer 74

14.

Answer 75

15.

Answer 76

Ok remember to number them when you answer so I can check them.. good luck and have fun

Answer 77

Lol, that's no riddle.. it is your HW =\

Answer 78

At least see if you get them correct and they arent HW

Answer 79

its made on the same platform as my work but isnt

Answer 80

ok dude I"ll work on number one you work on number two how does that sound?

Answer 81

Ok.. well let's see, not that I have ever seen this stuff but ok.
First question, I'd say B - cross-sectional, because the poll is a one-time thing that comes to describe the state at the moment it is taken.
Second, I'd say discrete data, because number of books cannot be fraction. The number of books is also not limited to a number of predefined categories, so I'd go with C - discrete..

Answer 82

Ok, dude I figured out number one: i was thinking b or c myseld so WHOAAA