Question

Please, someone explain this to me;
Solve for R in 1 equation (in terms of S and T and k): R is inversely proportional to S and R is directly proportional to the cube of T

Answer 1

r = t^3/s

Answer 2

in terms of t, s, AND k

Answer 3

actually i think it's:
r = k*t^3/s

Answer 4

"Please, someone explain this to me;"

Answer 5

directly proportional means equal to pretty much..
So if a is directly proportional to b, then a=b

Answer 6

inversely proportional means equal to 1/ that number

Answer 7

r = k/s
r = kt^3
I got this far but I'm not sure from here

Answer 8

No u just keep one constant

Answer 9

You are incorrect about inverse and direct
direct: y = kx
inverse: y = k/x

Answer 10

It's proportional to one and the inverse of the other at the same time..
I'm not incorrect, ignore the constant for now

Answer 11

why?

Answer 12

The constant is ALWAYS put all the way at the end

Answer 13

How come?

Answer 14

First you finish your equation, then you stick it on top.. unless the constant is initially given, because then when u multiply the values, u'll end up with k^2, which is still a constant, so it's still k

Answer 15

I mean just put it out in front all the way at the end

Answer 16

amistre i dunno how to explain this...

Answer 17

Oh, that makes sense, if you put it on both, then you would have 2 ks, is that what you are saying?

Answer 18

directly porportional is when the value of one increases the other decrease:

x*y = 5 is directly porportional; if x gets big, y has to shtink to retain the same value

Answer 19

amistre probably has an explanation lol

Answer 20

wait really???

Answer 21

i didnt learn it that way

Answer 22

i learned direct both increased and inverse one increased as the other decreased

Answer 23

amistre directly proportional is x=y, ur equation would give x = 1/y

Answer 24

indirectly is when the values increase or decrease at the same time

y/x = 5 is an indirect porportion since an increase in one results in the increase of the other to retain the same value

Answer 25

i could be hazy on it, so let me recheck the google :)

Answer 26

inversely proportional is x*y=constant

Answer 27

amistre i think you got it backwards

Answer 28

its possible :) but if so then youve got a pretty good bead on it

Answer 29

lol yea.. he prolly did this years ago

Answer 30

I just don't understand how to get one equation out of the two

Answer 31

just relate them to it in the same manner

Answer 32

will you show me?

Answer 33

All right listen:
R = kT^3/S

Answer 34

What does:

R is inversely proportional to S imply then? since your right lol

Answer 35

r = k/s

Answer 36

Inversely is 1/S

Answer 37

or k/s

Answer 38

good;

and what does and R is directly proportional to the cube of T imply?

Answer 39

r = t^3

Answer 40

kt^3 sorry

Answer 41

then we put those toghter to form:
\[r=k\frac{t^3}{s}\]

Answer 42

how exactly?

Answer 43

we just went over the how part

Answer 44

r is related to both s and t in these matters

Answer 45

manner

Answer 46

are you related to your mother and father?

Answer 47

but
kt^3 = k/s
kst^3 = k
st^3 = r

Answer 48

Yes, I am. Hopefully

Answer 49

we are not equating k with k; we are relating how r is related to t and s

Answer 50

k is just a byproduct that makes the whole thing consistent

Answer 51

mother = father is what your trying to determine as an analogy :)

Answer 52

?

Answer 53

stop equating the 2 parts and unite them under the constant of parent

Answer 54

I'm sorry

Answer 55

is mom = dad what I was doing, or what i need to be doing?

Answer 56

what you were doing, so stop it lol

Answer 57

okay, what am I trying to do?

Answer 58

r is related to s how?

r is related to t how?

Answer 59

r = k/s
r = kt^3

Answer 60

not "k"; just s and t

"k" is not a relation to r, its a consequence of it

Answer 61

but isnt r a consequence of s and k?

Answer 62

as r changes, k stays the same so it of no relation

as r changes both s and t change, they are related to r

Answer 63

Ah! Well worded! k always stays the same because it's a constant, but as one variable changes the other has to since k cant change!

Answer 64

yep

Answer 65

But now what do i do?

Answer 66

since r is related to s and t in some manner, combine the terms for s and t into their proper relations with r

when mom and dad are in the same room, their relationship with you doesnt change does it?

Answer 67

aunt betty comes over for dinner does the family disintegrate?

Answer 68

no it does not.

Answer 69

does aunt betty = k?

Answer 70

then r keeps its same reltaion to s and t as it always has

lol, aunt betty = some other relation to r that is not mentioned

k is just the house, or dinig room, or whatever keeps the family in the same place packed together

Answer 71

r = k(relations)

Answer 72

if r doesnt = k/s
then how would you write an equation for it, just replace it with a random constant?
r = 1/s?
then r = 1t^3?

Answer 73

r = 1/s is a stated relation; but we all know that 1/5 so we have a constant of variation that always allows the relation to stay solid

Answer 74

soo slow on here

Answer 75

I'm sorry I just don't understand, thanks for taking your time though. where'd you get 1/5?

Answer 76

does 3 = 1/5? was what i typed but got lost in the etheral void of openstudy

Answer 77

say when r = 3, s=5 what makes this relation solid?

Answer 78

no, so how do we write an equation for r in terms of s that excludes k?

Answer 79

the final result has a k so that the relations are consistent.

Answer 80

3 = 15/5

20 = 15/something else lol

Answer 81

well, if the constant of variation is given, you cant change the other two variables to not match up with it, they have to follow r=k/s, if you have 10 = 20/s, s has to be 2, if we have 10 = k/10, k has to be 100

Answer 82

the relations dont change; so pack everyone together in the same k(..) to keep it mathematically consistent and happy

Answer 83

10 to 10 isnt the proper relation then and its a fraud if you have to change the k

Answer 84

you cant change k though, its a constant

Answer 85

you have to change the variables to match up with it

Answer 86

right, so 10 to 10 is not a valid relation between r and s in that case since you had to change k to match it

Answer 87

yes

Answer 88

but how do you combine the relations? and why just randomly multiply k out in front?

Answer 89

when we have values for r and s and t then we can determine what the proper k will be, but until then we just use it as a genereal fill in

Answer 90

how do you know that k * combined relations = r?

Answer 91

it doesnt say that r is related to s only when t is not around; and when t is around s leaves so that r is related to t and such; it says that r is related to s and t together

Answer 92

in this manner as such and such

Answer 93

okay so I get the r = t^3/s, but how do you know where to put k?

Answer 94

k is just the constant that ties it all together so that no random false relations stick their head in at the family reunion it goes where its always gone; as a multiplier to keep the pease

Answer 95

It was not multiplied in r = k/s

Answer 96

Just forget about it. I don't think I'll get this. Thanks for your help and time.

Answer 97

I'll just teach myself by saying that r = k/s and r = kt^3
then wanting t somewhere in r = k/s, so asking myself what relation does k have with t, and saying it's multiplied by t^3 so r = kt^3/s, similarly, ks relation with s is k is divided by s so in r = kt^3 becomes r = kt^3/s. Not sure if that is the way to do it but I like that way.