Wikipedia:Reference desk/Archives/Mathematics/2013 September 16

= September 16 =

help understanding my math homework.
Hi I'm not asking for the answer to my math homework. I just need help understanding *why* the correct answer to my homework is correct. I'm having a bit of trouble with the radical, logarithmic and exponential equations I'm being assigned.

For example, I'm told that the answer to the equation 3^(-6x-7)= the 7th root of 81 is x = -53/42. BUT WHY?

Here's as far as I get when trying to solve the equation. I know that 81 is 3^4. so there fore the 7th root of 81 can also be expressed as 3^(4/7).

On the other side I can do a bunch of things. For example, 3^(-6x-7) is another way of saying (3^-6x)/(3^-7). But I don't know what to do to get the -53/42. Any hints you can give me? — Preceding unsigned comment added by 71.199.18.97 (talk) 04:41, 16 September 2013 (UTC)


 * Good, you are almost there:

3(-6x-7) = 81(1/7)

3(-6x-7) = 3(4/7)

-6x-7 = 4/7

-42x-49 = 4

-42x = 53

x = -53/42


 * StuRat (talk) 04:58, 16 September 2013 (UTC)

OK, thanks. I guess I wasn't thinking that if 3^(-6x-7) = 3^(4/7) I could just forget about the 3 altogether and just set the exponents equal to each other. I have a few other problems in this format, so I will use this technique. Thanks again. — Preceding unsigned comment added by 71.199.18.97 (talk) 05:55, 16 September 2013 (UTC)


 * You're quite welcome. StuRat (talk) 06:55, 17 September 2013 (UTC)

StuRat (talk) 06:55, 17 September 2013 (UTC)

Tensors
A few questions which any pointers on would be very helpful.

1) Under what conditions can a rank-3 tensor $$T_{ijk}$$ be decomposed into three matrices such that $$T_{ijk} = \sum_n A_{in} B_{jn} C_{kn}$$? Is there any other way of viewing this property?

2) The identity is preserved under pre and post multiplying by a matrix $$X$$ and its inverse, i.e. $$X I {X}^{-1} = I$$ or in index notation $$\sum_{nm} X_{in} \delta_{nm} (X^{-1})_{mj} = \delta_{ij}$$. What is the relationship between three matrices $$X,Y,Z$$ such that they preserve a $$\delta_{ijk}$$ (which is 1 for i=j=k and 0 otherwise)? In other words what is the relationship between three matrices such that $$\delta_{ijk} = \sum_{nml} X_{in} Y_{jm} Z_{kl} \delta_{nml}$$? — Preceding unsigned comment added by 128.40.61.82 (talk) 13:04, 16 September 2013 (UTC)

math notation help
Sorry, I have another question regarding my homework. This one is simply about math notation. I am given a polynomial function for f(x) and a rational function for g(x). I am then asked to calculate "f∘g(0)=". What does that mean? I understand that I take zero and take "g of zero" for the rational function. But then what do I do with that result. Do I MULTIPLY that result by f(x) or do I plug that result into function f(x)? In other words does "f∘g(0)" mean f(x) TIMES g of zero or does it mean f OF g OF zero? — Preceding unsigned comment added by 71.199.18.97 (talk) 14:22, 16 September 2013 (UTC)
 * f∘g(0) means calculate g(0) and then calculate f of that number, or alternatively f∘g(0) = f(g(0)). See Function composition. Hut 8.5 14:36, 16 September 2013 (UTC)
 * Thank you! I was familiar with the notation "f(g(0))" but I had never seen it written the other way.--2001:1948:212:8810:CD6C:DF2A:3FC9:8808 (talk) 16:47, 16 September 2013 (UTC) (At a different computer now)
 * I read it as "f of g(0)".   D b f i r s   07:21, 17 September 2013 (UTC)

That proof "negative time negative equal positive" is wrong | What would happen if proved wrong proof ?
That proof "negative times negative equal positive" is wrong — Preceding unsigned comment added by 37.238.41.181 (talk) 17:40, 16 September 2013 (UTC)
 * Such a proof would be highly dependent on what you mean by "negative" and "positive". A "trivial" counter example is -i * -i = -1. "Negative i" times "negative i" is equal to negative one, not positive one. Most people would regard this as cheating, though, as the statement "a negative times a negative is a positive" is typically implicitly restricted to the domain of real numbers, and excludes imaginary numbers. Furthermore, a fair number of people would quibble that "negative i" doesn't really count as a "negative number" anyway, as -i is equally distant from -1 and 1, that distance being the same as +i is from both -1 and 1. - Though you say "that proof" as if you have a specific one in mind. If so, any further details you could provide on it would be helpful. -- 205.175.124.72 (talk) 18:05, 16 September 2013 (UTC)

I have a proof on this but I know proof "negative times negative equal positive"

this is

according to proof wrong

-(-a)=a

-(-a)+0

-a+a=0

-(-a)+(-a+a)

-(-a)+(-a)+(+a)

-(-a)+(-a)=0

0+(+a)

=a or +(+a)

this is wrongObaidNgers (talk) 18:34, 16 September 2013 (UTC)


 * 1] -(-a)=a ((This is the equality you believe to be false. ))
 * 2] -(-a)+0 (( An expression, left side of [1] with zero added. I believe you plan to do operations to this to come up with the reslt of the right side of [1] ))
 * 3] -a+a=0 ((A different equality - I presume you accept this equation as true. ))
 * 4] -(-a)+(-a+a) ((Substituting [3] into 0 of expression [2] ))
 * 5] -(-a)+(-a)+(+a) (( rearranging parentheses in [4] ))
 * 6] -(-a)+(-a)=0 ((A different equality - I presume you accept this equation as true. ))
 * 7] 0+(+a) (( Substituting [6] into [5] }}
 * 8] =a or +(+a)

So you have shown (non-rigorously) that -(-a)=a. Which is fine and isn't wrong. Please explain you problem more clearly. -- 82.26.184.89 (talk) 23:02, 16 September 2013 (UTC)