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If the chain rule confuses you here is another way to look at it.

\(y=b^x\\ lny=lnb^x\\ lny=x*lnb\\ x=\frac{lny}{lnb}\\ \frac{dx}{dy}=\frac{1}{ylnb}\\ \frac{dy}{dx}=ylnb\\ \frac{dy}{dx}=b^xlnb\\ \)

I'm with our guest on this one.

Your question does not make sense tetre :/

Thanks Guest, I just wanted to think this one through myself :)

a=9k₁-1    that satisifes both the first and the last congruences

a=5k₂-1

a=7k₃-1

So if a is 1 less than a multiple of 5 and 9 and 7 then it must be 1 less than any common factor of 9 and 5 and 7

So the smallest one is 1 less than 315

answer 314

That’s a good answer too. But how do you know that is the discount in this world?

If you count the $20 rebate then the discount is minus 1900%

it's 50%...s

That’s true in this world, but in alternate realities, it can be anything. His question has an alternate reality to it, so an answer from an alternate reality seems apropos.

I came up with the answer without smoking any pot.  Maybe that would have helped in matching the answer to the question. 

But....he said, "the cheapest I pay it 1 dollar".

So.....if the cheapest price is 1 dollar, then it can't be at a 100% discount.

It’s not wrong. You don’t understand because you are smoking pot, or you are just a natural space cadet.

And...we posted it at almost the exact same time, LOL 

Wow! We approached the problem in an identical manner, and we explained our method nearly verbatim.

its wron.g...

Ok, answering this question requires some knowledge of functions. 

\(f(x)=3x^2-2x+4\)

\(g(x)=x^2-kx-6\)

When the question asks what is f(10)-g(10), the question is asking what the functions equal to when x=10.

Let's do just that first. I'll evaluate them separately.

Now, let's evaluate the other function.

Ok, now we have to do f(10)-g(10)=10:

Ok, I am done now! 

f( x )  =  3x² – 2x + 4                    To find  f(10)  , replace every instance of  x  with  10 .

f(10)  =  3(10)² – 2(10) + 4            Simplify.

f(10)  =  300 – 20 + 4

f(10)  =  284

g( x )  =    x² – kx – 6                    To find  g(10)  , replace every instance of  x  with  10 .

g(10)  =  (10)² – k(10) – 6              Simplify.

g(10)  =  100 –10k – 6

g(10)  =  94 – 10k

f(10) – g(10)  =  10                        Replace  f(10)  with 284  . Replace  g(10)  with  94 – 10k  .

284 – (94 – 10k)  =  10                 Now solve for k. Distribute the  -1  to both terms in parenthesees.

284 – 94 + 10k  =  10                  Combine  284  and  -94  .

190 + 10k  =  10                          Subtract  190  from both sides.

10k  =  -180                                 Divide both sides by  10  .

k  =  -18

The cheapest discount is 100%.

I often find places where I get the item free and they also pay me $20 to buy it.

help please

Ok, I will assume for this problem that the 5 is labeled in inches, even though it does not say in the diagram. Yet again, I'll attempt to create a makeshift diagram like I did for you before.

      A                      5in                            B

      ------------------------------------------------

    /  |                                                     |  \

   /   |                                                     |    \

  /    | (2*sqrt(3))in                                 |      \

 /     |                                                     |        \

/      |                                                     |          \

--------------------------------------------------------------

D    E                                                   F           C

Let's remember what an altitude is; an altitude is the height that runs perpendicularly from a base to a vertex of the figure. Therefore, \(m\angle AED =90^{\circ}\). We already know that \(m\angle D=60^{\circ}\) by the given info. Of course, by the triangle sum theorem, \(m\angle DAE=(180-(90+60))^{\circ}=30^{\circ}\).

What does this mean? We have identified a 30-60-90 triangle in the diagram, and that is a special one! Let me explain with a diagram:
 

this is aops!!!!!!1

2/8 =1/4 so is 0 remainder 1

Just take the volume of rectangular prism divide by the volume of cube

Incorrect.

Your solution to 2x+4 is wrong.

Since the LCM of  3, 5, 7, 9 =315, and the remainders are 1 less than the moduli in each case, therefore the smallest number that satisfies the congruences is:

315 - 1 = 314, so that you have:

315N + 314 and N =0, 1, 2, 3......etc. So:

a = 314, 629, 944.....etc. 

Do you mean \(2-x-2=4\)?

If so, I will solve it as so:
 

If you are ever unsure if you have the correct value for your unknown, just plug it back into the equation:

If you are going to list decimals, I would highly advise separating them with commas, as opposed with a numbered list. The decimals are confusing to read. If you want to use a numbered list still, I would do what I did below.

This is how I would revise your question:
 

Write each decimal as a fraction in simplest form.

1) 0.222

2) 0.1515

3) .0242424

4) 0.5555

5) -0.124124124

This is what I perceive the intended decimals to be, but I am not entirely sure, so correct me if I am wrong. 

I will start with the first decimal, 0.222.

I will do the next decimal, 0.1515

I will do the next decimal, as well.

Here goes the next one:

And, of course, here is the next one, -0.124124124.

You are done now!

yes its 96in^3