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Samantha worked for an hour at time-and-a-half and was paid $36.90.

Yes I can see why you find it confusing.

When I get confusing questions I change the numbers to easier ones to see what will happen.

If I can work out how to do an easier one then I can use the same method to do the hard one.

Say Samantha worked 1 hour at double time and got paid $20

(double time means 2*normal pay - So samantha would get paid twice as much as normal)  

Then normal pay would be $10 per hour, right?  Because   OR 2*10=20

okay, how can i put 2 and 20 together to get 10? Umm,    20$$\div$$2 = 10   That is good

$20  $$\div$$ 2 hours = $10 dollars per hour.

NOW  yours is time and a half that is 1.5 *normal pay and that equalled $36.90 for 1 hour

so normal pay must be $36.90 $$\div$$ 1.5     = $24.60

Think about it and tell me if that works for you.

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CPhill and I were doing this at the same time.  If you understand his method it is better than this one!

Thank you very much :)

(1hour + 1/2hour)* pay = $36.90

1.5*pay=$36.90  

divide both sides by 1.5

pay = $36.90/1.5

pay = $24.60

** You should learn to recognise this.

When you factorise a difference of 2 squares this is what you get. One bracket is the conjugate of the other.  Only the sign in the middle is different.

$$x^2-a^2=(x-a)(x+a)$$    

OR if you simplify

$$(x-a)(x+a)=x^2-a^2$$

Yours was 

(m-2)(m+2) so the answer should become obvious to you as  $$m^2-2^2=m^2-4$$

Thanks Alan

It's sin^-1 Melody:

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{11}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{13}}^\circ\right)}}{{\mathtt{6.8}}}}\right)} = {\mathtt{21.339\: \!374\: \!187\: \!23^{\circ}}}$$

I guess you just want this to be expanded?

(m+2)(m-2) = m² - 2m + 2m - 2² = m² - 2² = m² - 4

The equation -(1/2) = 6x + 10 represents a vertical line on a graph at a fixed value of x (at x = -7/4), so for the line y=mx to be parallel to this you must have m = ∞. 

However, if you meant the first equation to be -(1/2)y = 6x + 10, then this can be rearranged as y = -12x -20 so for y = mx to be parallel to this m = -12 (i.e. the gradients must be the same).

Approximately one third of the time. 

About 333 times

I will assume that it is 13 degrees and that you only want a first quadrant solution

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\mathtt{11}}{\mathtt{\,\times\,}}\left({\frac{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{13}}^\circ\right)}}{{\mathtt{6.8}}}}\right)\right)} = {\mathtt{21.339\: \!374\: \!187\: \!23^{\circ}}}$$

And that is the only solution.

I think that is right  

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**I had made 2 mistakes here (I think I have fixed both)

First, as Alan pointed out, I used cos-1 instead of sin-1.  

The second mistake I made was 'forgetting' that sin-1 is only defined for $$-90^0\le x \le 90^0$$

So I am going to fix both these problems and leave the answer correct. (That is the plan)

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**What is the symbol for integers in LaTex?

$$\frac{3}{4}=\frac{6}{8}\\\\
\frac{6}{8}+\frac{1}{8}=\frac{7}{8}$$

I love it!!!     Thanks guys.   You are hilarious!!

I can't stop laughing!!

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This is a thread that Morgan Tud is alluding to.

http://web2.0calc.com/questions/how-many-current-digits-of-pi-are-known#r102769

There's no question here, but I'm assuming you may want a graph of this??

Note that it's a line with a slope of (-1/3), a  "y intercept" of 7/3 and an "x intercept" of 7.

never mind i found the answer

Let's call the original price "x."  So, if the sale price was 20% off of the original price, it must just be on sale for 80% of its original price. Therefore....

80%   OF  x  = $68   

Now change the 80% to a decimal - .80 - and let's realize that "OF" means "multiply"

So we have

.80x = 68    Divide both sides by .80, and we have

x = 68/.80 = $85

And that's the original price.

No it is not. 0 is not greater than infinity.

I just did a quick internet search because I wasn't sure it radicals had to be irrational.  If they did then you question would have no answer.

But I found no evidence that this was the case so there are many answers.

$$\sqrt{8.7\times8.7}=\sqrt{75.69}\\\\
\sqrt{8.7\times8.7\times8.7}=\sqrt[3]{658.503}\\\\$$

These are just 2 of the answers.

anyone want to comment?

That is an excellent idea.  You want to write or reference it somewhere in the puzzle threads.

 Reinout takes good care of them, and i really appreciate that,  but they could do with being organised a little better.  Maybe we should brain storm this one.  A lot of things need to be reorganised now that the forum has been revamped.

Thanks....I actually didn't really know WHAT to do, at first. I was going to try something "complicated," but then I remembered a problem from a math "puzzles" book that I have that was similar to this. In fact, now that I think of it, I might post it to the forum just so some people can take a stab at it !!

Hi Chris,

That answer is really elegant.  I'm impressed!

Andre,

I have tried to work through yours - just in my head (which doesn't work very well)

But I don't get it.  Maybe I'll look again later.

Sisyphus Goes To The Beach......

Using the Chain Rule, we have

G'(x) = aπ cos ( π x)

And

G''(x) =  -aπ² sin (π x)

... King Arthur, is eager for another head to hang in the royal court. By Lady Guinevere

-----

Your Highness, if I may, there is a much better head for His Majesty to hang in the royal court.

Sir Cumference of the Round Table. He’s the sorcerer who started this paradox of contradiction.

Yea, Sir CPhill, whom His Majesty hath just Knighted, stood as a guard to the chambers of the Knights and did witness the circular pun and the leads to a circular paradox by Sir Cumference.

Sir Cumference’s head would grace the yard of the Royal Court, much more than your lowly servant.

Indeed, Your Highness, Sir CPhill would be pleased to lob off the sorcerer’s head, for it was he, who, by trickery and deceit, sent Sir Cphill to find the Roman zero in the Bolder of Sisyphus.

I pray thee, consider my petition, and count me worthy to live.

Your lowly servant,

Morgan Tud

So we have

1((1.5)¹² -1) / (1.5 - 1) =

((1.5)¹² -1) / (.5 ) =

$$\mathrm{\ }$$$${\mathtt{2}}{\mathtt{\,\times\,}}\left({\left({\mathtt{1.5}}\right)}^{{\mathtt{12}}}{\mathtt{\,-\,}}{\mathtt{1}}\right) = {\mathtt{257.492\: \!675\: \!781\: \!25}}$$

Let's write

4³⁰⁰       ???      3⁴⁰⁰

(4³)¹⁰⁰  ???   (3⁴)¹⁰⁰

64¹⁰⁰    ???       81¹⁰⁰

And it's obvious that the thing on the right is greater than the thing on the left.

So.....

4³⁰⁰       <      3⁴⁰⁰

And there you go....