kitty<3

Late to the party, as usual~

Thanks, Melody! As I recall, we do like to brighten things up around here . . . you know, with all these people like zegroes around:)

And hey CPhill, maybe you can convince zegroes to lose the "g" from his name. I'm sure he won't mind at all. Then, voilà! Enough zeroes to last you another M years!

You would use arccosine to solve this problem, since you have the cosine and need the angle:

cos(x) = -1/2

x = acos(-1/2)

x = $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)} = {\mathtt{120^{\circ}}}$$

* Which is also equal to 2pi/3 radians.

The formula for finding the sum of a polygon's interior angles is 180(n-2), where n is the number of sides/angles.

Thus, for an octagon:

Sum of interior angles = 180(8-2)

= 180(6)

= 1080

Since the 8 angles are congruent, simply divide 1080 by 8 for the measure of each angle:

1080/8 = 135 degrees

Yes, there is:) It is in the top left corner of the site calculator, next to "2nd."

I think Anonymous and Melody were both onto something . . . so I just took the liberty to expand on their reasoning a bit, if they don't mind:)

They both mentioned negative and positive, as "never" has a negative connotation and "always" has a positive connotation.

So,

"Never forget" would mean that something was such a horrible experience that you could not erase it from your mind (negative), while "always remember" would mean that something was such a good experience that you believe your memory has engraved it in your mind until the end of time.

So while both essentially mean that your brain has stored the memory, they would correspond to different emotions.

^That's my two cents' worth, anyways:)

Aw, thanks Rosala:)

"What's in a name," anyways? :P

Hello Melody! And hello TJM, nice to meet you this way:)

It is always great to drop by and see the forum is busier than ever

The way I interpreted it, the man wants to make a 20% profit on the bag after the 15 discount.

In this case, you would first find what 20% profit on $30 is, and then find what the total would be before the 15% discount:

So:

20% * $30 + $30

= 1.2 * 30

= 36

So the man would need to sell the bag for a final price of $36, after the discount.

Therefore, we now need to find the price of the bag before the 15% discount, which we can call x:

x - 0.15x = 36

0.85 x = 36

x =42.35

So he needs to sell it for $42.35 before the discount, or $36 after the discount.

Always welcome! :D

While the cosine of a given angle is used to find the ratio of its opposite side / hypotenuse, the arccosine does the opposite: it finds the measure of an angle from the given ratio of its opposite side / hypotenuse.

For example,  $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{45}}^\circ\right)} = {\frac{{\sqrt{{\mathtt{2}}}}}{{\mathtt{2}}}}$$

So $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{{\sqrt{{\mathtt{2}}}}}{{\mathtt{2}}}}\right)} = {\mathtt{45}}$$

So if you had the lengths of the opposite side and the hypotenuse for a right triangle, you would use arccosine to find the measure of the angle.