CPhill

The Queen seemeth to be off her rocker.....er, I mean throne......She claimeth that a "real" number was unspecified, yet, was not her answer a "real" number??? Further, this disputes M'Lady's assertion that a woman winneth the argument >95% of the time....Sir Cphill has given an answer which hath more power than the Queen's doth have.....thus, Sir Cphill hath won 100% of the time in this argument.....

Also, two things come, alphabetically, after a "Trilllion"....."Trilobite" (a Fossil) and "Tyrannosaurus" (a Dinosaur). But, the Fossil precedeth the Dinosaur....thus, the Fossil possesseth more precedence than the Dinosaur in all things.......

The Queen may now returneth to her rocker......er, throne......

Your Humble Answerer,

Sir CPhill

I'll help with a few, but I'm not going to give you the answers...I'll show you how to arrive at the answer for yourself.......deal???

1) When we have the form, y= mx ± b, the y intercept is given by  (0, ±b). Thus, if I have the equation y = -5x - 4, the y intercept is  just   (0, -4)...that should help you get started.....

2) To find the slope, subtract the y coordinates in any order. Then subtract the x coordinates in the same order. Then, put the first result over the second....that's the slope  !!!!    For example, suppose we have  (3,1) and (6,9). Subtract the y coordinates (9 - 1 = 8). Then subtract the x coordinates in the same order (6 - 3  = 3). Then the slope is 8/3.......

3) In equalities, I like to get the x's on the left side and everything else on the right. So. if I had, 5x - 5 <  2x + 9, I would first subtract the 2x from both sides giving 3x - 5 < 9. Now, add 5 to both sides and we have 3x < 14. Now divide both sides by 3 to get "x" on the left side by itself, and we have.......x < 14/3........

Work on these first and tell me how you're doing in a post.....I'd rather answer any questions you might have about these than going any further......

Sounds like fun.......enjoy..............!!!!

Are you going on a vacation???

True...but "integer" wasn't specified..........????

I think my sunglasses might be hiding in one of those cupboards......!!!!

Using the sum and difference identities for the sine, we have......

[sin(pi/4)cosA + sin(A) cos(pi/4)] * [sin(pi/4)cosA - sinAcos(pi/4)] =

[sin(pi/4)cosA]² - (sin(A)cos(pi/4)]² =

[(1/2)cos²A] - [(1/2)sin²(A)] =

(1/2)[cos²A - sin²A] =

(1/2)cos2A

Which is the same as your answer, Sasini .....  !!!!

We can't say......no matter what you might say comes next, I can always find a real number that lies between your number and a trillion.....

However, if you're just interested in the names of "large" numbers, here you go:

Melody is correct....there's not much you can do here, unless you would like to set this = 0 and graph it...in that case we get a "rotated conic"  (a hyperbola) which is kinda' cool.....(the presence of the "xy" term implies a "rotated" graph)

The cosine = 1/2 at 60 degrees and at 300 degrees.

So we need to divide both angles by two for 2 theta (or 2 sigma).

So we have 30 degrees and 150 degrees.

Using the tangent inverse, we get about 42.61°....But the tangent is also positive in the 3rd quadrant, so this angle may also be 180 + 42.61   =  222.61°