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It must be an integer that is not even and not divisible by 3.  It must have a remainder of 2 when divided by 7 (because the set starts with 2);

I make 2011 the first to satisfy these conditions.

n=6,3+i√32,3−i√32n=6,3+i32,3-i32, do you mean solve for n?

To find the area of triangle(ABE), we can use the formula  A  =  ½·base·height.

We can use AB for the base.

Since AH = 5 and ABGH is a square, AB = 5.

To find BE:  

  -- since AB = 5 and BC = 10, point B is 1/3^rd the distance from A to C.

  -- likewise, BE will be 1/3^rd the distance from C to D

  -- since CD = 10, BE  =  (1/3)·10  =  10/3

So, the area of triangle(ABE)  =  ½·(5)·(10/3)  =  8 1/3.

LOL, for some reason, titaniumrome is in the leaderboard now, for some reason, but then I scroll down for leaderboards rom is in the leaderboards, you know what I mean, hugo??

The formula for the volume of a cone is:  V  =  (1/3)·pi·r²·h

The diameter is 8 feet, so the radius is 4 feet.

The height is 75% of the diameter:  75% of 8 feet =  0.75 x 8 feet  =  6 feet.

V  =  (1/3)·pi·r²·h  =  (1/3)·pi·4²·6  =  32 pi  cubic feet.

If you want to cheat on AoPS homework at least arrange your latex properly.

I actually don't think that's possible...

Whymenottnewton

LOL

I can do this all day!

thanks, you too, maybe I should change my name, so you would stop making fun of me (JK....)!!

Well then everything must be increased by k times on the larger one.

Why?

It says "the larger circle is a dilation of the smaller circle by a factor of k", which means the larger circles is k times larger. Which means that all parts of it are k times larger.

If the smaller circle's circumference is 2πr, we have 2πr * k = 2πR.

Point P = (1,3)

Point R = (7,5)

First, let's find the coordinates of M, which is the midpoint of PR.

For x, half-way between 1 and 7 is 4.

For y, half-way between 3 and 15 is 9.

So the coordinates of M are (4,9).

This point is reflected over the x-axis -- which means that the x-value remains the same but

the y-value in now negative. This new point is (4,-9).

The sum of the coordinates of this image point is 4 + -9  =  -5.

So let's say x is the money they made at 10 dollars(a) and 12(b). The two variables are for the number sold.

They reversed it so that it was 12(a) and 10(b).

Thus

12a +10b = 10a + 12b + 378

Some rearrangement:

12a +10b - 10a -12 b = 378

2a - 2b = 378

a-b = 189

So we sold 661 tshirts.

661-189= 472,/2 = 236

So b = 236 and a = 236 + 189 = 425.

425*10 + 236*12 = 7082

Flip around, 425* 12 + 236 * 10 = 7460.

7460- 7082 = 278.

Thus 425 at 10, 236 at 12.

if you don't understand anything feel free to ask.

Great solution, whymeissmart hehehe

Sine, Cosine and Tangent are the main functions used in Trigonometry and are based on a Right-Angled Triangle. Before getting stuck into the functions, it helps to give a name to each side of a right triangle: "Opposite" is opposite to the angle θ "Adjacent" is adjacent (next to) to the angle θ. Does that help? whymenotsmart^m^.

Well, since x = 10 dollar shirts

Then:

661 - x = 12 dollar shirts

10x + 12 (661-x)  + 378 = 12x + 10(661-x)

10x +7932 - 12x + 378 = 12x +6610 -10x

So: x = 425    shirts at $10

Hope this helps, whymenotsmart^m^.

29400 in scientific notation is 2.94 x 10⁴.

The rectangular block 10 inches by 10 inches by 5 inches is cut into cubes, 1 inch per side.

This block has  10 x 10 x 5  =  500  of these 1 inch cubes.

Every block on the outside inch has some chocolate. Only those completely in the inside

do not. The inside consists of a block  8 inches by 8 inches by 3 inches.

There will be  8 x 8 x 3  =  192  blocks that have no chocolate.

The percentage is:  192 / 500  =  0.384  or  38.4%.

wow i didnt realize that that was that simple

thank you! thats perfect

As follows:

I'll leave you to sum the two values.

Don't simply accept the results I've presented - check them yourself!

Let's draw a graph.

SO we have a parellogram with base 6, height 8.

How do we calculate the area of a paralellogram? base * height. Why? If you cut off a triangle from the side and move it to the other side it forms a rectangle, but witht the same altitude and base.

6*8 = 48.

If you don't understand anything feel free to ask!

Angle PBC is 72 degrees.

First, you can check if its true for a = b = c = 0, because then all the roots are 0.

p:q = 3/5, so p + q = 8.