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V = [(3+8)/2] * 4 * 4.3  

They aren't allowed to repeat.

2)              first triangle              17--30--17

                 second triangle         17--16--17     

It says it's wrong I don't know why

" slightly"?!    area of a circle is exactly  10pi

r = sqrt( 10 ) = 3.16227766            angle (AOB) = 360º - 215º = 145º

A = 145º/360º * pi * r² = 12.65363708

A ≈ 12.654 

If cos(a) = 12/13, then the adjacent side is 12 and the hypotenuse is 13 (or a multiple of these).

If the adjacent side is 12 and the hypotenuse is 13, the opposite side is 5 (Pythagorean Theorem).

However, since the angle is in the 4^th quadrant, we'll have to make the opposite side = -5.

sin(2a)  =  2·sin(a)·cos(a)  =  2·(-5/13)·(12/13)  =  .......

cot(2a)  =  1 / tan(2a)  =  1 / (-5/12)  =  ........

The independent variable is the number of boxes of plums sold (because this can vary).

The dependent variable is the revenue because this depends upon the number of boxes sold.

Angle(AOB)  =  360^o - 215^o =  145^o.  

The radius of the circle appears to be slightly larger than 3, so the area of the whole circle is

slightly larger than  pi·3²  or a little more than 9 pi.

Since the central angle is 145^o, the area that we want is slightly more than

                  145/360·9pi  =  11.4 square units.

The closest answer seems to be 11 square units.

This expression will be undefined only when the denominator is zero

--->     a² - 4  =  0     --->     (a - 2)(a + 2)  =  0

So, the two times that the expression is undefined occurs when  a = 2  or  a = -2.

1 / |m|  >=  1 / 8

Multiply both sides by 8 and by |8|:

8  >=  |m|     --->     |m|  <=  8     --->     -8  <=  m  <=  8

The formula for the sum of the first n terms of a geometric series is:  Sum  =  a(1 - rⁿ) / (1 - r)

where         a = first term = ¼         r = common ratio = ½          n = number of terms

--->     255/512  =  (¼)·( 1 - (½)ⁿ ) / ( 1 - ½ )

--->     255/512  =  (¼)·( 1 - (½)ⁿ ) / ( ½ )

--->     255/512  =  (½)·( 1 - (½)ⁿ )

--->     255/256  =  1 - (½)ⁿ 

--->           (½)ⁿ  =  1 - 255/256

--->           (½)ⁿ  =  1/256

--->           (½)ⁿ  =   (1/2)⁸

--->                n  =  8 

Lol, clearly you're from AoPS. I can see your Avatar was created by a user... I forgot their name but they've made many avatars xD

First one:

1)  Since AP = PB = 4 and triangle(APB) is a right triangle:  AB²  =  AP² + BP² 

               --->   AB²  =  4² + 4²   -->  AB  =  .......

2)  Since BP = PD and P is the midpoint of BD   --->   BD = 8

     Since triangle(BDC) is similar to triangle(BPA), DC = 8.

3)  Since(triangle(BDC) is a right triangle:  BC²  =  CD² + BD² 

               --->   BC²  =  8² + 8²   --->   BC  =  .......

4)  Now, add up the parts.

Second one:   (use Pythagorean triples)

-- try a 13 -13 -20 isosceles triangle.

Use substitution to substitute -2x with y, and then factor!

If we simplify that expression we get: \(\frac{y+6}{(y-1)(y-4)}\). The expression is undefined when the denominator is equal to 0 which is when y=1 or 4. So the sum of 1 and 4 is \(\boxed{5}\). 

According to my computer, there are 1071 such odd numbers, provided the five odd digits (1, 3, 5, 7, 9) are allowed to repeat such as: 11357, 53379....etc.