thedudemanguyperson

We shall start by prime factorizing 2015. It is equal to 5*13*31. We want to minimize our number, so we must minimize it's prime factors. This means that our answer is (2^30)(3^12)(5^4)

Lowest is 3+4+5=12. Highest is 101+102+103=306. You can obviously get every number in between by increasing some variable or decreasing another. So ans is {12,13,14,...,306}

2*9+2*4=18+8=26

If first is x-2, second is x, third is x+2. (x-2)+x+8=3(x+2)-11 --> 2x+6=3x-5 --> x=11. The third is 11+2=13

By similar triangles 2x+25=(14+x)/2 --> 4x+50=14+x --> 3x+50=14 --> 3x=-36 --> x=-12

GE = 14+(-12)=14-12=2

a--> 3y=36x+24 --> y=12x+8 --> slope=12

12=3b --> b=4

c=b/2 --> c=4/2 --> c=2

Add first two --> 3x-2z=5 --> 3x=2z+5 --> x=(2z+5)/3

Add second and third --> 3x-y+3z=3 --> 2z+5-y+3z=3 --> 5z-y=-2 --> y=5z+2

Use last eqn. --> (2z+5)/3+5z+2+2z=-4 --> 2/3z+5/3+7z=-6 --> 23/3z=23/3 --> z=1

So y=5*1+2=7, and x=(2*1+5)/3=7/3

Ans: (7/3, 7, 1)

12=2^2*3^1 --> has (2+1)(1+1)=3*2=6 factors, in positive. By symettry, this is the same for negative. So 6+6=12.

The formula is \(S_{n}=\frac{(T_1+T_n)n}{2}\). Note that t_12=(26+2)-(2*12)=28-24=4. Note that t_1=26. So we have \(S_{12}=\frac{(4+26)12}{2}=\frac{30*12}{2}=30*6=\boxed{180}\)

It is not. It doesn't pass the horizontal line test at any value for y, where y<=-5.

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