Imcool

\(x+y=10 \)

\(x^3 + y^3 = 300 + x^2 + y^2\)

\(x^3+y^3=(x + y)(x^2 − xy + y^2)\)

\(10(x^2-xy+y^2)=300+x^2+y^2\)

\(9x^2-10xy+9y^2=300\)

\(9(x+y)^2-28xy=300\)

\(28xy=600\)

\(xy=\frac{150}{7}\)

\(x+y=10,xy=\frac{150}{7}\)

I think you can solve on your own now. If you are having trouble, leave a note and ill do the rest.

\(14 = 1\cdot14,2\cdot7\)

\(m = 15,9\)

2

\(500,25, 5/4, 5/80\)

But 25 is negative because of the negative sign on the common ratio, so heres the updated list greater than 1.

\(500,-25,5/4\)

There are only 2 numbers of the sequence greater than 1

15 members = 45 minutes

5 members = 135 minutes

20 members = 135/4 minutes = 33.75 minutes

Im gonna hard bash it. Its requires extreme patient which I do not have. I shall be using a calculator to shorten the process.

Oh well....

\(N = 2^{20}+2^{19}+2^{18}+2^{17}+2^{14}+2^{13}+2^{12}+2^{10}+2^{6}+A\cdot2^{5}+B\cdot2^{4}+C\cdot2^{3}+2^{1}\)

\(N=1995842+A\cdot2^{5}+B\cdot2^{4}+C\cdot2^{3}\)

\(1995842 \cong 2\mod7\)

\(A\cdot2^{5}+B\cdot2^{4}+C\cdot2^{3}\cong 5\mod7\)

\(32\cong4\mod7,16\cong2\mod7,8\cong1\mod7\)

\(32+8\cong4+1=5\mod7\)

\(A=1,B=0,C=1\)

\(x^2 + 15x + k = 0\)

\(\Delta = \sqrt{225-4k} = 0\)

\(225-4k = 0\)

\(4k = 225\)

\(k = \frac{225}{4}\)

hmm. are you sure this is it? or can you give some context. Im not sure what the x is doing in this equation, and it doesn't cancel out.

The left hand side would be equal to ^{\([C_0(1+r)](rx+1)\), so maybe \(rx+1=r+1\), so \(x=1\). Thats the only way i can think of}

Each gallon covers 400 square ft, which is 20ft x 20ft, which is around6x6 meters which is around 36 sq meters. 900/36 will be 25 gallons.