Few More...

[smeag]

Consider the geometric series: 24 + 38.4 + 61.44 + 98.304 + ... FInd the sum of the first ten terms.

Nsguy has 6 pairs of socks, of which no two pairs are the same color. Nsguy randomly selects two socks from their drawer. Find the probability that nsguy gets a matched pair.

Find the length of the minor axis for an ellipse with equation 9x^2 + 16y^2 - 54x + 64y + 1

[Salvadoramerican]

well geometric series take on the form sum(ar^(n-1)) where r is the multiplying ratio and a is the 1st term. So in this equation we need to find r so we take the 1st term 24 and the next term and create a ration 38.4/24 =1.6=r. The formula for sum of the n number of terms is a*(1-r^n)/(1-r) so its 24*(1-1.6^10)/(1-1.6) which is equal to 4358.05.

I'll leave nsguy with probability because I'll just confuse myself

The minor axis of the ellipse can be found by putting it into standard form (x-h)^2/a^2+(y-k)^2/b^2=144. So we will use completing the square method for this so we move the one to the other side and group like variables together
(9x^2-54x)+(16y^2+64Y)=-1
I would factor out the 9 and 16
9(x^2-6x+_)+16(y^2+4Y+_)=-1
Complete the squares and remember to add to the other side
9(x^2-6x+9)+16(y^2+4y+4)=-1+9(9)+16(4)
9(x-3)^2+16(y+2)^2=144
divide by 144
(x-3)^2/16+(y+2)^2/9=1
since the minor axis is the smaller number or b in this case *2
so b=3 because the square root of 9 is 3
so minor axis = 3*2=6
If I made a mistake anywhere tell me because I don't know how to use the equation generator on here to make it clearer.

[Salvadoramerican]

I meant ratio not ration now that i reread that

[nsguy1350]

Ok, I have 6 pairs of socks, which have the same color in each pair, but no two pairs have the same color.
When I need a pair of socks, and randomly draw one, I have a 0% chance of getting a sock that is unmatched. There is no other sock to match with, so this is a 'free' run.
The second sock has to match the first one. You originally had 12 socks, and now you have 11 to choose from. From these 11, only one matches the first sock. Therefore, you have a 1/11 chance of getting the second sock to match, which gives a matching pair.

Is the answer 11 1/9 percent?