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Source: — Problem Solving |
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by adamsmith2009 » Tue Dec 08, 2009 5:41 pm
1) x(x-1) = 20

2) 2^9

Explanation:

1. 3^X - 3^(X-1)= 162 then x(x-1) =


Factor: 3^(x-1)*(3-1) = 162

3^(x-1)(2) = 162

Divid 2 by both sides:

3^(x-1) = 81

Solve for x - 3^4 = 81. So x would be 5 and 5*4=20

2. 2+2+22+23+24+25+26+27+28
Again simplify = 2^9
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by okigbo » Fri Dec 11, 2009 5:44 pm
3. equilateral triangle and square areas

t^2*sq.rt.3/4=s^2

t^2*sq.rt.3=4s^2 -- take sq. rt of both sides

t*quad root 3=2s

ratio of t:s = 2:quad root 3
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by heshamelaziry » Fri Dec 11, 2009 8:52 pm
To solve question 2, use geometric progression formula: a(r^n-1)/ r-1 ----> 2(2^8 - 1) / 2 -1 ----> 2^9 - 2 / 1 -----> bring the first 2 from the question -----> (2^9 - 2 + 2) / 1 = 2^9
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