Posted by Anonymous on Sunday, December 9, 2012 at 6:44pm.
A straight line passes through the point (1,27) and intersects the positive x-axis at the point A and the positive y-axis at the point B.Find the shortest possible distance between A and B..
Pleaase could you help me?
Thank you in advance
- Math -urgent :) - Damon, Sunday, December 9, 2012 at 8:10pm
y = m x + b
when x = 0, y = B so b=B
y = m x + B
when y = 0, x = A
0 = mA+ B
m = -B/A
y = -Bx/A + B
when x = 1, y = 27
27 = -B/A + B
27 A = - B + BA
27 A = B (A-1)
B = 27 A/(A-1)
dB/DA = 27 [ (A-1)-A] /(A-1)^2
d^2 = A^2 + B^2
d d^2/dA = 0 for min
= 2 A + 2B dB/DA
0 = 2 A + 2B[ 27 [ (A-1)-A] /(A-1)^2
0 = 2A(A-1)^2 - 54 B
0 = 2A(A-1)^2 -54 [ 27 A/(A-1) ]
27 [27/(A-1) ] = (A-1)^2
27^2 = (A-1)^3 = 729
A-1 = 9
A = 10 amazing. You take it from there.
- Math -urgent :) - Damon, Sunday, December 9, 2012 at 8:13pm
oh well curious now
B = 27(10)/9 = 270/9 = 30
d^2 = 10^2 + 30^2 = 1000
d = 10 sqrt(10)
or about 31.6
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