Quadratic Function and Diagonals of a DiamondDate: 6/14/96 at 14:15:44 From: Anonymous Subject: Quadratic function and diagonals of a diamond Hello! My question is the following: "'The sum of the diagonals of the following lozenge is maximum when angle a=30 dgrs.' /I\ / I \ / I \ <-------> \ I / \ I / The sides measure sqrt2 \I/ Angle a is the angle between the biggest diagonal and the sides." I tried to answer this question by using a quadratic function, and by calculating its maximum value [-(b^2 - 4ac)/4a]. Am I right? Date: 6/14/96 at 18:27:43 From: Doctor Anthony Subject: Re: Quadratic function and diagonals of a diamond The length of side = L and angle between the diagonal and side = A The Total of both diagonals is then T = 2L*cos(A) + 2L*sin(A) To find maximum or minimum value for T we differentiate: dT/dA = 2L(-sin(A) + cos(A)) = 0 so sin(A) = cos(A) tan(A) = 1 and A = 45 degrees So the figure would be a square. and this is a maximum since the second differential 2L (-cos(A) - sin(A)) would be negative at A = 45 degrees. Then T = 2L(1/sqrt(2) + 1/sqrt(2)) = 2L(2/sqrt(2)) = 2L*sqrt(2) -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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