Quadratic Spline.Show how to obtain the constants below (a1,b1,c1 etc...) from the equations above through algebra particularly substitution or elimination. Please show complete solution and and also neat handwriting. Condition #1: From the Interior knots: Q, Rat point Q:a,(4)? + b;(4) + c, = 2egn 1az(4)? + b2(4) + C2 = 2egn 2at point R:az(7)² + b2(7) + C2 = 8as(7)? + b3(7) + C3 = 8eqn3egn 4-------Condition #2: From the exterior knots: P, SAt point P:a;(3)² + b;(3) + c, = 5At point S:as(9)? + b3(9) + C3 = 6egn 5egn 6Condition #3: First derivatives of the interior knots are equal2a,x + bị = 2a,x + b22a,x + b2 = 2a,x + b3----- eqn 7egn 8Condition # 4:a, = 0eqn 9From the 9 equations, by solving for the unknowns algebraically, we will getthe following:a1 = 0a2 = 15/9a3 = -4b1 = -3b2 = -49/3b3 = 63c1 = 14c2 = 122/3c3 = -237

We have to show complete solution of how each constants a1,a2,a3,b1,b2,b3,c1,c2 and c3 are obtained…

at point Q: a;(4)² + b;(4) + c, = 2 ------ egn 1 az(4)² + ba(4) + C2 = 2 ------- egn 2 at point R: az(7)° + b2(7) + c2 = 8 as(7)° + b,(7) + C3 = 8 ---- egn 3 ------- egn 4 Condition #2: From the exterior knots: P, S At point P: a;(3)² + b;(3) + c, = 5 ------- eqn 5 At point S: as(9)? + ba(9) + C3 = 6 ------- egn 6 Condition #3: First derivatives of the interior knots are equal 2a,x + b, = 2a,x + b2 2a,x + b2 = 2a3x + b3 egn 7 egn 8

at point Q: a;(4)² + b;(4) + c, = 2 ------ egn 1 az(4)² + ba(4) + C2 = 2 ------- egn 2 at point R: az(7)° + b2(7) + c2 = 8 as(7)° + b,(7) + C3 = 8 ---- egn 3 ------- egn 4 Condition #2: From the exterior knots: P, S At point P: a;(3)² + b;(3) + c, = 5 ------- eqn 5 At point S: as(9)? + ba(9) + C3 = 6 ------- egn 6 Condition #3: First derivatives of the interior knots are equal 2a,x + b, = 2a,x + b2 2a,x + b2 = 2a3x + b3 egn 7 egn 8

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter1: Line And Angle Relationships

Section1.6: Relationships: Perpendicular Lines

Problem 27E

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