Question

• • Show all of your work for each problem. Draw a line separating each problem. 1) Find an equation of the sphere that passes through the point (6, -2,3) and has center (-1,2,1). 2) Find the values of x such that the vectors (3,2,x) and (2x, 4,x) are orthogonal 3) Find the velocity, speed, and acceleration of a particle moving with position function r(t) = (2+2 - 3)i + 2tj. Sketch the path of the particle and draw the position, velocity, and acceleration vectors for t = 1. I 4) Find the maximum rate of change of f(x,y) = xy + y at the point (2,1). In which direction does it occur? 5) Identify a real-life problem in your academic discipline which involves mass and center of mass. Explain why these are important or useful concepts as it relates to the real-life problem and describe their general relevance to your academic discipline.

Answer 1

according to the rules only one question will be answered.Have a nice day

1.) center = C= (-1,2,1) P= (6,2,3) radius r= CP= V(22-26 ) + (Y2-4,)² + (Z2-31)2 = √ (6+1) 7 (-2-2) + (3-122 = √49+16+4 = √69. Equate os of the sphere is (2+13+14+2)+ (2-1=69 r+y+z+ 2x+4y+27 -63-0). Two vectors are orthogonal eft Q1 Q₂ + bi bat GC2: Cord (2) 3(2x)+ 2(4)+ 2(x) = 0 6x+8+ x²=0 x²+64 +8=0 (2+2)(x+4)=0 x= -2,-4)