Find the shape of the quadratic surface. (1) a2-5y2 + 7y - 322 5 (2) 3x2...
(1 point) Find the points on the surface 3x2 + 4y2 3z2 -1 at which the tangent plane is parallel to the plane ) and We were unable to transcribe this imageWe were unable to transcribe this image(1 point) Consider the surface xuz48 A. Find the unit normal vector to the surface at the point (3, 4,4) with positive first coordinate. B. Find the equation of the tangent plane to the surface at the given point. Express your answer in...
question #6
1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
3y+ 6z = 11 on the surface 22y2522 = 1 4. Find the closest point to 5. Find the smallest value of r22y2322 if Minimum is at the point , ,9) y + 3z = 4 6. Find the extremes of the following functions over the region R:the triangle (0,0), (1,0) and (1, (a) f(x, y) 3x2+4 Min: 0 at (0,0), Max: 7 at (1,1 (b) f(r, y) = V + Min: 0 at (0,0), Max: 2 at (1,1) (c)...
Exercise 3. Find and identify the trace of the given quadric surface in the specified plane of coordinates. f) x2 + 2y – 2z2 – 2 = 0, xz-plane. g) x = y2 + 4, xy-plane. a) A + B + * = 1, xy-plane. b) x2 + 4y2 – 4z2 – 16 = 0, xz-plane. c) -4x2 - y2 + z2 = 1, yz-plane. d) x2 + – z2 = 0, yz-plane. e) x2 + x2 – 4y+4= 0,...
is Find an equation for, and identify, the surface that results when the surface x2 - y2 – 2z2 reflected about the plane Y = 2. b) Find an equation for, and identify, the surface that results when the surface x2 – 4y2 + x2 = ( is translated to the point D(2,-1,-4).
5. Let p be a prime with p Ξ 1 (mod 4). Suppose that ai, a2, . . . ,a(p-1)/2 are the quadratic residues of p that lie between 1 and p - 1. Prove that 1,0 (P-1)/2 i- 1 Hint: If a is a quadratic residue less than or equal to (p-1)/2 then what is p - ai?
5. Let p be a prime with p Ξ 1 (mod 4). Suppose that ai, a2, . . . ,a(p-1)/2 are...
1.Find fxy(x,y) if f(x,y)=(x^5+y^4)^6.
2. Find Cxy(x,y) if C(x,y)=6x^2-3xy-7y^2+2x-4y-3
Find (,,(Xy) if f(x,y)= (x + y) fxy(x,y) = Find Cxy(x,y) if C(x,y) = 6x² + 3xy – 7y2 + 2x - 4y - 3. Cxy(x,y)=0
1) Find the arc length for the following curves. a. y2 = 4(x + 4)3, b. x= 0<x<2 1 sys2 + 4y2 2) Find the surface area resulting from the rotation of the curve about X axis a. 9x = y2 + 18, b. y = V1 + 4x, 2<x< 6 1<x<5 3) Find the surface area resulting from the rotation of the curve about th Y axis. a, y = 1- x2 0 SX S1
2) (a) If P=r cost and r sint -2te' = 0, find dP/dt (b) If z= cos(xy), show that x - y = 0 3) Find the maximum and minimum points of the functions in (a) and (b) (a) x2 - y2 + 2x - 4y +10 (b) x - y3 - 2xy +2 4) (a) Find the shortest distance from the origin to the the quadric surface 3x2 + y2 - 4xz= 4 (b) Find seadu dx Jx In(x+u)
3. Write the following systems of linear equations using augmented matrix form a. 6x+7y= -9 X-y= 5 b. 2x-5y= 4 4x+3y= 5 C. x+y+z= 4 2x-y-z= 2 -x+2y+3z= 5 4. Solve the following Systems of linear equations using Cramer's Rule a. 6x-3y=-3 8x-4y= -4 b. 2x-5y= -4 4x+3y= 5 c. 2x-3y+z= 5 X+2y+z= -3 x-3y+2z= 1