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Matching: Match the equation of each plane to its scalar form 2x-y-2-6.0 b.y Answer Alternate Equation 17 [x, y, :1...
1. (Sections 2.11,2.12) The parametric equations of three lines are given below: 4 : (x, y,...
1. (Sections 2.11,2.12) The parametric equations of three lines are given below: 4 : (x, y, z) = (1,0,0) + (1,0,-1), TER 19 : (x,y, 2) = (1.0.-1) + (0.1, -1), TER 13: (1.7.2) = (1.-1,-1) + (1,1,0), TER Two of these lines intersect. Which two? What is the equation of the plane that they describe? Give full reasons for your answers. 2. (Sections 2.11,2.12) Given the two planes 2-y-z = 0 and r+y-:-1=0. Find a parametric equation for the...
Find the plane determined by the intersecting lines. L1 x= -1 +41 y=2+t z= 1 -...
Find the plane determined by the intersecting lines. L1 x= -1 +41 y=2+t z= 1 - 4 L2 x = 1 - 4s y= 1 + 25 z=2-2s The equation of the plane is (Type an equation.)
1. Consider the solid in the first octant bounded by the coordinate planes, the plane x= 2,and th...
1. Consider the solid in the first octant bounded by the coordinate planes, the plane x= 2,and the surface z= 9-y^2. The density is(x,y,z) = (x+ 1)(y+ 1)(z+ 1). Calculate the x,y, and z coordinates of the center of mass. Express your answer in decimal form. 2. Find Iz for the hollow cylinder (oriented along the z-axis) with inner radius R and thickness t. The base is the xy-plane, the height is h, and the density is(x,yz,) =kz^2.
(1 pt) Consider the sphere (x - 4)2 + (y - 3)2 + (z - 5)2...
(1 pt) Consider the sphere (x - 4)2 + (y - 3)2 + (z - 5)2 25 (a) Does the sphere intersect each of the following planes at zero points, at one point, at two points, in a line, or in a circle? The sphere intersects the xy-plane ? The sphere intersects the xz-plane ? The sphere intersects the yz-plane ? (b) Does the sphere intersect each of the following coordinate axes at zero points, at one point, at two...
(1 point) Match each differential equation to a function which is a solution. FUNCTIONS A. y...
(1 point) Match each differential equation to a function which is a solution. FUNCTIONS A. y = 3x + x2, B.y= e 4x, C.y=sin(x), D.y=x2, E. y = 3 exp(62), DIFFERENTIAL EQUATIONS 1. y' +y=0 2. 2x²y" + 3xy' = y 3. y' = 6y 4. y" + 10y' + 24y = 0
For each plane curve, find a rectangular equation. State the appropriate interval for x or y....
For each plane curve, find a rectangular equation. State the appropriate interval for x or y. x=612 y=t+3, fort in (-00,00) O A. x=3(y - 6)? OB. y=3(x - 6)2 OC. y = 6(x - 3)2 OD. x= 6(y - 3)2 Choose the correct interval for the rectangular equation. OA -00 <y< OB. Osy<oo oc. Osxoo OD. -00<x<00
3. For x = 1-2, 17 and y = [1,0]" in R, find || x ||...
3. For x = 1-2, 17 and y = [1,0]" in R, find || x || , ||y|| , and || X – y|| using the inner product given by (x,y) = x+ Ay where 1 - 1 A= _1 - 1 A =
Find the x-intercept and the y-intercept of each equation. 33. - 3x + 2 y =...
Find the x-intercept and the y-intercept of each equation. 33. - 3x + 2 y = 12 34 34. 2x – 3y = 24 CHAP FUN Find the slope of the line through each pair of points. 36. (-8, 6) and (-8,-1) In ma relati types an ir 35. (-12, 3) and (-12, -7) 37. (6, -5) and (-12,-5) Find the slope of each line. 38. 3x – 2y = 3 40. x = 6 39. y = 5x +12...
1. Use the given equation to answer the question in each part. (a) Draw the intersections of the ...
1. Use the given equation to answer the question in each part. (a) Draw the intersections of the graph with the ry-plane, yz-plane, and az-plane. (Make sure to label your axes and the coordinates of intersections with the axes in each plane.) (b) Draw the level curves for the heights z3,z1,z 0,z1, and z 3 (c) Describe in words how the graph of the equation looks. off dxdy 2. Calculate a_ and a_ for the function f(x,y) уз ezy
1....
Exercise 1. Tangent plane (15 pts) Let (S) be the surface given by the following equation....
Exercise 1. Tangent plane (15 pts) Let (S) be the surface given by the following equation. x+y2 = 1 + z2 An equation of the tangent plane to (S) at A(1,2,2) is: a. 2x + 4y - 4z = 1 b. x +y - z = 0 c. x + 2y – 2z = 1 d. x + y -z = 2 e. None of the above a b d. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy...
1. (Sections 2.11,2.12) The parametric equations of three lines are given below: 4 : (x, y, z) = (1,0,0) + (1,0,-1), TER 19 : (x,y, 2) = (1.0.-1) + (0.1, -1), TER 13: (1.7.2) = (1.-1,-1) + (1,1,0), TER Two of these lines intersect. Which two? What is the equation of the plane that they describe? Give full reasons for your answers. 2. (Sections 2.11,2.12) Given the two planes 2-y-z = 0 and r+y-:-1=0. Find a parametric equation for the...
Find the plane determined by the intersecting lines. L1 x= -1 +41 y=2+t z= 1 - 4 L2 x = 1 - 4s y= 1 + 25 z=2-2s The equation of the plane is (Type an equation.)
(1 pt) Consider the sphere (x - 4)2 + (y - 3)2 + (z - 5)2 25 (a) Does the sphere intersect each of the following planes at zero points, at one point, at two points, in a line, or in a circle? The sphere intersects the xy-plane ? The sphere intersects the xz-plane ? The sphere intersects the yz-plane ? (b) Does the sphere intersect each of the following coordinate axes at zero points, at one point, at two...
(1 point) Match each differential equation to a function which is a solution. FUNCTIONS A. y = 3x + x2, B.y= e 4x, C.y=sin(x), D.y=x2, E. y = 3 exp(62), DIFFERENTIAL EQUATIONS 1. y' +y=0 2. 2x²y" + 3xy' = y 3. y' = 6y 4. y" + 10y' + 24y = 0
For each plane curve, find a rectangular equation. State the appropriate interval for x or y. x=612 y=t+3, fort in (-00,00) O A. x=3(y - 6)? OB. y=3(x - 6)2 OC. y = 6(x - 3)2 OD. x= 6(y - 3)2 Choose the correct interval for the rectangular equation. OA -00 <y< OB. Osy<oo oc. Osxoo OD. -00<x<00
3. For x = 1-2, 17 and y = [1,0]" in R, find || x || , ||y|| , and || X – y|| using the inner product given by (x,y) = x+ Ay where 1 - 1 A= _1 - 1 A =
Find the x-intercept and the y-intercept of each equation. 33. - 3x + 2 y = 12 34 34. 2x – 3y = 24 CHAP FUN Find the slope of the line through each pair of points. 36. (-8, 6) and (-8,-1) In ma relati types an ir 35. (-12, 3) and (-12, -7) 37. (6, -5) and (-12,-5) Find the slope of each line. 38. 3x – 2y = 3 40. x = 6 39. y = 5x +12...
1. Use the given equation to answer the question in each part. (a) Draw the intersections of the graph with the ry-plane, yz-plane, and az-plane. (Make sure to label your axes and the coordinates of intersections with the axes in each plane.) (b) Draw the level curves for the heights z3,z1,z 0,z1, and z 3 (c) Describe in words how the graph of the equation looks. off dxdy 2. Calculate a_ and a_ for the function f(x,y) уз ezy
1....
Exercise 1. Tangent plane (15 pts) Let (S) be the surface given by the following equation. x+y2 = 1 + z2 An equation of the tangent plane to (S) at A(1,2,2) is: a. 2x + 4y - 4z = 1 b. x +y - z = 0 c. x + 2y – 2z = 1 d. x + y -z = 2 e. None of the above a b d. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy...
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