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2a) aind at Plt,2) at X iration of ithe 314 LJ b Find +he plane 4hroush...
Find the point of intersection of plane 4x+5y-52-4=0 and the following line: (x-4)/5 = (y+3)/3 =...
Find the point of intersection of plane 4x+5y-52-4=0 and the following line: (x-4)/5 = (y+3)/3 = z/3 If they have a point of intersection, enter the x-value of point in the following box. If the line is on the plane, enter ON in the box. If the line is not on the plane, and they are parallel, enter P in the box.
Please explain b! 2. Let z = f(x, y) = ln(4x2 + y2) (a) Use a...
Please explain b!
2. Let z = f(x, y) = ln(4x2 + y2) (a) Use a linear approximation of the function z = f(x,y) at (0,1) to estimate f(0.1, 1.2) (b) Find a point P(a,b,c) on the graph of z = f(x, y) such that the tangent plane to the graph of z = f(x,y) at the point P is parallel to the plane 2x + 2y – 2=3
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...
QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y =...
QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y = 5 + 2t, z=t-1 and 1 1 - 2 L2 : =y-3 = 2 4 i. Check whether the lines Lị and L2 parallel, intersect or skewed? (5 marks) ii. Find the shortest distance from the point (1, 2, -1) to the line Li- (3 marks) b) Given two planes 71 : 20 - 4y +z = 5 and T2 : 7x + y...
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25....
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x, y, z] = [2,-2, 0] + r[2 kx+Zy-4: = 12. -3] is parallel to the plane (2 marks)
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x,...
Consider the ellipsoid x^{2}+4y^{2}+2z^{2} = 26. Find all the points where the tangent plane to this...
Consider the ellipsoid x^{2}+4y^{2}+2z^{2} = 26. Find all the points where the tangent plane to this ellipsoid is parallel to the plane 6z-\left(2x+4y\right) = 0.
B and D Sum of cubes: a³ + b³ = (a + b)(a² – ab +...
B and D
Sum of cubes: a³ + b³ = (a + b)(a² – ab + b²) Difference of cubes: a3 - b -btVb?-4ac -by Vertex formula: f ) Quadratic formula: x = 2a 2a Y2 - Y1 X2 - X1 y = mx + b т3 1) Find the slope-intercept form of the line satisfying the following conditions Perpendicular to y =x and passing through the point (7, 5) a. b. Parallel to 2x - 7y = -24 and...
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d =...
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d = 0 C(0, -2,1). Put the plane equation B(3,1, 0) х — 3 z+2 = y+5 = 2 L: Find the intersection point between 2 lines whose symmetric equations are: 4 х-2 L, : у-2 = z-3 -3 Find the parametric equation for a line that is going through point A(2,4,6) and perpendicular to the plane 5х-3у+2z-4%3D0. Name: x-3y4z 10 Find the distance between 2...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent p...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
Find the solution to the linear system of differential equations {?′?′==−2?+12?−?+5?{x′=−2x+12yy′=−x+5y satisfying the initial conditions ?(0)=1x(0)=1...
Find the solution to the linear system of differential equations
{?′?′==−2?+12?−?+5?{x′=−2x+12yy′=−x+5y satisfying the
initial conditions ?(0)=1x(0)=1 and ?(0)=0y(0)=0.
د (1 point) Find the solution to the linear system of differential equations { -2x + 12y -x + 5y satisfying the initial conditions x(0) = 1 y د and y(0) = 0. x(t) = yt) =
Find the point of intersection of plane 4x+5y-52-4=0 and the following line: (x-4)/5 = (y+3)/3 = z/3 If they have a point of intersection, enter the x-value of point in the following box. If the line is on the plane, enter ON in the box. If the line is not on the plane, and they are parallel, enter P in the box.
Please explain b!
2. Let z = f(x, y) = ln(4x2 + y2) (a) Use a linear approximation of the function z = f(x,y) at (0,1) to estimate f(0.1, 1.2) (b) Find a point P(a,b,c) on the graph of z = f(x, y) such that the tangent plane to the graph of z = f(x,y) at the point P is parallel to the plane 2x + 2y – 2=3
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...
QUESTION 1 (15 MARKS) a) Given the line Lj: I = 2 - 2t, y = 5 + 2t, z=t-1 and 1 1 - 2 L2 : =y-3 = 2 4 i. Check whether the lines Lị and L2 parallel, intersect or skewed? (5 marks) ii. Find the shortest distance from the point (1, 2, -1) to the line Li- (3 marks) b) Given two planes 71 : 20 - 4y +z = 5 and T2 : 7x + y...
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x, y, z] = [2,-2, 0] + r[2 kx+Zy-4: = 12. -3] is parallel to the plane (2 marks)
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x,...
B and D
Sum of cubes: a³ + b³ = (a + b)(a² – ab + b²) Difference of cubes: a3 - b -btVb?-4ac -by Vertex formula: f ) Quadratic formula: x = 2a 2a Y2 - Y1 X2 - X1 y = mx + b т3 1) Find the slope-intercept form of the line satisfying the following conditions Perpendicular to y =x and passing through the point (7, 5) a. b. Parallel to 2x - 7y = -24 and...
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d = 0 C(0, -2,1). Put the plane equation B(3,1, 0) х — 3 z+2 = y+5 = 2 L: Find the intersection point between 2 lines whose symmetric equations are: 4 х-2 L, : у-2 = z-3 -3 Find the parametric equation for a line that is going through point A(2,4,6) and perpendicular to the plane 5х-3у+2z-4%3D0. Name: x-3y4z 10 Find the distance between 2...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
Find the solution to the linear system of differential equations
{?′?′==−2?+12?−?+5?{x′=−2x+12yy′=−x+5y satisfying the
initial conditions ?(0)=1x(0)=1 and ?(0)=0y(0)=0.
د (1 point) Find the solution to the linear system of differential equations { -2x + 12y -x + 5y satisfying the initial conditions x(0) = 1 y د and y(0) = 0. x(t) = yt) =
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