For the following exercises, rotate through the given angle based on the given equation. Give the...
For the following exercises, rotate through the given angle based on the given equation. Give the new equation and graph the original and rotated equation. x ^2/ 9 + y ^2/ 4 = 1, θ = 30°
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For the following exercises, rotate through the given angle
based on the given equation. Give the...
In Exercises 21-22, give the equation of the line that is the intersection of the given...
In Exercises 21-22, give the equation of the line that is the intersection of the given planes. 21. p1: 3(x-2) +(y 1)+4z 0, and p2: 2(x-1)-2(y+3) +6(2-1) 0 In Exercises 23-26, find the point of intersection between the line and the plane. 26. line: (1,2, 3) +t (3, 5,-1), plane: 3x-2y- z=-4 In Exercises 27-30, find the given distances. 27. The distance from the point (1, 2,3) to the plane 3(x-1)+(y 2)+5(2-2) 0.
In Exercises 21-22, give the equation of...
If a curve whose polar equation is r-r0) is rotated about the pole though an angle φ, then an equation for the rotated curve is r " no- Write an equation for the limeçon「-4-sin θ after it...
If a curve whose polar equation is r-r0) is rotated about the pole though an angle φ, then an equation for the rotated curve is r " no- Write an equation for the limeçon「-4-sin θ after it has been rotated counterclockwise by the given amount. Uso a graphing utility to graph the rotated limaçon for θ m/4, θ-n/2, θ π, and 3a/2. (Match the rotation to the correct graph.) (a) θ π/4 rotation r- graph (b) /2 rotation r- graph...
For the following exercises, find the equation of the tangent line to each of the given...
For the following exercises, find the equation of the tangent line to each of the given functions at the indicated values of x. Then use a calculator to graph both the function and the tangent line to ensure the equation for the tangent line is correct. [T] f (x) = 5 cot x, x = T 4.
using a Matlab 2. A unit cube is situated in the first octant with one vertex at the origin. first, rotate the cube through an angle of π/4 about the y-axis ; then rotate this image through an ang...
using a Matlab
2. A unit cube is situated in the first octant with one vertex at the origin. first, rotate the cube through an angle of π/4 about the y-axis ; then rotate this image through an angle of π/4 about the z-plan. Find the image of all eight vertices of the starting cube. do not solve it wi hand but writing a program)
2. A unit cube is situated in the first octant with one vertex at the...
Find an equation of the line that satisfies the given conditions. Through (-1, -14); perpendicular to...
Find an equation of the line that satisfies the given conditions. Through (-1, -14); perpendicular to the line passing through (2,-2) and (6,-4) Find an equation of the line that satisfies the given conditions. Through (-9, 1); parallel to the line x = 7 Find an equation of the line that satisfies the given conditions. Through (1, 1); parallel to the line y = 9x - 7 Find an equation of the line that satisfies the given conditions. Through (9,...
2) Assume that we had an equation of the form Ax? + Bxy + Cy? +Dx...
2) Assume that we had an equation of the form Ax? + Bxy + Cy? +Dx +Ey + F = 0 and we found that by rotating the axes through an angle of 30' we end up with the following equation: yig State the major axis, the major and minor vertices. Provide a sketch of the graph below. Make sure to sketch how the axes have rotated before you place the points and sketch the curve. 15 pts 4 3...
Let T : R2 → R2 be the linear transformation given by T(v) = Av that consists of a counterclockwise rotation about the origin through an angle of 30 2, Find the matrix that produces a countercloc...
Let T : R2 → R2 be the linear transformation given by T(v) = Av that consists of a counterclockwise rotation about the origin through an angle of 30 2, Find the matrix that produces a counterclockwise rotation about the origin through an angle of 30°. Be sure to give the EXACT value of each entry in A. a. b. Plot the parallelogram whose vertices are given by the points A(0, 0), B(4, 0), C(5, 3), and D 1, 3)...
31 and 33 please For the following exercises, graph the equation and include the orientation. 28....
31 and 33 please
For the following exercises, graph the equation and include the orientation. 28. x = t2, y = 3t, 0 <t<5 29. T = 2t, g = t2, - 5 <t< 5 30. D =t, g = V25 - t2, 0<< 5 31. x(t) = -t, y(t) = Vt, t > 0 32.2 = -2 cos t, y=6 sin t, 0 <t< 33. x = - sec t. y = tan t, - ; <t<
Equation B provides an approximation of Equation A, based on the small angle approximation This approximation...
Equation B provides an approximation of Equation A, based on the small angle approximation This approximation is said to be vaild for angles up to 30. Complete the table below to convince yourself of the quality of your experiment. Comment on your results Table 4: Quality of Approximation Initial Angle We define period of a the time required for a complete oscilation. Since the lrthe·ngle θ is small, less than 30, i. equation A the terms in sineandsmsarse mall that...
Write a slope-intercept equation for a line passing through the given point that is parallel to...
Write a slope-intercept equation for a line passing through the given point that is parallel to the given line. Then write a second equation for a line passing through the given point that is perpendicular to the given line. 43. (3,5), y = 4x+1 44. (-1,6), f(x) = 2x + 9 45. (-7,0), y = -0.3x + 4.3 46. (-4.-5), 2x + y = -4 47. (3.-2), 3x + 4y = 5 48. (8,-2), y = 4.2(x - 3) +...
In Exercises 21-22, give the equation of the line that is the intersection of the given planes. 21. p1: 3(x-2) +(y 1)+4z 0, and p2: 2(x-1)-2(y+3) +6(2-1) 0 In Exercises 23-26, find the point of intersection between the line and the plane. 26. line: (1,2, 3) +t (3, 5,-1), plane: 3x-2y- z=-4 In Exercises 27-30, find the given distances. 27. The distance from the point (1, 2,3) to the plane 3(x-1)+(y 2)+5(2-2) 0.
In Exercises 21-22, give the equation of...
If a curve whose polar equation is r-r0) is rotated about the pole though an angle φ, then an equation for the rotated curve is r " no- Write an equation for the limeçon「-4-sin θ after it has been rotated counterclockwise by the given amount. Uso a graphing utility to graph the rotated limaçon for θ m/4, θ-n/2, θ π, and 3a/2. (Match the rotation to the correct graph.) (a) θ π/4 rotation r- graph (b) /2 rotation r- graph...
For the following exercises, find the equation of the tangent line to each of the given functions at the indicated values of x. Then use a calculator to graph both the function and the tangent line to ensure the equation for the tangent line is correct. [T] f (x) = 5 cot x, x = T 4.
using a Matlab
2. A unit cube is situated in the first octant with one vertex at the origin. first, rotate the cube through an angle of π/4 about the y-axis ; then rotate this image through an angle of π/4 about the z-plan. Find the image of all eight vertices of the starting cube. do not solve it wi hand but writing a program)
2. A unit cube is situated in the first octant with one vertex at the...
Find an equation of the line that satisfies the given conditions. Through (-1, -14); perpendicular to the line passing through (2,-2) and (6,-4) Find an equation of the line that satisfies the given conditions. Through (-9, 1); parallel to the line x = 7 Find an equation of the line that satisfies the given conditions. Through (1, 1); parallel to the line y = 9x - 7 Find an equation of the line that satisfies the given conditions. Through (9,...
2) Assume that we had an equation of the form Ax? + Bxy + Cy? +Dx +Ey + F = 0 and we found that by rotating the axes through an angle of 30' we end up with the following equation: yig State the major axis, the major and minor vertices. Provide a sketch of the graph below. Make sure to sketch how the axes have rotated before you place the points and sketch the curve. 15 pts 4 3...
Let T : R2 → R2 be the linear transformation given by T(v) = Av that consists of a counterclockwise rotation about the origin through an angle of 30 2, Find the matrix that produces a counterclockwise rotation about the origin through an angle of 30°. Be sure to give the EXACT value of each entry in A. a. b. Plot the parallelogram whose vertices are given by the points A(0, 0), B(4, 0), C(5, 3), and D 1, 3)...
31 and 33 please
For the following exercises, graph the equation and include the orientation. 28. x = t2, y = 3t, 0 <t<5 29. T = 2t, g = t2, - 5 <t< 5 30. D =t, g = V25 - t2, 0<< 5 31. x(t) = -t, y(t) = Vt, t > 0 32.2 = -2 cos t, y=6 sin t, 0 <t< 33. x = - sec t. y = tan t, - ; <t<
Equation B provides an approximation of Equation A, based on the small angle approximation This approximation is said to be vaild for angles up to 30. Complete the table below to convince yourself of the quality of your experiment. Comment on your results Table 4: Quality of Approximation Initial Angle We define period of a the time required for a complete oscilation. Since the lrthe·ngle θ is small, less than 30, i. equation A the terms in sineandsmsarse mall that...
Write a slope-intercept equation for a line passing through the given point that is parallel to the given line. Then write a second equation for a line passing through the given point that is perpendicular to the given line. 43. (3,5), y = 4x+1 44. (-1,6), f(x) = 2x + 9 45. (-7,0), y = -0.3x + 4.3 46. (-4.-5), 2x + y = -4 47. (3.-2), 3x + 4y = 5 48. (8,-2), y = 4.2(x - 3) +...
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