Homework Answers
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 +...
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
Find the position vector for a particle with acceleration, initial velocity, and initial position given below. a(t...
Find the position vector for a particle with acceleration, initial velocity, and initial position given below. a(t) (4t, 2 sin(t), cos(2t)) 5(0) (0, 5,5) r(t) Preview Preview Preview The position of an object at time t is given by the parametric equations Find the horizontal velocity, the vertical velocity, and the speed at the moment wheret - 4. Do not worry about units in this problem. Horizontal Velocity - Preview Vertical Velocity- Preview Preview peed-
Find the position vector for...
An object is moving in the plane and has parametric equations (6) 2+1 +1 The corresponding...
An object is moving in the plane and has parametric equations (6) 2+1 +1 The corresponding derivative functions are x) 2/(1+0) YO (2+1) where to is in units of seconds and the units on the coordinate axes are feet (a) The horizontal velocity of the object at time is (b) The vertical Velocity of the object at time is (c) The tangent line to the path is horizontal at time to (d) The object crosses the y-axis at time to...
Find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A. A...
Find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A. A 01 0 0 10 0 0 0 0 0 1 00 - 29 10 et 0 0 el 0 -t 0 et 0 0 et O A. X(t) = 1 0 OB. X(t) = 0 51(5 cos 2t - 2 sin 2t) e5t (5 sin 2t+2 cos 2t) 0 0 2t2 cos 5t - 5 sin 5t) 2 (2 sin 5t + 5 cos...
3.) The position of a particle is given by x(t) = 3t3 – 2t2 – 5t...
3.) The position of a particle is given by x(t) = 3t3 – 2t2 – 5t + 10, where t is in seconds and x is in meters. Find the initial position of the particle. Find the position of the particle after 5 seconds. Find the average velocity from 0 sec to t = 5sec Find the instantaneous velocity as a function of time Find the instantaneous velocity at t = 2 seconds. Find the instantaneous velocity at t=4 seconds...
An object travels along the sinusoidal path defined by the y sin(0.5(rad/m) x). If the component...
An object travels along the sinusoidal path defined by the y sin(0.5(rad/m) x). If the component of velocity along the x axis is t? m/s where t is in seconds, determine the objects distance from the origin O and its acceleration when t- 1.5 s. When t 0,x-O,y-0
1) The polar coordinates of an object are r = 2t+4t m and O=t-trad. What are...
1) The polar coordinates of an object are r = 2t+4t m and O=t-trad. What are the radial and transverse components of the total external acceleration on the object at t=1s? A player kicks a ball with a speed of 80 m/s and at an angle of 30° (a) Determine X (horizontal distance) and Y (vertical distance) att 55 (b) Determine the maximum possible height of projective. (c) Determine horizontal distance that the ball.
Consider the function given by f(x) = 4x4 + 7x3 - 29x2 - 72x - 36...
Consider the function given by f(x) = 4x4 + 7x3 - 29x2 - 72x - 36 that you analysed in Task 1. Using the information in Task 1.2, explain why the total area enclosed by the curve y = f(x), the x and y-axes and the line x = 5 has to be calculated in two parts. Obtain this total area. The root mean square value of a voltage v(t) (in mV) between times t = a and t =...
Suppose you are climbing a hill whose shape is given by the equation z = 1400-0.005x-0.01, where x, y, and z are me...
Suppose you are climbing a hill whose shape is given by the equation z = 1400-0.005x-0.01, where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1366). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? ascend descend At what rate? vertical meters per horizontal meter (b) If you walk northwest, will you start to...
help me with this problem 1. Determine the corresponding rectangular equation: a. x=t?, y=t-1 b. x=...
help me with this problem
1. Determine the corresponding rectangular equation: a. x=t?, y=t-1 b. x= 9coso , y = 5sino 2. Determine all horizontal, vertical, tangent lines if any: x= tsint + cost, y = sint – tcost 3. Find the area of the region common of Interior of r = 2 – V3sing and r= –2 + V3sino 4. Find the arc length enclosed by r = 2(1 + cose), and r = 2 5. Find the slope...
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
Find the position vector for a particle with acceleration, initial velocity, and initial position given below. a(t) (4t, 2 sin(t), cos(2t)) 5(0) (0, 5,5) r(t) Preview Preview Preview The position of an object at time t is given by the parametric equations Find the horizontal velocity, the vertical velocity, and the speed at the moment wheret - 4. Do not worry about units in this problem. Horizontal Velocity - Preview Vertical Velocity- Preview Preview peed-
Find the position vector for...
An object is moving in the plane and has parametric equations (6) 2+1 +1 The corresponding derivative functions are x) 2/(1+0) YO (2+1) where to is in units of seconds and the units on the coordinate axes are feet (a) The horizontal velocity of the object at time is (b) The vertical Velocity of the object at time is (c) The tangent line to the path is horizontal at time to (d) The object crosses the y-axis at time to...
Find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A. A 01 0 0 10 0 0 0 0 0 1 00 - 29 10 et 0 0 el 0 -t 0 et 0 0 et O A. X(t) = 1 0 OB. X(t) = 0 51(5 cos 2t - 2 sin 2t) e5t (5 sin 2t+2 cos 2t) 0 0 2t2 cos 5t - 5 sin 5t) 2 (2 sin 5t + 5 cos...
3.) The position of a particle is given by x(t) = 3t3 – 2t2 – 5t + 10, where t is in seconds and x is in meters. Find the initial position of the particle. Find the position of the particle after 5 seconds. Find the average velocity from 0 sec to t = 5sec Find the instantaneous velocity as a function of time Find the instantaneous velocity at t = 2 seconds. Find the instantaneous velocity at t=4 seconds...
An object travels along the sinusoidal path defined by the y sin(0.5(rad/m) x). If the component of velocity along the x axis is t? m/s where t is in seconds, determine the objects distance from the origin O and its acceleration when t- 1.5 s. When t 0,x-O,y-0
1) The polar coordinates of an object are r = 2t+4t m and O=t-trad. What are the radial and transverse components of the total external acceleration on the object at t=1s? A player kicks a ball with a speed of 80 m/s and at an angle of 30° (a) Determine X (horizontal distance) and Y (vertical distance) att 55 (b) Determine the maximum possible height of projective. (c) Determine horizontal distance that the ball.
Consider the function given by f(x) = 4x4 + 7x3 - 29x2 - 72x - 36 that you analysed in Task 1. Using the information in Task 1.2, explain why the total area enclosed by the curve y = f(x), the x and y-axes and the line x = 5 has to be calculated in two parts. Obtain this total area. The root mean square value of a voltage v(t) (in mV) between times t = a and t =...
Suppose you are climbing a hill whose shape is given by the equation z = 1400-0.005x-0.01, where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1366). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? ascend descend At what rate? vertical meters per horizontal meter (b) If you walk northwest, will you start to...
help me with this problem
1. Determine the corresponding rectangular equation: a. x=t?, y=t-1 b. x= 9coso , y = 5sino 2. Determine all horizontal, vertical, tangent lines if any: x= tsint + cost, y = sint – tcost 3. Find the area of the region common of Interior of r = 2 – V3sing and r= –2 + V3sino 4. Find the arc length enclosed by r = 2(1 + cose), and r = 2 5. Find the slope...
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