1. r(t) = t²i- cos (8t) + sin (8t) k

(2) / (2 sin r - e) dr.

(2) uha For the function y=3 sin (2x-T/2) +4. * find f, g & h ro

4. A car supported by a MacPherson strut (shock absorber system) travels on a bumpy road at a constant velocity v. The equation modeling the motion of the car is Tut 80x + 1000x = 2500 cos where r = x (t) represents the vertical position of the cars axle relative to its equilib- rium position, and the basic units of measurement are feet and feet per second (this is actually just an example of a forced, un-damped harmonic oscillator, if that is any help). The constant numbers above are related to the characteristics of the car and the strut. Note that the coefficient of time t (inside the cosine) in the forcing term on the right hand side is a frequency, which in this case is directly proportional to the velocity v of the car. (a) Find the general solution to this nonhomogeneous ODE. Note that your answer will have a term in it which is a function of v.

(5) / sin(3r) dr.

Please use implicit differentiation to solve question 2 and 3 only. Thanks??

I do not understand how to go about doing this question. Can you please help and show the work step by step so I can know how to do this problem as well as others?

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion  s = 2 sin(?t) + 5 cos(?t),  where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average velocity during each time period. (i)    [1, 2]  cm/sI got this one, because I can easily find the value of 2pi for each of the sine and cosine values. sin(2pi)=0 and cos(2pi)=1.(ii)    [1, 1.1]  cm/sWhen I get to these questions with [1, 1.1], I do not know how to find the value sin(1.1pi) and cos(1.1pi). When I try to put the whole equation in the calculator it gives me 'syntax error' or undefined. So I am not sure what to do with the 1.1(iii)    [1, 1.01] cm/s(iv)    [1, 1.001] cm/s (b) Estimate the instantaneous velocity of the particle when t = 1. cm/s

An object is moving on a straight line according to the following position function. (a) The velocity and the acceleration of this displacement are v(t) = a(t)= x(t) = = -9 cos(5t) - 9√/3 sin(5t) meters (b) This position is in simple harmonic motion since (c) We rewrite x (t) as A cos(wt + o). A = a(t) = == W3 (d) Find the amplitude, the period and the frequency of (t). Amplitude = meters. Period= ² x (t) seconds. Frequency= m/s m/s2 1/seconds.

How would i find the derivatives of this inverse trig. problem? y = (1+Tan-1x)2