2. A dragon is flying around in a pattern given by the parametric curve r(t) (cos(t) cos((sin(t) sin(t) cos(t)j. cos(t) - cos sin(t)-sin(t) cos(t))j (a) Find a formula for the velocity of the dragon at time t (b) Find all the times at which the dragon's speed is zero. Explain your reasoning. c) Does the path of the dragon contain any cusps? Explain your reasoning
2. A dragon is flying around in a pattern given by the parametric curve r(t)...
e-30 sin() -1 backward substitution method 4. Given A = sin(t) cos(t) tanto find the following 0 a. Matrix of minors (2pts) b. Matrix of cofactors (2pts) c. Adjoint matrix (2pts) d. Determinant of A (2pts) Inverse of A using the Adjoint matrix. (2pts) e. 1 v T.
T Find the length of the curve e' cos(t) e' sin(t) for 0 < t < 2 y (Hint: You can simplify the integrand by expanding the argument inside the square root and applying the Pythagorean identity, sinº (0) + cos²O) = 1.)
Assume sin S = {}, cos S = 4, sin T = 1, cos T = Find the given quantities without using a calculator. Give answer as a fraction (for instance on half would be written 1/2) Sin (S +T)= Cos (S+T)=
1. (a) You have seen that the Fourier transform of cos(wt) and sin(wt) func- tions results in even and odd combinations of delta functions in the frequency domain. Prove the opposite. That is, find the combination of delta functions in the time domain that give cosine and sine functions in the frequency domain. (b) Use the signum function to relate these two combinations of delta functions and use the convolution theorem to show that sin (wt) = cos (wt) *...
e-27 2. Calculate L et sint+e-2t cos st sint+e-2 cos 3t+t%e3+ + ✓at ec [e*sin U2n(t) sin 2t sin 21
(USING MATLAB) Given two differential equations X= sin(t)(exp(cos(t))-2cos(4t)+sin(t/12)^5) And Y = cos(t)(exp(cos(t))-2cos(4t)+sin(t/12)^5) where 0<t<20pi is a vector of 5000 points created by using (linspace) command : Write script to plot X and Y with red color ?
If u(t) = (sin(2t), cos(3), t) and v(t) = (t cos(3), sin(2t)), use Formula 4 of this theorem to find lu(e) • vce). dt
The terminal point P(x, y) determined by a real number t is given. Find sin(t), cos(t), and tan(t). 3 sin(t) cos(t) tan(t)
4. Given Lt = the ti + cos e a sin е дф) lae prove that (a) [1_,e-1 sin o) = 0 (b) [...cos 0] = hesin e