(t), For this question, this system has two inputs. The first input is the velocity of The following figure depicts...
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [0, 2T] and φ in [0, π] -3 cos(θ) sin(φ), 5 sin(θ) sin(φ),-15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 3 cos(9) sin(9),-5 sin(θ) sin(9), 15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 v 16 sin2(0) sin2@c 216 cos2@t9(3 cos(θ) sin(φ), 5 sin(θ) sin(φ) , 15 cos(q) 216 cos(φ)...
In the figure below, find each of the following. 5.00 3.00 4.00 (a) the side opposite (b) the side-adjacent to ф (c) cos θ (d) sin ф e) tan For the triangle shown in the figure below what are each of the following? (Let y 60.0 m and r 65.0 m. Assume the triangle is a right trilangle.) a) the length of the unknown side x b) the tangent of o c)the sin of φ Need Help?
please i need the question 15 for the detailed proof and explaination ! thanks ! 233 42 Isometries, Conformal Maps 14, we say that a differentiable map ф: S,--S2 preserves angles when for every p e Si and every pair vi, v2 E T (S,) we have cos(u, 2) cos(dp, (vi). do,()). Prove that pis locally conformal if and only if it preserves angles. 15. Letp: R2 R2 be given by ф(x, y)-(u (x, y), u(x, y), where u and...
a. Use the Chain Rule to find the indicated partial derivatives. z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s ∂z ∂t ∂z ∂u when s = 1, t = 2, u = 3 b. Use the Chain Rule to find the indicated partial derivatives. w = xy + yz + zx, x = r cos(θ), y = r sin(θ), z = rθ; ∂w ∂r ∂w ∂θ when r = 8, θ = pi/2 c. Use the...
Suppose two 5-meter poles are fixed to the ground in upright position [in red], one in San Diego, CA and the other 392 miles due east near Phoenix, AZ. Assume both lie on the earths equa tor. Suppose at noon the pole in San Diego casts NO shadow, while the pole in Phoenix casts a shadow of 0.51 meters [in blue]. Based on this information and the diagram shown, se- lect the true statement/s, assume r is unknown, and refers...
4. LTI Systems and Erponential Response. (12 pts) (a) (2 pts) Suppose an LTI system has input-output relationship y(t) 2r(t+3). What is the transfer function H(jw) of the given system. Show that H(jw)2. Hint: H(jw(tejdt (b) (5 pts) Suppose an LTI system has input-output relationship y(t)2r(t+3) as Problem 4-(a). Find the output y(t) using the complex exponential response method as discussed in lecture for the input r(t) = ej2t + 2 cos2(t). Hint: cos2(0) 1 (20 cos(26) an d 1-ejot...
questions are connected. please show steps to all Consider the system characterized by the characteristic polynomial D2+4D+4. (0) Find the zero-input response go(t) of the system, such that vol(o) 0 and o(0) -1. Impulse Response and Zero-State Response 4 Consider the system characterized by the following diferential equation where z() represents the iaut and y(t) the output (D2 +4D+4) y(t) Da(t) (i) Determine the impulse response h(t) of the system. (i) Compute the convolution h r(t) for r(t) eu(t). Hint:...
NOTE: PLEASE DO Q.3 Part d and e Answers are given below: Question 3 (16 marks) Consider the periodic signal T v(t)24 cos(2t ) - 4 sin(5t - 2 The signal v is given as an input to a linear time-invariant continuous-time system with fre- quency response 4 0 lwl 2 2 jw H(w) lwlT 2, 1 2 jw (a) 3 marks] Find the fundamental period To and frequency wo of v (b) [3 marks] Express v in cosine sine...
Question 1. Determine whether or not \(\mathrm{F}(x, y)=e^{x} \sin y \mathbf{i}+e^{x} \cos y_{\mathbf{j}}\) is a conservative field. If it is, find its potential function \(f\).Question 2. Find the curl and the divergence of the vector field \(\mathbf{F}=\sin y z \mathbf{i}+\sin z x \mathbf{j}+\sin x y \mathbf{k}\)Question 3. Find the flux of the vector field \(\mathbf{F}=z \mathbf{i}+y \mathbf{j}+x \mathbf{k}\) across the surface \(r(u, v)=\langle u \cos v, u \sin v, v\rangle, 0 \leq u \leq 1,0 \leq v \leq \pi\) with...
D1 = 7 D2 = 4 Any assistance would be greatly appreciated Question 3 Left end (x 0) of a copper rod of length 100mm is kept at a constant temperature of Temp - 10+d2 degrees and the right end and sides are insulated, so that the temperature in the rod, u(x,t). obeys the heat partial DE, CD11 mms copper. where D-1 mm's for copper (a) Write the boundary conditions for u(x, 1) of the problem above. Note that for...