83 • Compute 2 + (XA), XER M+N N+M AEIR tr • Compute the Jacobian (Tenson) of the following functions 5.5 (7) 5.6 g (+) 5.5) Consider the following functions: f1 (7) = sin (x1) cos (x2), XEIR² T fe casy = x²y, 1 YER" ₤3(+)-**** EIR" I What one नेते the dimensions of b.) Compute the Jacobians 5.6) Differentiate of with respect to t and g with respect to X, where fets- sin clog (++), tεIRD gas = tr(A+B) >> PXE EXP AEIR ) XER BEIR" fap where tres denotes the trace.

Q5.4 Let Lcg) (^) 4y) =an you? (x) where the be the following: (n-1) nth + + an-ly Aos Air order Suppose you know 9 2x I 4(y) Ly) = sẻ cosxxẻ xe an linear 2x 2x that: Ly()] = 3 xe when when L[Y₂ (x)] = 7e²x sinxe L[y₂ (x)] = 6e ²x cos x when 2x our e (x) (*) + constants Consider differential equation Find a particular solution be a symbolic function of x any decimals. contain any (x) + a₂ y(x) ал 9, (х) = 6 же ча в 4₂(x) = 14e²x cos x уг 2x 22 93 (x) = 54e²x Cos x + 108€ ²³" sinxe to (*). Your answer should and must not

hey im so confused.when i use the formula in the picture i get 1.69 (1+0.7^2+0.2^2+0.4^2)x 1 =  1.69

Two waves on a string are given by the following functions: yı (x, 1) = 4 cos(201 – 30x) (cm) y2(x, 1) = -4 cos(201 + 30x) (cm) where x is in centimeters. The waves are said to interfere constructively when their superposition lys| = ly1 + y2|maximum, and they interfere destructively when lys| is a minimum. (a) What are the directions of propagation of waves y1 (x.f) and y2(x, t1)? (b) At t = (= (T/50) s, at what x location y do the two waves interfere constructively, and what is the corresponding value of ys|? (c) At t = (7/50) s, at what locationx do the two waves interfere destructively, and what is the corresponding value of lys?