A 2.0-kg particle has an initial velocity of (Si-4) m/s, Sometime later, its velocity is 7i +3j assuming no energy is lost in the process? m/s. How much work was done by the resultant force during this time interval, b. 49 J c. 19 d. 53 J e 27
Y(z) c(t), C(s) r(t), R(S) + - et), E(S) E*(s), Ez To- D(z) G (s) = (1-e-STºys H(s) 32. If the system above has Y(z)R(z)= 1+z), and if the input is the unit step r(t)=u(t), then the signal y[n]= u[n]-e-Tou[n-1) | u[n]+u[n-1] a) c) u[n] + u[n-1) d) none above 33. If the system above has Y(z)/R(z)= 1+z), the dc gain of the system is C(z)/R(z)= b) 1/2 c)2 d) none above a) o 34. If the system above has...
Suppose that (Wn: n 2 0) is an autoregressive sequence of order 1, so that for n 2 0, where the Z's are i.i.d. and independent of Wo. a) Express Wn as a function of Wo, Z1, , Zn Suppose that |ρ| 〈 1 and var(WD+var(ZI) 〈 OO b) Compute cov(Wm, Wn) for m, n 2 0 c) Prove that there exists a deterministic constant a for which as n -oo and compute a. (Hint: Compute var(Wn)) Suppose, in addition,...
Suppose u = 7i – 3j+k, v=-4j+3k. Find proj, u. OA. 21 9 51-3j+ 3 +-k B. 15 i 59 4 15 j+ 59 59 k Ос. 12 50+ +-k OD. 105 45 j+ 59 15 -k 59 59 O E. 60 45 59j+ 59 Click Save and Submit to save and submit. Click Save All Answers to save all answers. L P]
Suppose u = 7i – 3j+k, v=-4j+3k. Find proj, u. OA. 21 9 51-3j+ 3 +-k B. 15 i 59 4 15 j+ 59 59 k Ос. 12 50+ +-k OD. 105 45 j+ 59 15 -k 59 59 O E. 60 45 59j+ 59 Click Save and Submit to save and submit. Click Save All Answers to save all answers. L P]
4. Suppose T (n) satisfies the recurrence equations T(n) = 2 * T( n/2 ) + 6 * n, n 2 We want to prove that T (n)-o(n * log(n)) T(1) = 3 (log (n) is log2 (n) here and throughout ). a. compute values in this table for T (n) and n*log (n) (see problem #7) T(n) | C | n * log(n) 2 4 6 b. based on the values in (a) find suitable "order constants" C and...
5. Let Zli_ {a + bi l a,b E Z. i2--1} be the Gaussian integers. Define a function for all a bi E Zi]. We call N the norm (a) Prove that N is multiplicative. This is, prove that for all a bi, c+di E Z[i] (b) Prove that if a + r є z[i] is a unit of Zli], then Ma + bi)-1. (c) Find all of the units in Zli 5. Let Zli_ {a + bi l a,b...
question 3 and 4 (3) Prove that nen! T($) = lim n70s(s+1)...(s+n) (4) (a) Prove Wallis's formula T_2.2 4.4 2m. 2m 2" 1.3 3.5 (2m – 1)(2m + 1) *** (b) Use it to prove the identity t(s)[(s +1/2) = V721–25T(28)
8. Suppose b 2 a z 0 for all k E N. a. lf 2. bconverges, prove that £f.i ai converges b. If Ea diverges, prove that £** b, diverges.
ECE 320 Circuit T Midterm Exam 03/06/201 Q.1. Find Z for (a) and (b) in polar form. (20) Z [(5 + 2j). (-3 + 3j)- 5460°]" (b) Z 5430 7j 11-10j Q.2. Find the input impedance, Zin, seen by the volta