(20 points) Josh makes deposits of 1000 at time 0 and X at time 4. His...
4. Find d > 0 such that d 1000, 5 | d, d| 60, and d/2 | 75
dx Determine x= f(t) for (t? +4t) 4x + 4,t> 0; f(1) = 3. dt For (1? + 4t) dx dt = 4x +4, x= f(t) =
Prove this using the definition R7: log(n*) is O(log n) for any fixed x > 0
Please include step-by-step solution. D19. Solve t2x" +3tx -3 x-t', t>0.
5. (20 pts). Solve the following initial-value problem: Ut + 2uuz - 0<x<, 0 <t<oo 0 1 <1 > 1 u(t,0) = Then draw the solution for different values of time.
Consider the signal x(t) = te-atu(t), a > 0 Find to = 1.00 /*(t)?|dt Find to = 10lx(t)2|dt Can simplify to → %*tx?(t)dt x2(t)dt
5. Consider the system in the figure below with X (12) = 0 for 221 > 20007, and the discrete-time system a squarer, i.e. yn = t[n]. What is the largest value of T such that y(t) = I.(t)? x[n] Hiscrete-time y[n] system D/C
4. Rank the following types of electromagnetic radiation in order of decreasing energy. X-rays > Ultraviolet > Visible > Microwaves b) Microwaves > Visible > Ultraviolet > X-rays c) Microwaves > Ultraviolet > Visible > X-rays d) X-rays > Visible > Ultraviolet > Microwaves 24. Which of the following arrangements is in order of increasing size? a) Ca2+> K+ > C1-> S2- b) Ca2+ <K+ < Cl< S2- c) 52-> Cl- > Ca2+> K+ d) $2- < Cl- <K+ <...
Please explain your answer clearly. 4. Use the Fundamental Theorem of Calculus to find v(t) and a constant A such that A+ ſ vo(t)dt =z, where I >0.
Could someone explain how these to get these phase portraits by hand with ẋ=y and ẏ=ax-x^2 especially for a=0 case where you have eigenvalues all equal to zero? 6.5.4 a>0 Sketch the phase portrait for the system x = ax-x, for a < 0, a = 0, and For a -(0 We were unable to transcribe this imageFor a>0 ES CS