8) Using component notation and the definitions (2.2), (2.12) and (2.14), derive the following identities:
Using floor, ceiling, and standard arithmetic notation, give an expression for a real number x 2.12 for example, 7.5 rounds to 8.) 2.13 2.14 rounded to the nearest 10-*, for an arbitrary number k of digits after the decimal point. rounded to the nearest integer. "Round up" for a number that's exactly between two integers- rounded to the nearest 0.1.
2. Asymptotic Notation (8 points) Show the following using the definitions of O, Ω, and Θ. (1) (2 points) 2n 3 + n 2 + 4 ∈ Θ(n 3 ) (2) (2 points) 3n 4 − 9n 2 + 4n ∈ Θ(n 4 ) (Hint: careful with the negative number) (3) (4 points) Suppose f(n) ∈ O(g1(n)) and f(n) ∈ O(g2(n)). Which of the following are true? Justify your answers using the definition of O. Give a counter example if...
2.14 Repeat Example 2.12, assuming that there are eight houses connected on each DT and that there are a total of 120 DTs and 960 residences supplied by the primary feeder Example 2.15 Assume that a 5 kW air conditioner would run 80 % of the time (80% duty cycle) and, during the peak hour, might be limited by utility remote control to a duty cycle of 65%. Determine the following a. The number of minutes of operation denied at...
Use sum and difference identities to verify which of the following are identities. 1) sin(Q+8) - 1-tan & tan 8 sin a 2-cot a cot 8 2) cos(a+8) - 2 sin a sin 8 Both the equations are identities. None of the equations are identities Only the first equation is an identity. Only the second equation is an identity.
cos 2x </ 0.8x-1.9 = O TRIGONOMETRIC IDENTITIES AND EQUATIONS Using a graphing calculator to solve a trigonometric inequality Use the ALEKS graphing calculator to solve the inequality cos2x<0.8x-1.9 with x in radians. Write your answer using interval notation, with values rounded to 2 de (0,0) [0,0] (0,0) (0,0) DUO -00 8. X 5 ?
PLEASE DONT do 8! 9 Is the one I'm confused about. 8. Using just basic definitions derive the expression ( ) - Cp - PC . T-20°C Folded T-90°C Unfolded 3292 I 9. On the right is a real differential scanning calorime- try (DSC) scan of a protein undergoing denaturation. Analyze the scan to show what thermodynamic param- eters can be obtained; number them. Show or draw on the plot just where (using your numbers) and/or how these parameters are...
simplify the following boolean expression using boolean identities(A' means NOT A): X=(AB'C')+(AB'C)+(ABC)
Derive ground state term symbols for each of the following atoms. Use notation 2S(1/2) for state 2S1/2 a) S b) Ca c) Si d) Cr
Problem 2.2 Using the same methods shown in lecture, mathematically derive: (a) The voltage conversion ratio equationwhen the Buck-Boost is operating in Discontinuous Conduction Mode (DCM). Your answer should be a function of D, Ro, T, and L (b) The value of the inductor discharge duty cycle coefficient; D1.Your answer should be a function of Ro, T, and L. Hint 1: Other than assessing the current waveforms, you will also need to apply the assumption of 100% efficiency from Problem...
Simplify the following functional expression using Boolean algebra and its identities. List the identity used at each step. x(y+z)(x'+z')