Mila had math and reading homework tonight. mila can solve each math problem in 5 minutes and she can read each page in 2.5 minutes. mila completed a total of 17 math problems and pages of reading in 55 minutes. write a system of equations that could be used to determine the number of math problems mila solved and the number of pages she read. define the variables that you use to write the system.

Ece 202: problem set 1 due: june 14, 2019 (friday) the first 3 questions of this homework assignment covers some fundamental mathematical concepts that will play a role in this course. the remaining questions are on basic signals and laplace transforms. 1. a review of complex numbers. (a) compute the magnitude and the phase of the complex numbers −4 +j, and write them in polar form (i.e., of the form rejθ). also, plot the complex number in the complex plane. (b) simplify the complex number 1 4 − √ 1 2 − j √ 2 22 and write them in cartesian form. (c) consider the complex number s = z1z2 · · ·zm p1p2 · · · pn , where each zi is a complex number with magnitude |zi | and phase ∠zi , and each pi is a complex number with magnitude |pi | and phase ∠pi . write the magnitude and phase of s in terms of the magnitudes and phases of z1, z2, . . , zm, p1, p2, . . , pn. 2. a review of differentiation. (a) find df dx for the following functions. i. f(x) = (1−4x) 2 √ x . ii. f(x) = √ 1 + tan x. (b) find dy dx for the equation e x sin y + cos2 x cos y − x 3 = 0.