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1. (i) How many digits does the number 101000 have when written to base 7 ? (ii) Use the prime number theorem to estimate the proportion of prime numbers among the positive inte
a restrained steel bar is heated from 20 degrees to 194 degrees and not permitted to expand. the bar is 10mm diameter, determine the thermal stress in the bar
The data of the table below give details of the components, prices and standard quantities used in making a kind of chemical. Measure the composite index with 2007 as base year us
In the x,y plane, divide up the x-axis by placing marks at x=a, x=b, and x = -2. Suppose φ is harmonic in the upper half plane and on the segments of the x-axis defined by your mar
Parents put $1000 into a saving account at birth of their children. If the account earns interest at 7% p.a compounded yearly, how much money will be in the account when their chil
At 8am particle A is at point (0,0) and moves horizontally to the right with constant velocity of 60km/hr. At the same time particle B is at the point (0, A+B+C+5) and moves horiz
Question 1 Find all solutions of the following equations in the interval [0, 2π) (a) sin(2x) = √2 cos(x). (b) 2 cos 2 (x) + 3 sin(x) = 3. 2. Sketch the graph of the ci
As with the first order system, there is a general differential equation that governs the response of a second order system. The equation is of the form: Where: So
A research analyst for an oil company wants to develop a model to predict miles per gallon based on highway speed. An experiment is designed in which a test car is driven at speeds
Given the loop transfer function G(s)H(s) = k/s(s+3)(s+4)(s+5) (a) Sketch the root locus plot for G(s)H(s). (b) What is the system gain at s = -1+ 2i? (c) Calculate the
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