QUANTUM BIOLOGY - EXAMPLE 33.5 : (a) In the measurement of the number of photons received by a plant during photosynthesis, quantum meter is used. At 8 AM, 11 AM, 12 PM, 2 PM and 4 PM of the same day, the measured readings of the meter are 10, 70, 60, 120 and 120 units. Find the mode, median and min of the readings of the quantum meter. (b) Microtubule is used to carry information in a cell. If the cross-sectional area of the microtubule has a diameter of 25 nanometers, find the volume of the microtubule of 1 nanometer in height. State the assumption of calculation.
QUANTUM BIOLOGY - ANSWER 33.5 : (a) Mode = 120 (2 readings, greater than others with 1 reading). Median = 70 (since 70 is the middle, when the values are rearranged orderly as 10, 60, 70, 120, 120). Min = (sum of readings) / (number of readings) = (10 + 70 + 60 + 120 + 120) / 5 = 380 / 5 = 76. (b) Assumption : Microtubule is a cylinder. Let V = 3.142 x h x d x d / 4 where V = volume, d = diameter, h = height. Then V = 3.142 x h x d x d / 4 = 3.142 x n x 25 n x 25 n / 4 = 490.9375 n x n x n = 4.909375 x 10^2 x 10^(-9) x 10^(-9) x 10^(-9) = 4.909375 x 10^(-25) meters, where ^ is the symbol of power, n is nano or 10^(-9). The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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ENGINEERING MECHANIC - EXAMPLE 15.3 : A biochemical trolley of mass 15 kg is towing a trailer of mass 5 kg along a straight horizontal pathway. The trailer and the trolley are connected by a light inextensible tow-bar. The engine of the trolley exerts a driving force of magnitude 100 N. The trailer and the trolley experience resistances of magnitude 10 N and 30 N respectively. (a) Form 2 equations with unknowns T and a, that represents the equilibrium for the 2 systems of the trolley and trailer. (b) Solve the simultaneous equations from the 2 equations that are obtained in part (a) of this question. T is the tension of the tow-bar and a is the acceleration.
ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.28 : In the development of a small engineering facility for biochemical processing, completed contract method is applied in its construction accounting. In a short contract period, let the (contract price) = A. Let the (costs to date) = B; (estimated cost to complete) = C. (a) Find the values of : (i) estimated total costs; (ii) total estimated profit; (iii) percent completion to date. (b) If the project contract is 100 % completed : (i) find the total gross profit recognized; (ii) what is the exact numerical value of C?
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