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M137assign1 - Math 137 ASSIGNMENT 1 Fall 2006 Submit all...

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Unformatted text preview: Math 137 ASSIGNMENT 1 Fall 2006 Submit all boxed problems and all extra problems by 8:20 am. September 22. All solutions must be clearly stated and fully justified. TEXT: Section 1.1 — 111 14 17, I 34 36,- I 52, I, 60 66 Sectionl.2— 8, 1] 14 161)) Section 1.3—3,- 11 12, 16 17 23 I 28,- I Appendix A — 12, if), 25, m, I, 51, I, 63 EXTRAS: Ell Sketch the graph of y = Notes. 1 using the reciprocal method on page 16 of the Course 2 Sketch the given function using the definition of the absolute value function and/ or graphical operations on basic functions. 1 [22—1 W2 E13 A cylindrical tank of diameter 2m and height 6111 is being filled with water. a) (1+ 1w |)2 +1 b) (2x +2)”3 0) a) Let (1. 111 be the depth of water when the tank is partially filled. \N’I‘ite down a formula for the volume l/(d)1'n3 of water in the tank, and sketch a graph of V(d). b) Write a formula for depth d as a function of V, and sketch a graph of d.(V). c) Suppose the flow rate of the water filling the tank is 10 litres per minute. Assuming the tank is empty at t: 0 find a formula for depth d(l )1“,n and sketch d(t ) over a suitable range oft (i.e., until the tank if full). Note that 10006- — 11112 . Ely-"1 A cylindrical cable of radius r0 carries electric charge. The electric field strength E (7) at P, a radial distance 7" from the central axis of the cable is given by E0") = {Icr2 for r 3 7'0. 1113:} for 7' > 7'0 Sketch a graph of E (7“) 131.5 Each of the roughly (iiculai organisms in a colony has radius 7 cm and density 0.4 g/e1112.The1e are 10 000 organisms in total The energy consumpi 1011 of the colony is % where m is the total mass. TI’L E = 2'0—— 0 1000+m Show that the energy consumption can be written as either E = 250 (1 — 0rE=250(1— 1 ). 1+47rr2 1000 ) 1000+m Discuss the behaviour of E as the organisms grow larger. What happens to the energy consumption per unit mass as m increases? Give a biological intgerpretation. Sketch a qualitative graph of E as a function of m. [HINT: Start with %; you Will need a reflection, two shifts, and two scales. Use two separate diagrams to avoid confusion among the six graphs] ...
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