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a 5. [S] The total resistance (R, in N2) of a circuit depends on the length of the circuit (L, in cm) and the thickness of the wire use (k, in mm). Using collected data, we have a function R(L,k). We know that R(10,0.5) = 8.5, and that R_(10,0.5) = 1.5 and Rk(10,0.5) = -0.5. In varying weather conditions, the length or thickness of the wire can fluctuate, which affects the resistance. If the resistance changes too much at once, this can affect the signal being transmitted. =

(a) If we expect the length to increase by 5% and the thickness to increase by 10%, then by how much do we expect the resistance to change? (b) If the length is currently 10 cm, and the thickness is 0.5 mm, then what is the fastest possible instantaneous change in resistance? What change in length and thickness would be needed to produce this fastest change? (c) Let's say we know how the length and thickness will change in the next hour: L(t) 10+ 3t – t2 and k(t) = {e=t/2. How quickly is the resistance changing right now, when t = 0? ze

5. (a) 0.725 a (b) 10 b (c) 4.625 2