Question

by differentiating implicitly. Express your answers in terms 5. (2 marks) Find of x and y. dx a) 3ay – y2 = 5 b) 2y = x2 – 3x +2y 6. (2 marks) The position of an object "S" (in meters) at time tis given by the function: s(t) = (31)cos(t)+41. a) What is the velocity when t = 24 seconds? Indicate the correct units and round your answer to one decimal place. b) What is the acceleration when 1 = 20 seconds? Indicate the correct units and round your answer to one decimal place. 2 of 3

Answer 1

G 3x9-4²5 both side with respect to a > differentiate d (3xy) -dly)= d (5) dr da dné 2 y dy 2 0 3 (x de pe + 9.1) - dr → N 3ady da + 3y - 2y dy de 2) -34 (3x-2ydy da 3 TO dy da N -34 (32-29) dy 39 24-3x 2 da

ly3 a²-3x+2y sides with respect to a differentiate both 642 dy da 22 -3 + 2 dy da (692-9) dy 2x-3 2 극 da dy da ㅠ 2 2.X-3 642_2

@ @ SH)= 3tcoolt) + 4+2 velocity S'H) VW d (st cost f 4+2) dt VH) = 31 t. 4-sint) + tøst] + 8+ VID) 3 - 3 t Sint +3 Copt+8+ so velocity at (tz21) = V(28) 2-3x2Sin (29) +36127+167 V9I+E+O つ 53-3 83 velocity = 53-3 meters/second]

80 acceleration at (t = 20$ a (en) 6 acceleration VIH act) d (-34 Sint +3 cost+8+) dt alt = -3 -3[tfast + Sint'] +3(-sint) +? alt) = -3t cost - 3 Sint - 3 sint +8 -3 t cost-esint +8 acu =-3497 Cos() - 6 Sin 97 +8 6x0+8 -3x29x1 -6A +8 > 5-10.8 acceleration = -10.8 mites (econde 80
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