By E. J. McShane
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Additional info for Unified Integration (Pure and Applied Mathematics (Academic Pr))
Example text
5 = Get 5x alone on one side of the equation by adding 15 to both both sides. 5x - 15 15 • = 5* 15 5x= 20 Divide both sides by _5x 20 5 5 1Z\ A25 W = I -'4 W - ma i"^ " - "lo- mad 5- A23 2a 3a * * 4b 4b - b 3o + 35 = a * b - a * b - b = A26 *n'mR If you got this answer, you can feel confident of youf ability to Kandle simple equations. If you missed this problem, review frames 24 and 25, and then try again. Should you still have trouble, asl( your teacher for help. A24 3o o 3fc = Subtract 3o from both sides.
35 3 c Subtract 3o from both sides. 2 Multiply both sides by R^' FR^ = Gm,m2 Divide both Sides by F: „2 Take . Cm ,m2 the square root of both sides: ma \f^ A23 Eliminote o by solving the equation v and sub = of for o. A21 3fc = 3i or i c - 3o c - 3o c - 3o = -J - o A24 Substitute the value of equation (2) F mto equotion W = Fd but F - ma so W = (ma) (d) or Mf B mad m (1): 22 Here another equation with a quantity is 5(x Solve 25 for X 3) = in parentheses: 5 following the three steps used in the last three frames.
_,,) = {_1)(3-S2) s, = -3 = s, - S2 -3 A18 PiV,T2 P2V2niT, P,V, (P,V,)n2 P,V,n2 A17 5v 2(m - A15 A16 6 - X 6 - X . = y X - y • X 6 = y + X 6-y=y»x-y 6 - y = X A20 02X2 (i) Multiply both sides by (ii) Divide both sides by P2 A19 (0 \T} V = of (ii) I (ill) Divide both sides by a: 17 Here is another similar equation: Sit = Solve this equation 5f + 15s for k. 21 Perform the two operations listed for in P,V, P2V2 n "zTi , Ti A20 to solve the equation V2. 20 OUR PROBLEM: If v = of and d = jat^, find a in terms of v Substitute the value we have found and for t equation, and do any necessary simplification.