Question

Two poles are connected by a wire that is also connected to the ground. The first pole is 10 meters tall and the second pole is 20 meters tall. The poles are located 30 meters apart. Find the distance, x, where the wire should be anchored to the ground to minimize the amount of wire needed. Enter your answer rounded to the nearest whole number. Do not enter units with your answer.

Answer 1

ght Goen figure .. h of the wire ret and 7 Either x-100 or af 20.0 3x10 (x f-30 impossible) Therefore, the exitical point û x210: Now, from @ we have What 100.- 2. VaVp100 cm + - 1130-132P 400 – (30-6). h 944100 (20-09-p pro Also-w) ZIBO- 400 Ao-amefore to-ametre and on al meters . Then the total len 1 = arb. Since coax then OD = 3o.x. There fore from the triangle toe, we showe Q>- 104+x" po - a = warp 100 and from the triangle OBD , we howe W = (30-x) - 20² GEN (30 x 2100 from o no, 8 = Vafloof / 120 - x 54 400 we have to to minimize 8. · Vit 100 - V 220-23-6900-en outlet are (wo (30-0) of 100 auf 100 ar Nato do near the + xhu-uzado. A130-22_0 W PLVO (27 + 100) 100 60-a) of 400 - (3 00- x) ~ {(30-x) + 400} (30-x) 7400 - 400 (377100) Torproo +400V Bora) 4400 Then Now, aro di 228 Too 28% roo xVEY) 100 + (20-). Vampion (Vrivo) (V120-457 400) den 7 a 1120-17271460 + 80-19. vekaimo zo a? (60-x)*400) = (a-)" (s*p100) Fax (0602.4900 4400)- 69-609 +900)( a.p100) I ar la con1900) + 400 2 z 22 (7-601-6700) A/10( 42=601 1900) g 1002 1002-60000 of 90000 & 308x + 6000k - 90000 to x 200 - 300 to 1 x + 300-10x - 300 20 2(x+30) - 10 (2430) - (2-10) (af 30) 0 that is omova - Hova yo. yoyo Hence the the wire minimum should be distance malom anchored to the are such that

. Either x-100 or afzo co x=10 (af-30 impossible) Therefore, the critical point ñ no10. Now, from ③ we have - da stvario** + 44100 (50-) -V130-132P too – (30-4). zuen (30-4 jr too 2 vx100 - x² Vit 100 V (20- 400 - (30-x) 2 V 30-4.p400 arp (vo (30-0) 400 24 100 ar (2 + 100) 27100 Bora) 400 - (300-x) ~ (20-2) 400} & (60-x) 7400 100 400 100 (6*410) Vapoo 3130-2) p qood V 150 m) 4 00 Now, ao dan = 2200 Too . 28% raro nova - Hové so. * is I yo. darlanol Hence the minimum distance alom such that the wire should be anchored to the ground. That is o hored to the growne

polo Given figure in wen the 120 m 10 m ) D 30- 30 the wire t Ao-ameters and oba bo meters. Then the total length of 1 = arb. Since coax then OD = 3o.x. Therefore, from the triangle toe, we howe a = 104n0 a = √22p 100 and from the triangh OBD ,we howe V= (30-x) .P 207 be N 20-0277100 © from 4②, 8 = vrtloo & √ 120 x 57400 - we have to to minimize 8. Noco. Con e st + x two-windore A.2012_0 2 καιρινό Then 2 x V 80-33%p 100 + (20-4). Va pivo (vorreioo) (V (10-2)2 800) da o 7 2 V 1720-1777400 + (0-1). Vaimo 20. g ? (60-x)+100) = (-20)”.(*p100) I am (–608 4900 4400) - 64-609 +900) ( 278100) I on (otor +909) 2400 27 6014900) 100(0-609 49 00) poolt. 190260008 + 90000 & 300 x + 60000 90000 to x 200 - 300 to 3 x+302-104 - 300 20 » 2(x+30) - 10/2430) = ☆ (@-10 ( 14 30) 20