Question

A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 24 ft from the house, the base is moving away at the rate of 7 ft/sec. a. What is the rate of change of the height of the top of the ladder? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? c. At what rate is the angle between the ladder and the ground changing then? 25-At ladder y(t) 0 ft/sec a. The rate of change of the height of the top of the ladder is (Simplify your answer.)

Answer 1

Solution: A as ift P- B ->244 dn dt efflrec. In SAOB OA²+ 0B²- ABZ g²+ m2 = (2512 : 24- y? (25722412,= 49 y = Jas = 7 2 n²+42 25 나 differentiate abow with respect to d dat (2?xy?)= alt (272) O 2nde at + zy dy dt 2x24 x 7+2x7 dy dy dt 5-24 ft/ sec.

Now Area of tringle formed in gian by A = 1 (Base) breight) 2 A = £ny da =ź (y are dt of a day dt ) dA at ( 7x7+ 2ax.4-24) unit 2 da dt = 527 2 o be thang the angle Let alt a dt a tanda ( 9 ) see 2o do xyla ya' It - 25 also Seco= 24 Heypotencous Base 2 24% (-21) – 7X67) do 25 24 dt ( 24,2 628 = 1 rod/ser. at 625 oft /sec. Answers 9! -24 t/xc2 (5 l - 527 2 rad Isec. (c FI