calculus 1

1. There is a constant inow of a liquid into a conical vessel 15 feet deep and 17.5 feet in diameter at the top. Water is rising at the rate of 2 feet per minute when the water is 4 feet deep. What is the rate If inow in cu. ft. per minute. a. 3.14 b. 146 c. 6.23 (1. Not applicable 2. A ladder 10 meters long is leaning against a vertical wall inclined 60to the horizontal. Ifthe bottom of the ladder is being moved horizontally towards the wall at 1.5 meters per minute, how fast is the top of the ladder moving when the bottom is 4 meters from the foot of the wall? a. 0.956 mfmin b. 0.456 mlmln c. 1.056 ml min d. Not applicable 3. Find the rst and second dewva of y (parametric eqUationsJ. x=t2+ 1 A y=t 1 a. U2t. - 1MP b. 1f2t, 1MP c. -1.f2t. - lit-it3 d. Not applicable 4. A sherman on a wharf is pulling in a sailboat. His hands are 10 meters above the level of the point on the boat where the rope is tied. Ii'he is pulling in the rope at 2 meters per minute. how fast is the angle that the rope makes with the horizontal increasing when there are 26 meters of rope out? a. 0.032 rad/min b. 0.32 rad/min c. 3.2 rad/min d. Not applicable 5. Find d'y/dx' if fix} = (If!) (2h?) + x 3. 42(1 _ mix\" 13. 2(3 6)}3' c. 20: + 6N1\" d. 2(x Elli-1" 6. Find dydxlfxy=x+y a. 1/(1 1}2 h. lx 1}!2 t. 1/(1- 1}'2 d. - 1/(x+ 1}]2