One of the problems posed by the Marquis de l’Hospital in his calculus textbook Analyse des Infiniment Petits concerns a pulley that is attached to the ceiling of a room at a point C by a rope of length r. At another point B on the ceiling, at a distance d from C (where d>r), a rope of length
Notice that this expression is independent of both W and
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- William is staying in a cottage along a beautiful and straight shoreline. A point on the shoreline is located 3 kilometers east of the cottage, and an island is located 2 kilometers north of Q (see image below). William plans to travel from the cottage to the island by some combination of walking and swimming. He can start to swim at any point P between the cottage and the point Q. If he walks at a rate of 7 km/hr and swims at a rate of 5 km/hr, what is the minimum possible time it will take William to reach the island? Enter an exact answer or round to the nearest hundredth of an hour. Cottage Shoreline 3 km Provide your answer below: hours Island Water 2 kmarrow_forwardTwo LORAN (long-range navigation) stations A and B are situated along a straight shore, where A is 200 miles west of B. These stations transmit radio signals at a speed of 186 miles per millisecond. The captain of a ship traveling on the open sea intends to enter a harbor that is located 40 miles east of station A. Due to its location, the harbor experiences a time difference in receiving the signals from both stations. The captain navigates the ship into the harbor by following a path where the ship experiences the same time difference as the harbor. (a) What time difference between station signals should the captain be looking for the ship to make a successful entry into the harbor? (b) If the desired time difference is achieved, determine the location of the ship if it is 75 miles offshore.arrow_forwardA hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring 13 feet. The ball is started in motion from the equilibrium position with a downward velocity of 4 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second.arrow_forward
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- Kindly show your complete solution. Thank you.arrow_forwardTask 2. a) The p.d., V, between the plates of a capacitor C charged by a steady voltage E through a resistor R is given by the equation dV CR+V = E . dt Solve the equation for V given that at t = 0,V = 0.arrow_forwardㅠ 10) Find the exact value of sec. 12arrow_forward
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