A ship passes a lighthouse at 3:15 p.m., sailing to the east at 10 mph, while another ship sailing due south at 15 mph passes the same point half an hour later. How fast will they be separating at 5:45 p.m.? Round any intermediate calculations, if needed, to no less than six decimal places, and round your final answer to three decimal places.

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: From the Pythagorean theorem, BC2+AB2=AC2

Q: Starting from the same point, Royden starts walking eastward at m/s while Nilo starts running…

A: We use Pythagoras theorem  (Hypotenuse)2 = (perpendicular)2+(Base)2

Q: aveling at 50 ft/s when the brakes are fully applied, producing a constant deceleration of 18 ft/s2.…

A:

Q: A boat is pulled into a dock by a rope attached to the bowof the boat and passing through a pulley…

A: Let the distance of the boat B from the dock D be x meter. And the length of the rope is r passing…

Q: 3. A boat is pulled to a dock by a rope attached to the bow of the boat and passing through a pulley…

A: Explanation of the answer is as follows

Q: An ice cube that is 3 cm on each side is melting at a rate of 2cm^3 per min. How fast is the length…

A:

Q: The formula for the volume of a right circular cylinder of radius r and height h is V = πr^2h. At…

A: We will find that how fast is the height of the cylinder changing at this same instant?Below find…

Q: A 4.5 ft tall man is walking away from a 25 ft tall lamp post.  If he is walking at a rate of 2…

A:

Q: Two people start from the same point. One walks east at 5 mi/h and the other walks northeast at 4…

A:

Q: A 20-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A:

Q: A boat is being pulled with a rope towards a dock that is 10 ft above the water, as shown in the…

A: Let the distance of the boat= x ft y=length of the rope.  So,  given that dy/dt= 1.5 ft/min We have…

Q: A man 1.85 m tall approaches a street light 5.4 m above the ground at the rate of 23 mis. How fast…

A: To calculate the rate of change of the shadow of the man.

Q: An 8-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A:

Q: At noon, ship A is 100 km west of ship B. Ship A is sailing south at 25 km/h and ship B is sailing…

A:

Q: Ship A is sailing due south at 16 mi/h, and ship B, 32 miles south of A, is sailing due east at 12…

A:

Q: Two buses are driving along parallel freeways that are 5mi apart, one heading east and the other…

A:

Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: Given: The length of a rectangle is increasing at a rate of  9cm/s and its width is increasing at a…

Q: A rope is attached to a boat at water level, and a man on the dock is pulling on the d) rope at the…

A: Draw a schematic diagram of given figure.

Q: A Ferris wheel of radius 36 feet needs 5 minutes to complete a full revolution. At what rate is a…

A:

Q: A street light is at the top of a 13 ft tall pole. A woman 5.75 ft tall walks toward the pole with a…

A: Given problem:- street light is at the top of a 13 ft tall pole. A woman 5.75 ft tall walks toward…

Q: An electrician is working at the top of a ladder that is 20 ft long and leaning against the wall…

A: Heights and distances  (application of derivatives)

Q: A 14-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A:

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A:

Q: A van is 5km due north of a bus at 2:00PM. If the van is traveling northward at the rate of 60 kph…

A:

Q: Suppose car A is heading south at 85 km/h and car B is heading east at 90 km/h. Both are headed for…

A: Consider

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: Given : The pulley is 1 m higher than the bow The rate at which rope is pulled dydt=-1m/s and x=8.…

Q: Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that…

A:

Q: A spherical balloon is inflating with helium at a rate of 80 pie ft^3 /min. How fast is the balloons…

A:

Q: A lighthouse, L, is on an island 8 mi away from the closest point, P, on the beach. If the…

A: Given: A lighthouse rotates clockwise at a constant rate of 17 revolutions/min.

Q: A girl starting at 11 A.M., travels east at 4 km/hr while a boy, starting at noon from the same…

A:

Q: A 16-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A: Let us consider that, lowermost end of ladder is y foots away from wall and height of wall is x…

Q: Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that…

A:

Q: A water trough is 800 cm long and a cross-section has the shape of an isosceles trapezoid that is 40…

A:

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: Let A= Pulley , B= Boat Given that AC=1  Let, x= distance of the boat from the dock. y=length of the…

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A:

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: The dock is 1m higher than the bow of the boat. Pulled rate of the rope of 1.4m/s To calculate the…

Q: A 14-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A:

Q: At noon, ship A is 140 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing…

A:

Q: A Chinese patrol ship was spotted 150 kilometers north of a Philippine fishing boat at 6:00 a.m. The…

A: This question is related to differentiation, We will solve it using given information.

Q: A car traveling with an initial velocity of 29.81 m/s to the east, sees a wall 56.42 meters to its…

A:

Q: At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing…

A:

Q: Two people start from the same point. One walks east at 6 mi/h and the other walks northeast at 5…

A:

Q: A man 6.50 ft tall approaches a street light 17.0 ft above the ground at the rate of 5.00 ft/s. How…

A:

Q: A 10-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A: Height = 10 foot 3 feet/sec Ladder is 3 feet from the wall

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

Q: Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min, and its coarseness is such that…

A: Now given that

Q: The base of a 45-foot ladder is being pulled away from a wall at a rate of 6 feet per second. How…

A: Use Pythagoras theorem

Q: Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min, and its coarseness is such that…

A: The volume of the pile is increasing at a rate of 10 ft3/min. so,dvdt=10 The diameter and height are…

Q: A man 7.00 ft tall approaches a street light 16.0 ft above the ground at the rate of 6.00 ​ft/s. How…

A: Given data: The height of the man is CD=7 ft. The height of the street light is AB=16 ft. The rate…

Q: A car starting at 12:00 noon travels west at a speed of 30 kph. Another car starting from the same…

A: Given: A car starting at 12:00 noon travels west at a speed of 30 kph. Another car starting from the…