Homing pigeons avoid flying over water. Suppose a homing pigeon is released on an island at point C, which is 5 mi directly out in the water from a point B on shore. Point B is 12 mi downshore from the pigeon's home loft at point A. Assume that a pigeon flying over water uses energy at a rate 1.25 times the rate over land. Toward what point S downshore from A should the pigeon fly in order to minimize the total energy required to get to the home loft at A? 12-x 12 Total energy = (Energy rate over water) • (Distance over water) + (Energy rate over land) • (Distance over land) Point S isO miles away from point A. (Type an integer or decimal rounded to three decimal places as needed.)

Q: Suppose the edges of a cube are increasing at a constant rate of 8 m/hr. Then, the volume of the…

A:

Q: Consider a tank with volume 100 liters containing a salt solution. Suppose a solution with 2…

A:

Q: Consider a reservoir with a volume of 8 billion cubic feet (ft^3) and an initial pollutant…

A:

Q: A 40 gal tank initially contains 11 gal of fresh water. At t = 0, a brine solution containing 1.2 lb…

A: Given: The initial volume of water v(0)=11 gallons The initial amount of salt s(0)=1.2 lb Since rate…

Q: consider a tree with a tr

A:

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A:

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A: Formula of volume V=43πr3 Given: Radius, r=8 mm drdt=-1mm/month

Q: A 13-foot ladder is placed against a wall. If the top of the ladder is sliding down the wall at 3…

A:

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

A:

Q: Suppose the edges of a cube are increasing at a constant rate of 11 m/hr. Then, the volume of the…

A: Let the side of the cube = x Edges of the cube increasing rate dx/dt = 11 m/hr

Q: Suppose at the end of the d perature stays constant at M furnace/air conditioner rate A

A:

Q: Show that a projectile attains three-quarters of its maximum height in half the time it takes to…

A: Show that a projectile attains three-quarters of its maximum height in half the time it takes to…

Q: The kinetic energy K of a movingobject varies jointly with its mass m and the square of itsvelocity…

A: Given, The kinetic energy K of a movingobject varies jointly with its mass m and the square of…

Q: In order to stay awake during class, a professor keeps a 200 ounce capacity coffee maker in his…

A: Given coffee maker capacity is 200 ounces. it contains 40 ounces coffee which has 500 mg caffeine.…

Q: A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a rate…

A: Solve by making differential equation

Q: A substance cools in moving air at a rate proportional to the difference between the temperature of…

A:

Q: The upper end of the ladder 5 m long leans against a vertical wall. Suppose the foot of the ladder…

A:

Q: Worker A is a loader and worker B is an unloader. Worker A can load a truck in 10mins, while worker…

A: The time taken by worker A to load the truck is = 10 min  The time taken by the worker B to unload…

Q: A 200-liter tank initially full of water develops a leak at the bottom. Given that 10% of the water…

A:

Q: Mauritius  island  is  2  km  due  south  of  its  closest  point  along  a  straight  coastline.…

A:

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given that,  At time, t=0, the amount of cane sugar in water =75kg At time, t=30minutes, the amount…

Q: A tank contains 4000 liters (L) of a solution consisting of 120 kg of salt dissolved in water. Pure…

A: Here, ri = 4, ci = 0, r0 = 5, The differential equation is There is no inflow of salt, thus the…

Q: Water is discharged from an inverted cone-shaped tank with a height of 12 meters and a radius of 6…

A: Given: The height of the inverted cone-shaped tank, h = 12m. Also, its radius, r = 6m. From the…

Q: Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km3, and water flows…

A: Here we have consider 3 lakes. i.e A,B and C.                               Volume of lake B=2650…

Q: Suppose that a car starts from rest, its engine providing an acceleration of 10 ft/s², while air…

A:

Q: Assume that a snowball melts so that its volume decreases at a rate proportional to its surface…

A: Let V denote the volume and A denote surface area. Rate of melting is proportional to its surface…

Q: A flag is raised vertically from a pole at a constant rate of 1m/s. A point B on the ground level…

A: Given: Vertically raising speed of flag at constant rate=1 m/s……1Horizontal distance from flagpole…

Q: snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate (in cm/min)…

A: Given query is to find the rate at which diameter of snowball is decreasing.

Q: A tank contains 5000 liters (L) of a solution consisting of 182 kg of salt dissolved in water. Pure…

A:

Q: Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km2, and water flows…

A:

Q: 10) Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm…

A:

Q: High-speed train is to have a maximum speed of 450 km/h. Regulations require that the brakes must…

A: We will find the constant rate of deceleration qs following .

Q: Tank A contains 402 litres of brine holding 123 N of dissolved salt, and tank B contains 402 litres…

A:

Q: If the area A = s of an expanding square is increasing at the constant rate of 8 square inches

A:

Q: It is believed that life appeared on Earth when 2 sets of proteins merged together to form the first…

A: a) Let at a intermediate time t amount of life Ct. Amount of protein A needed to form Ct amount of…

Q: A radioactive element decomposes at a rate proportional to the amount present. The amount remaining…

A:

Q: At what rate is the height of the water rising at the instant the tank is half full?

A: To find the rate at water rising

Q: he surface area of a cube is increasing at a rate of 122.2 cm2/s. At what rate is the side length of…

A:

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

A:

Q: A tank contains 50 gallons of a solution composed of 90% water and 10% alcohol. A second solution…

A:

Q: Consider a reservoir with a volume of 8 billion cubic feet (ft³) and an initial pollutant…

A: Given: Volume of the reservoir is 8 billion cubic feet, V=8×109 ft3 Now initial polutant V is,…

Q: A tank contains 2000 liters (L) of a solution consisting of 182 kg of salt dissolved in water. Pure…

A:

Q: In a room containing of air 20,000 m3 of air, 600 m3 of fresh air flows in per minute, and the…

A:

Q: A tank contains 1000 liters (L) of a solution consisting of 195 kg of salt dissolved in water. Pure…

A: Solution is given below:

Q: A 60-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 Ib…

A:

Q: A tank with a capacity of 25 L originally contains 15 L of brine with a concentration of 5 g/L of…

A:

Q: A 50-gallon tank initially contains 10 gallons of fresh water. At t= 0, a brine solution containing…

A: We will find out the required time.

Q: A flag is raised vertically from a pole at a constant rate of 1 m/s. A point B on the ground is…

A: solution:- draw a right angle triangle:-

Q: A tank initially holds 80 gal of a brine solution containing of salt per gallon. At t=0, another…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.