A certain mold grows at a rate proportional to its present size. If the original amount doubles in one day, what proportion of the original amount will be present: A) in 5 days? B) in 7 days?

Q: 4. A boy is flying a kite at a height 150 ft. If the kite moves horizontally away from the boy at…

A: Given query is to find the rate of change of length of string.

Q: 5. A kite 100 feet above the ground is being blown away from the person holding its string in a…

A: So, here x2+1002=s2...(1) Given dxdt=10 Now, at s=200, from (1):…

Q: How fast is the volume of a parallelepiped increasing if the length, width, and height of the…

A:

Q: 1. The Louvre museum in Paris features an inverted square pyramid with a height of 10 m. The side of…

A:

Q: A ladder is 27 feet long and is leaning against the side of a house. The base is moved away at 3 ft…

A: Solution is given below:

Q: A kite is 40 ft. high with 50 ft. of cord out. If the kite moves horizontally at 5 mi. per hr.…

A: Draw the position of kite as shown below.

Q: Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank…

A: To solve the following problem and find the amount of water left at 6:10pm.

Q: 3. How much does 1 kg of butter cost at the rate shown in the picture at the left?

A: We will solve the following using unitary method.

Q: A fifteen-foot ladder leans against a wall and slides down, with the base of the ladder observed to…

A:

Q: 18. A kite string is paid out at a constant rate of 3 ft/s. If the wind carries the kite…

A:

Q: A 600 gallon brine tank is to be cleared by piping in pure water at 1 gal/min. , and allowing the…

A: Let S be pounds of salt in tank at time t, so: or Rewritting the equation above we get:…

Q: The requirement for computer server capacity at a particular company is expected to increase at a…

A:

Q: A force is applied to a particle, which moves in a straight line, in such a way that after each…

A: A geometric series is convergent if common ratio is less than 1. Sum of infinite geometric series is…

Q: A tank contains 2,000 L of brine. Brine containing 5 kg/L of salt flows in at 10 L/min, and the…

A:

Q: A truck is 300 kilometers due east of a car and is traveling west at a constant speed of 30km/hr.…

A: (a) Let the initial position of the car be at the origin. Take the x-axis from west to east and the…

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: certain culture of bacteria, the rate of increase is proportional to the numberpresent. (a) If it is…

A: (a) Consider y as the number of bacteria at time t and the rate of change of bacteria can be written…

Q: In, a culture, bacteria increases at the rate proportional to the number of bacteria present. If…

A:

Q: A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds…

A:

Q: 17. A boat is being pulled toward a dock as shown in the figure. If the rope is being pulled in at 3…

A: Follow the procedure given below.

Q: The sides of a triangle measuring 40 m, 32 m, and 16 m increase at the rates of 2 m/s, 5 m/s and 3…

A: Area of triangle: If x, y and z are sides of triangle then area A of triangle is given by A = s(s -…

Q: (d) If the ornithologists observe that birds of a certain species reach the shore at a point 3 km…

A:

Q: 3. A man rows downstream at the rate of 5 mph and upstream at the rate of 2 mph. How far downstream…

A: Let the man goes x miles downstream. Assume, the man takes t1 hour to go downstream and t2 hour to…

Q: 1. a) A car is driving toward an intersection from the east at 40 mi/h, and a second car is driving…

A: Here the two cars are approaching each other at right angles with different speeds. Therefore the…

Q: 2.) A new building has used 18 tons of cement and is only 30% built. At this rate, how many tons of…

A:

Q: A 10​-footladder is leaning against a vertical wall​ (see figure) when Jack begins pulling the foot…

A:

Q: udent is walk

A: Here it is given that,  A student is walking towards the foot of a flagpole 20 meters high at the…

Q: A simple pendulum, consisting of a mass of 8.237 kg, is attached to the end of a 2.68 m length of…

A: To calculate the speed of the mass (in m/s) at the bottom of the swing. Given that: Mass = 8.237 kg…

Q: If the tank is completely full, how much is overflowing if 530 GPM is being taken off the bott

A: Given: Let the rate of filling be Qin = 1250 GPM  the rate of draining be Qdrain = 530 GPM Because…

Q: A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are…

A:

Q: A kite is flying at a fixed height of 30 ft. If 50 feet of stringis out alreadyfrom the spool, what…

A: Given: A kite is flying at a fixed height of 30 ft. If 50 feet of string is out already from the…

Q: A tank contains 1,000 gallons of brine in which 500 lbs of salt are dissolved. Fresh water runs into…

A: Given:-amount of brine in the tank=1000 gallonssalt are dissolved in brine=500 lbsrate of fresh…

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 tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in…

A: We have to find rate of change of  height of pyramid.Information is given below:

Q: 2. It takes a car salesman 2.5 hours to drive from one city to another if he drives at a constant…

A: We know that , distance = velocity×Time

Q: A conical tank full of water is 25 ft high and 15 ft in diameter at the top. If water is flowing out…

A: Given that,  Rate of water is flowing out of a cavity at the bottom is dVdt=3ft3/min Diameter of the…

Q: Assume the rate at which the zombies spread is jointly proportional to the number of encounters…

A: Given: Let the total number of student is 300 in the campus.

Q: Two buses are driving in opposite directions along parallel freeways that are ?=7 miles apart.…

A:

Q: A Ferris wheel with a radius of 5 m is rotating at a rate of one revolution every two minutes.…

A:

Q: vulcanizing shop has a trapezoidal drum that is 5 meters long, 1.5 meter wide at the top, 1 meter…

A: Solution of the problem as follows

Q: an ice cube is shrinking uniformly at a rate of 8 cubic inches per hour. when the cube has a volume…

A: We are given the rate of change of volume of ice cube is shrinking uniformly at a rate of 8 cubic…

Q: The number of germs in a certain culture increases at a rate proportionai to the number present. If…

A: Given that, the number of germs in a certain culture increases at a rate proportional to the number…

Q: Sugar dissolves in water at a rate proportional to the amount still undissolved. If there were 70 kg…

A: The amount of sugar present initially is 70 kg and at the end of 4 hours only 30 kg is left. The…

Q: A moving sidewalk at an airport moves at a rate of 1.6​ft/sec. Walking on the moving​ sidewalk, a…

A:

Q: A stream containing 80 grams per liter of a dye is pumped into a mixing tank with 400 liters of…

A: The answer is 32kg

Q: In developing a paint line process for an appliance manufacturer, a given component on a conveyor…

A: We will find the solution in the following step.

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: The requirement for computer server capacity at a particular company is expected to increase at a…

A:

Q: A and B start toward each other at the same time from points 150 miles apart. If A went at the rate…

A:

Q: 1. A tank is shaped like an upside-down pyramid, with a base of 4 meters and a height of 12 meters.…

A: