41. Weather Balloon Weather balloons are filled with hydrogen and released at various sites to measure and transmit data about conditions such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of 0.5 fr/s. Initially, the balloon contains 2 ft’ of hydrogen. (a) Find a linear function V that models the volume of hydrogen in the balloon at any time t. (b) If the balloon has a capacity of 15 ft’, how long does it take to completely fill the balloon?

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Q: 3. A balloon, in the shape of a right circular cylinder, is being inflated in such a way that the…

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Q: 4. . A balloon is at a height of 50 meters, and is rising at the constant rate of 5 m/sec. A…

A: Let us consider a right angled triangle  ∆ABC, right angled at B. The height of balloon is h meter…

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Q: 12. The height of a right circular cone is increasing at 3mm/s and its radius is decreasing at…

A: Volume of a right circular cylinder is given by formula,  V=πr2h , where r is the radius of circular…

Q: 16.Suppose that the dimensions of a cylinder change at constant rates: the radius of the base is…

A: Use the derivative and substitute the given values.

Q: 3. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a…

A:

Q: A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.1 cm/min.…

A: givendddt=0.1 cm/minor we can write in terms of radiusdrdt=0.12 cm/mindrdt=0.05 cm/mind=14 cmor…

Q: 2. A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is…

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Q: 2. An object moves along the graph y = x° – 2x – 17, starting from the point (0, –17) at time t = 0,…

A: Given that dx/dt= 3 m/sec is constant for all x. So at t=1, x=3, because in 1-second x will move 3m…

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Q: Suppose a brine containing 2 kg of salt per liter runs into a tank initially filled with 500 L of…

A: Set up a differential equation. Let A(t) denote the amount of salt in the tank at a time t. The tank…

Q: 5) Suppose a liquid is to be cleared of sediment by pouring it through a cone-shaped filter. Assume…

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Q: A tank that contains 20 gal of water in which 3 kg of salt has been dissolved completely is to be…

A: Given Volume of water=20 gal  Amount of Salt=3kg Rate of pump in =4gal/min  Rate of pump out=4…

Q: A boat travels 100 miles upstream against a 10 mile/hour current. When the boat's velocity is v…

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Q: 2. The radius of a cylinder is increasing at a rate of 1 meter per hour, and the height of the…

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Q: A swimming pool is 50 m long and 20 m wide. Its depth decreases linearly along the length from 3 m…

A: answer is in next step

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Q: A 100 L mixing tank initially contains 50 L of brine solution with 16 g/L concentration. Brine…

A: Let V be the volume of the tank. Thus, Vt=50+4+2-5t       =50tL where, t is the time in minutes.

Q: 3. The radius of a cylinder is increasing at a rate of 4cm/sec. The surface area remains constant at…

A: Given

Q: 5. A tank originally contains 100 gallons of fresh water. Then water containing 2 lb of salt per 2…

A: We will find out the required value.

Q: The length of a rectangle is increasing at arate of 5 cm per second and its width is decreasing at…

A: Given :- The length of a rectangle is increasing at a rate of 5 cm per second and its width is…

Q: 4. A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t = 0,…

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Q: (4) The temperature at a point (x, y) is given by T(x, y) = xy + x². (a) (2, –1)? What is the rate…

A: (1) The rate of change in temperature can be determined by finding the gradient,…

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Q: 1. Assume that the rate at which a hot body cools is proportional to the difference in temperature…

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

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Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 20 meter…

A: Given: Mass of bucket = 10kg Mass of the rope = 0.1kg/m Height of the Building = 20 meter

Q: It is known that a bacterial culture increases at a rate that is proportional to its current amount.…

A: Given- Number of bacterial fibers after 1 hour=1000 Number of bacterial fibers after 4 hour=3000

Q: One hundred strands of bacteria are placed in a nutrient solution in which a plentiful supply of…

A:

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 30 meter…

A: Given:    Mass of the bucket =10 kg   Mass of the rope =0.2 kg/m  Height of the building =30 m…

Q: 9. The altitude of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is…

A: Area of triangle = 12×b×h Where b is base and h is height . And height of the triangle is equal to…

Q: The price P of gasoline increases to a maximum and then stays at a fixed price. What is the rate of…

A: Given: The price P of gasoline increases to a maximum and then stays at a fixed price. What is the…

Q: A bucket that has a mass of 25 kg when filled with sand needs to be lifted to the top of a 25 meter…

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A: To find: The time when the concentration of salt becomes 0.15 kglt. Given: The capacity of tank is…

Q: 5. Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other…

A: Given that the lengths of the rectangle are begin increased at the rate of 20 mm /sec. The other two…

Q: 4. According to Newton’s law of cooling, the rate at which a body cools is proportional to the…

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Q: 44. The dimensions of a rectangular plate are changing so that the plate maintain its rectangular…

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Q: Find the rate of bubble volume increasing when the radus is 4cm if its surface area is increasing at…

A: Given: dSdt=4  cm/secdVdt|r=4 cm=?

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 10 meter…

A:

Q: A tank contains 45 liters of a chemical solution prepared by dissolving 80 g of a soluble substance…

A: Let's find.

Q: A tank initially contains 40 gal of sugar water having a concentration of 3 lb of sugar for each…

A: A tank initially contains 40 gal of sugar water having a concentration of 3 lb of sugar for each…

Q: 4.) A light is placed on the ground 32ft. from a building. A man 6ft, tall walks from the light…

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Q: What is the result of integrating a population growth rate between two times t= a and t=b, where…

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Q: 5. The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the…

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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.