Sound exerts a pressure on the human ear. This pressure P, measured in dynes per square centimeter, increases as the loudness of the sound increases. As the loudness D, measured in decibels, increases, the pressure increases by 12.2% per decibel. Furthermore, a sound of loudness 97 decibels produces a pressure of 15 dynes per square centimeter. When the pressure on the ear reaches a level of about 200 dynes per square centimeter, physical damage can occur. What decibel level should be considered dangerous? a) 125.6 decibels b) 119.5 decibels c) 117.6 decibels d) 113.9 decibels

Q: A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The…

A: Let x = number of gallons drainedAccording to the given question,Bleach content of original solution…

Q: . A tank contains 1,500 liters of water and 20 kg. of dissolved salt. Fresh water is entering the…

A: Using mixing problem formula we find the general amount of salt at any time t minutes and then…

Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

A: GIven: Altitude is increasing at a rate of 1 cm/min Area is increasing at a rate of 4.5 sq. cm/min…

Q: The Corona Virus, that started to spread in many countries in early 2020, is more contagious than…

A: It is given that: Infection rate = 10 to 25 people per million (PPM) Mortality rate = 1000 to 2500…

Q: A tank contains 1000 liters of brine with 15 kg of dissolved salt. Pure water enters the tank at a…

A: Let x represents the amount of salt after t minutes. Given that, the initial amount of salt is 15…

Q: An oral medication is absorbed into the bloodstream at the rate of 4e-0.04 milligrams per minute,…

A:

Q: A tank contains 60L of water contaminated with Mercury at a concentration of 0.03 mg/L. Clean water…

A: Here we need to find and then solve the differential equation for the concentration of mercury using…

Q: Each side of square is increasing at rate of 4 cm/s. At what rate is the area of the square…

A:

Q: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

A:

Q: oil

A: We will find how much oil is left in the rank after 3 hours.

Q: A tank contains 100 liters of brine, with 50 kg total dissolved salt. Saltwater, with a…

A:

Q: An oral medication is absorbed into the bloodstream at the rate of 3e−0.04t milligrams per minute,…

A:

Q: The side of a cube increases at the rate of 3 m/s, when side of the cube is 8m . Then the rate of…

A:

Q: The height of a rectangular box is 10 in. Its length increases at the rate of 2 in./sec; its width…

A: Volume of rectangular box = l b hwhere, l = length of boxb= width of boxh = height of boxRate of…

Q: A culture of bacteria initially contains 153 cells and grows at a rate proportional to its size.…

A:

Q: The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is…

A: Let the base of triangle be denoted by b Let the altitude be denoted by a  So, area of triangle…

Q: The volume of a cube decreases at a rate of 13 m³/sec. Find the rate at which the side of the cube…

A:

Q: c) What happens to the pH level of a mouth as the time since eating the sugary food increases?

A: answer is in step 2

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A: Find the base where area and altitude is already given, then the formula of the area of a triangle…

Q: A 20 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: The concentration of an antihista-mine in the bloodstream of a healthy adult is modeled by C = 12.5…

A: 6 hour period means from t=0 to t=6That is from start of the medication  to 6 hours after medication…

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A:

Q: The population of a country doubles in 50 years. How many years will it be five times as much?…

A: We will find in how many year the population of country will be five times as shown below

Q: A tank contains 1,500 liters of water and 20 kg. of dissolved salt. Fresh water is entering the tank…

A:

Q: An oral medication is absorbed into the bloodstream at the rate of  4e−0.04t  milligrams per…

A: Find the total amount of medication absorbed within the first 20 minutes

Q: The population of country doubles in 100 years. How many years will it be five times as much? Assume…

A: Denote T as the total population of the country, denote S as the initial population in the country…

Q: The growth rate of a culture of bacteria is proportional to the number of bacteria present and after…

A:

Q: shrinking

A:

Q: An oral medication is absorbed into the bloodstream at the rate of 7e−0.04t milligrams per minute,…

A: An oral medication is absorbed into the bloodstream at the rate of 7e-0.04t.

Q: A box is partially filled with sand. The length of the box is 12 mm. The width of the box is 18 mm.…

A:

Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: In this we are going to use formula for area of triangle and then differentiation of that. So I'm…

Q: Water flows into an empty reservoir at a rate of 3000 + 20t liters per hour (L/h; t is in hours).…

A:

Q: The sides of a cube increase at a rate of K cm/s. When the sides have a length of 2 cm, the rate of…

A:

Q: Pure water is poured at a rate of 3 m³/min into a tank containing 300 kg of salt dissolved in 100 m³…

A: Initially 300 kg of salt dissolved in 100 m3 of water,Rate of pouring in pure water = 3m3min,Rate of…

Q: A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The…

A: Given Information :  A health clinic uses a solution of bleach to sterilize petri dishes in which…

Q: 3. Brine containing 3lb/gal of salt enters a tank at the rate of 4gal/min and the solution…

A:

Q: The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the…

A:

Q: An IV bag contains 1,000 mL dextrose in saline solution with a drop factor of 15 gtt/mL and has been…

A: Given: Total volume = 1,000 mL Drop factor = 15 gtt/ml Time = 4 hours To determine: Rate of flow in…

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A: Let height of altitude=h ,Base=b and Area=A  Given dh/dt=3cm/minutes And dA/dt=4cm2/minutes

Q: Radium decomposes at a rate proportional to the amount present. In 100 yrs, 100 mg of radium…

A: Initial radium quantity Ni = 100 mg after t = 100 years N = 96 mg

Q: half-life of Palladium-100 is 4 days

A: We have to find out the initial mass and the mass after 6 weeks.

Q: A partially filled tank with 100 gallons of water in which there are 10 pounds of dissolved salt. a…

A:

Q: The number N of bacteria in a culture grewat a rate proportional to N. The value ofN was initially…

A:

Q: By Newton's Law of Cooling, the rate at which an object cools is directly proportional to the…

A: let T denote the temperature of an object and T0 the surrounding temperature. If t denotes time,…

Q: A 20 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: The  given problem we can be formulated as  a differential equation and solve.

Q: An oral medication is absorbed into the bloodstream at the rate of 7e−0.04t milligrams per minute,…

A: Find the equation for the rate at which the oral medicine is being observed. Then integrate the…

Q: A 30 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: Volume of the tank is 30 m3 The tank is full of brine with 40 kg of dissolved salt. Pure water…

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

A: Given that: Altitude of a triangle is increasing at a rate of 3cm/minArea is increasing at 4.5…

Q: A 631-kg elevator starts from rest and moves upward for 3.30 s with constant acceleration until it…

A: Step:-1 Part (A):- Average power = Force (F) × Average Velocity (vavg.) Given that elevator starts…

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.