In physics, we have the formula ρ = m/v where ρ is density, m is mass, and v is volume. Suppose an object starts with a mass of 2 kg and a volume of 10cm3. The object begins to lose mass at a rate of 0.2 kg/s and gain volume at a rate of 1cm3/s. What is the rate of change of the density when the mass is 1 kg?

Q: The rate of growth, in dollars per year, of the net worth, f(t), of a company is given by…

A:

Q: Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

A: Given Data The length of the rectangle is y=9 ft. The width of the rectangle is x=7 ft. The rate of…

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

A:

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm²/min, find the decreasing…

A: To find- Radius is decreasing at the rate of

Q: Assume that the rate of evaporation for water is proportional to the amount of water in a bowl. If…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: The average energy E (in kcal) needed for a lizard to walk or run distance of 1 km has been modeled…

A: Given that      The average energy E(in kcal) needed for a lizard to walk or run a distance of 1 km…

Q: The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: Let's find rate of area increasing when W=4cm and l=10cm.

Q: Is the rate of change of a cube's volume linearly proportional to the rate of change of its side?

A: Rate of change of volume of cube

Q: In a certain culture of bacteria the rate of increase is proportional to the number present. a. If…

A: Explained below

Q: A hot-air balloon is 140 ft above the ground when a motorcycle (traveling in a straight line on a…

A: Given the height in which the hot air balloon placed above the ground is 140 ft. Velocity of the…

Q: With snow on the ground and falling at a constant rate, a snowplow began plowing down a long…

A:

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: To find the rate of change of the carbon monoxide levels per population when t=2

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: 4. A beach ball is deflating at a constant rate of 10 cubic centimeters per second. When the volume…

A: NOTE: You have posted multiple questions we have given answer to the first question if there is a…

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: The length / of a rectangle is increasing at a rate of 2 cm/s while the width w is decreasing at a…

A:

Q: The management of a large chain of frozen yogurt stores in New England believes that t days after…

A: Here, V =70000+70000 e-0.47t

Q: Assume that the rate of change of air pressure with altitude (distance above the earth) is…

A: Topic:- Differential equation

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

A:

Q: Suppose you drive your car on a perfectly flat road at a constant speed with no wind. In this case,…

A: As given in the question, The amount of fuel is directly proportional to the distance Travelled. ⇒y…

Q: For a certain animal, the surface area S of the body is related to the body's weight W according toS…

A: The surface area S of the body is related to the body's weight W according to S is:

Q: In a certain culture of bacteria, the rate of increase is proportional to the number present. (a) If…

A: Model the given problem dpdt=kp if p is the present number of bacteria integrate it on both sides…

Q: At 9 p.m., a cylinder containing 240 liters of brine in which 12kg of salt is dissolved. Brine…

A: We will find how much salt in the cylinder is by 9.30

Q: Let  x(V) = V1/3  be the length of the side of a cube in terms of its volume. As V decreases, does…

A: V is decreasing that is dv/dt is negative  Let dv/dt =-k where k is constant.

Q: Where k is constant. If the temperature is increasing at 4 kelvins per hour, what is the rate of…

A: We need to find the rate of change of pressure  when temperature is 150K and pressure is 450…

Q: 2. In a certain culture of bacteria, the rate of increase is proportional to the number present. If…

A:

Q: In the equation, x² + y² = 45, what is the value of the rate of change in y with respect to time t…

A: To solve this problem we have to first differentiate the given function with respect to 't' and then…

Q: Suppose the value of yy and the value of xx vary together at a constant rate of change (so that…

A: 1.The value of y and x vary together at a constant rate of change and the value of y = 1.5 and x =…

Q: A 400-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 1 lb…

A:

Q: In a certain culture of bacteria, the rate of increase is proportional to the number present. (a) If…

A: In a certain culture of bacteria, the rate of increase is proportional to the number present. We…

Q: In the equation, x² + y² = 45, what is the value of the rate of change in y with respect to time t…

A:

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A: Hair we use the application of derivative to find the solution of given problem. You must know about…

Q: In a certain bacteria culture the rate of increase in a number of bacteria is proportional to the…

A: Follow the steps below to solve a differential equation(in terms of x and y) by the variable…

Q: Suppose the constant rate of change y with respect to x is -2.5 and we know that y=-6.75 when x=1.5…

A: Given,The constant rate of change of y with respect to x = -2.5.We know that,Slope = rate of change…

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A:

Q: (a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level…

A: Given,   A trough is 12 feet long and 3 feet across the top and its end are isosceles triangles with…

Q: Charley stands 34 meters west of Robert. Robert starts walking north at a speed of 2 m/s, and…

A:

Q: The value of a computer t years after purchase is V(t) = 2, 000e-0.35t dollars. At what rate is the…

A:

Q: If V(t) is the volume of water in a reservoir at time t (seconds), v(t) is the rate of change,  then…

A: Rate Change: Rate change is defined as the change in one quantity with respect to any other quantity…

Q: Suppose a and y are related by a constant rate of change Ay and = 2, and y 4 when x = 3. Ax

A: Suppose x and y are related to the constant rate of change and ∆y∆x=2and y = 4 when x= 3

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A:

Q: In 10 minutes, the body cools from 75 to 55 degree Celsius when temperature of the surrounding is 31…

A:

Q: a drug concentration curve is given by C(t)= 20te^-0.2t, which C in mg/ml and t in minutes. What is…

A: A drug cocentration curve isC(t)=20te-0.2tTo find the rate of concentration. We have to…

Q: At a temperature of 20°C, the volume V (in liters) of 1.33 g of O2 is related to its pressure p (in…

A:

Q: A boat takes 2/3 as much time to travel downstream from C to D, as to return, If the rate of the…

A: A boat takes 2/3 as much time to travel downstream from C to D, as to return. If the rate of the…

Q: In the equation, r? + y² = 45, what is the value of the rate of change in y with respect to time t…

A: On solving this we will get

Q: It follows from Poiseuille's Law that blood flowing through certain arteries will encounter a…

A: Given  R(x) = 0.25(1 + x)4

Q: The width of a rectangle is increasing at a rate of 2cm/sec, while the length increases at 3cm/sec.…

A: Suppose that the length of rectangle is “l” and width is “w”   So according to the question, dwdt=2…

Q: if the rate of growth of the population of deer in a forest is modeled by R(t)= 2000e^(0.23t) deer…

A: The rate of growth of the population of deer in a forest is modeled by R(t)= 2000e(0.23t) deer per…

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.