A tank contains 24 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let t represent the number of hours since the water began draining and let v represent the volume of water in the tank. Write a formula that expresses v in terms of t.

Q: Neglecting air resistance, the height h (in meters) of an object thrown vertically upward from the…

A:

Q: A cup of coffee is poured at 190˚F, and is allowed to cool in a 70˚F room. If the temperature of the…

A:

Q: An arrow is shot vertically upward at a rate of 230 feet per second from ground level.  Use the…

A: Initial speed of the arrow, v0 = 230 ft/sec. Initial height of the arrow, h0 = 0 ft Projectile…

Q: If n birds eating continuously consume V in³ of seed in T hours, how much does in bird consume per…

A: topic- algebraic operations

Q: Certain cells grow according to the formula y = 200e0.5t, where y is the number of cells present t…

A: Given number of cells as a function of t  y=200e0.5t

Q: A model for the basal metabolism rate, in kcal/h, of a young man is given by the formula below,…

A: The total basal metabolism is given by, ∫024R(t) dt

Q: how much bacteria would be present at 3 hours? show working  ii) how long would it take to have…

A:

Q: Neglecting air resistance, the height h (in meters) of an object thrown vertically upward from the…

A:

Q: A rectangular box has a height of S, the length is twice the height, and the width is 6 greater than…

A:

Q: In physics, we have the formula ρ = m/v where ρ is density, m is mass, and v is volume. Suppose an…

A: Given, The density of an object, ρ=mv   ......(1) Initial mass of an object, m1=2 kg Initial volume…

Q: a) An electrical voltage E is given by E = (15sin50nt + 40cos50rt) volts, where t is the time in…

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems. These 2 are…

Q: The music you hear when listening to a magnetic cassette tape is the result of the magnetic tape…

A: Given formula T=LS Where T is the time in seconds, L is the length of the tape in inches and S is…

Q: The length of the sides of a square are initially 0 cm and increase at a constant rate of 9 cm per…

A: Given that, The initial side length of the square is 0 cm. It increase at a constant rate 9 cm per…

Q: A rocket can rise to a height of h(t) = t3 + 0.9t2 feet in t seconds. Find its velocity and…

A:

Q: A radioactive substance follows A(t) = 500(0.87)^t , where t is in months and A(t) is in grams. How…

A: Given that: A(t)=500(0.87)t, where t is in months and A(t) is in grams.

Q: Neglecting air resistance, the height h (in meters) of an object thrown vertically upward from the…

A: Velocity v(t) = rate of change of height, h(t)Hencev(t) =dh(t)dt Given:h(t) = v0t-12gt2

Q: (b) Find the constant of propontionality for a windmill that produces 136 watts of power when the…

A:

Q: It takes pump A 3 hours less time than pump B to empty a swimming pool. Pump A is started at 8:00 am…

A: Explained below

Q: Lisa and Sarah left their homes at 7 pm and walked toward a park bench to meet. Lisa lives in…

A: Refer to the question. Lisa lives in 1950feet west of the bench and walks 310 feet per minute. Sarah…

Q: gt+*=ドg

A: If the relation between the variables x and y are given by an equation and the equation can not be…

Q: The formula V = kr4, discovered by the physiologist Jean Poiseuille (1797–1869), allows us to…

A: The given relation between the volume and the radius of the artery is V=kr4.

Q: The speed, s, meters per second, at which a liquid flow from a small hole in a (19. 6h) 2, where h…

A:

Q: A car moving 20m/s, increases its speed to 60m/s. The increase in speed happens over 10 seconds.…

A: We find acceleration

Q: P is directly proportional to the cube of Q. When Q = 15, P = 1350. a. Find a formula for P in terms…

A: Given that p is directly proportional to the cube of cube hence p= k q^3

Q: A coffee has a temperature of 90°C when freshly poured. After 5 minutes, the coffee has cooled to…

A: This question is based on Newton's law of cooling.

Q: An arrow is shot vertically upward at a rate of 210 feet per second. Use the projectile formula h =…

A:

Q: One way to measure the amount of energy that a moving object (such as a car) possesses is by finding…

A: Solution

Q: The length of the sides of a square are initially 0 cm and increase at a constant rate of 7 cm per…

A:

Q: Suppose a car driven by Emma G. passes a crosswalk while driving at a constant speed of 5 meters per…

A:

Q: The height g metres, of a ball hit vertically upwards t seconds after it is hit, is given by g()=…

A: The height of the ball thrown vertically upwards is given by gt=4t-t2 where t is time in seconds.…

Q: After the initial injection, the amount of a drug in the bloodstream decreases by 5% each hour.…

A: Initial amount of drug=DoK=-5 % per hourt= t hoursUsing formulaA=Ao1-Ktwhere A= Ending value…

Q: During the first 45 seconds of a rocket flight, the rocket is propelled straight up so that in t…

A:

Q: The total amount of money in an account with P dollars invested in it is given by the formula A = P+…

A: use the formula for findng the amount.

Q: The formula v = /2gs represents the velocity (v) of an object that has fallen a distance of 5 feet,…

A: A square is a number that produces a specific quantity when multiplied by itself. That is, if x is…

Q: solve for g  E=10gh

A:

Q: A rectangular box has a height of S, the length is twice the height, and the width is 6 greater than…

A: follow next step

Q: It can be shown that when the water level is h meters from the bottom of the tank, (see the figure),…

A:

Q: A rocket can rise to a height of h(t) = t3 + 0.9t2   feet in t seconds. Find its velocity and…

A:

Q: A candle is lit and burns until it is burned out, and the length of the candle changes at a constant…

A: topic - differential equations

Q: Jose is standing 9 feet east of a mailbox when he begins walking directly east of the mailbox at a…

A: Given that, Jose is standing 9 feet east of a mailbox when he begins walking directly east at a…

Q: When earthquakes occur under the sea, they can cause large tidal waves called tsunamis. Scientists…

A: Here we have given the equation of speed os tsunami.

Q: A model for the basal metabolism rate, in kcal/h, of a young man is given by the formula below,…

A:

Q: Ben starts walking along a path at 4 mi/h. One and a half hours after Ben leaves, his sister Amanda…

A:

Q: At a constant temperature of 15°C, the barometric pressure can be approximated by the formula P =…

A:

Q: an oral medication is absorbed into the bloodstream at the rate of 5e^-0.4t milligrams per minute…

A: Given: An oral medication is absorbed into the bloodstream at the rate of 5e-0.4t milligrams per…

Q: A car traveled 50 miles in 40 minutes. Assume that the car will continue at this constant rate of…

A: Option (C) M=75 h is correct.

Q: The distance d (in ft) required to stop a car that was traveling at speed v (in mph) before the…

A: a.Obtain the distance required to stop the car going 50 mph.

Q: The time t in seconds that it takes for a pendulum to complete one full swing is given by the…

A: The formula for the time in seconds for the pendulum to complete one swing is given The objective is…

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.