The traffic flow rate (cars per hour) across an intersection is r(t)=200+600t−210t2, where tt is in hours, and t=0 is 6am. How many cars pass through the intersection between 6 am and 7 am?

Q: f. A truck travelling southwards at 40 kph and a car traveling eastward at a rate of 60 kph are…

A:

Q: What is the daredevil’s acceleration at t = 3 seconds?

A:

Q: Initially a tank holds 100 gal of a brine solution containing 4 lb of salt. At t = 0, brine…

A: Solution :-

Q: A 40 gal tank initially contains 11 gal of fresh water. At t = 0, a brine solution containing 1.2 lb…

A: Given: The initial volume of water v(0)=11 gallons The initial amount of salt s(0)=1.2 lb Since rate…

Q: consider a tree with a tr

A:

Q: A 600 litre tank initially contains 200 litres of water in which 10 grams of salt are dissolved.…

A: (a) A 600 litre tank initially contains 200 liters of water. 10 grams of salt are dissolved in it.…

Q: The rate at which ice is melting in a pond is given by R (t) = V1+ 2', where Ris measured in cubic…

A: We use substitution method to solve integration to find out amount of ice melting in first 5 minutes

Q: A spherical balloon is deflating and its radius r is decreasing at the rate of 5 mm per minute.…

A:

Q: Describe the change in accuracy of dz as an approximation of ∆z as ∆x and ∆y increase.

A: Given , z=fx,yWe do dz using the partial derivates zx & zy .So , dz=zx.dx & zy.dywhere zx…

Q: Consider the function f(x, y) = y³ – 2y – x². Find the direc- tion of greatest increase at the point…

A:

Q: A honeybee population starts with 100 bees and increasesat a rate of n'(t) bees per week. What does…

A: Given data: The initial honeybee population is n(0)=100. If n'(t) is the rate at which the…

Q: A sewage disposal plant has a big concrete holding tank of 100,000-gal capacity. It is % full of…

A: Let M(t) be the mass of the organic material in the tank at time t and Mt=CtVt, where C(t) and V(t)…

Q: In order to stay awake during class, a professor keeps a 200 ounce capacity coffee maker in his…

A: Given coffee maker capacity is 200 ounces. it contains 40 ounces coffee which has 500 mg caffeine.…

Q: An auto A is moving at 20 ft/s and accelerating at 5 ft/s2 to overtake an auto B which is 384 ft…

A:

Q: A 25ft ladder is sliding down a wall at -6ft/s. How fast is the bottom of the ladder sliding out…

A: Given, Length of ladder= 25 ft  Rate of sliding down = -6 ft/s  We have to find how fast is the…

Q: A tank is initially filled with 1000 gal. of salt solution containing 500 H of salt. Fresh water…

A: Let At the amount of salt at the time t Then the rate of change of the amount of salt dAdt=0lbL.10…

Q: Because a new employee must learn an assigned task, production will increase with time. Suppose that…

A: To find the number of units completed in t hours by the new employee, integrate the rate of…

Q: A 200g-tank holds 100 gallons of fresh water upon first. At t = 0, a 5 gal/min salt solution…

A: Given initial quantity of freshwater in the 200-gallon tank = 100 gallons At t=0, salt solution is…

Q: A tank has 72 gallons of water. Brine solution with 2lbs of salt per gallon of solution enters at a…

A: here we can use differential equation to solve this question.

Q: Find the total derivative dy dw. Y=3x+2w+5z x=4 In(w*) z=e43x³

A: Given, y=3x+2w+5z2x=4ln(w2)z=e-z+3x-3

Q: The lower base of a trapezoid is 8 m. If its height is increasing at the rate of 0.5m/sec while its…

A:

Q: The volume of water in a hemispherical bowl of radius 30cm is given by V =36x2 – x³ ) where x - X cm…

A:

Q: Find the net change in velocity over [1, 4] of an object with a(t) =8t - t2 mls2 .

A: Given, Acceleration is, a(t)=8t-t2 ,ms2

Q: A tank with a capacity of 400 gal originally contains 150 gal of water with 25 lb of salt in…

A:

Q: A tank contains 4000 liters (L) of a solution consisting of 120 kg of salt dissolved in water. Pure…

A: Here, ri = 4, ci = 0, r0 = 5, The differential equation is There is no inflow of salt, thus the…

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

A:

Q: A tank initially holds 10 gal of fresh water. at t=0, a brine solution containing 1/2 lb of salt per…

A:

Q: If a hemisphere bowl of radius 6 cm contains water to a depth of x cm, the volume of the water is rx…

A: This question is related to application of derivatives.

Q: A 450 gal tank initially contains 110 gal of brine containing 52 Ib of salt. Brine containing 1lb of…

A:

Q: The rate of change of y is proportional to y. When t = 0, y = 2, and when t = 2, y = 4. What is the…

A: Given that rate of change of y is proportional to y that is, dydt=ky        ...(1)

Q: A tank contains 5000 liters (L) of a solution consisting of 182 kg of salt dissolved in water. Pure…

A:

Q: The brakes of a car are applied when it is moving at 80 km/h and provide a constant deceleration of…

A:

Q: An oil storage tank ruptures at time t =0 and oil leaksfrom the tank at a rate of r(t)  = 100e-0.01t…

A: Given: Oil leaks from the tank at the rate r(t)= 100e-0.01t liters per minute. we have to find how…

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram…

A: Question is solved.

Q: The side of a cube is increasing at a rate 9m/s, then the rate at which the volume of the cube…

A: The function f(t) is a rule that associates or fixes a number to the particular point t. The…

Q: A 400-gal tank initially contains 100 gal of brine containing 75 lb of salt. Brine containing 2 Ib…

A: The solution of above question is written below.

Q: A cyclist rides down a long straight road at a velocity (in m/min) given by v(t) = 400 – 20t, for…

A: Solve the following

Q: A 50 gallons tank initially contains 10 gal of fresh water. At t = 0, a brine solution  containing 1…

A: It is given that a 50 gallon tank initially contains 10 gallon fresh water. A brine solution with 1…

Q: The tempature at any point on a cordinate plane is T=3x2+4y2+5. What is the rate of change from the…

A: Note: We know that, We need to find the rate of change from the origin, considering it's the same…

Q: Car A is traveling west at 50 mih and car B is traveling north at60 mih. Both are headed for the…

A: Since, we have been given that Car A is travelling west at 50 mi/hand Car B is travelling north at…

Q: In 30 minutes, a thousand eight hundred tank of water empties from the bottom.The amount of water…

A: Proceed as shown below

Q: Water is drained from a pool at a rate of R(t) = 50e-0.08t gallons per hour. If the drain is left…

A: 625 gal. water drains from the pool.

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: Given

Q: A tank contains 1000 liters (L) of a solution consisting of 195 kg of salt dissolved in water. Pure…

A: Solution is given below:

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: The diameter of a sphere is 5(2x+ 5), the rate of change of its surface area with respect to x is

A:

Q: A baseball thrown directly upward at 160 ft/sec has velocity v(t) = 160- 32t ft/sec at time t…

A:

Q: A 50-gallon tank initially contains 10 gallons of fresh water. At t= 0, a brine solution containing…

A: We will find out the required time.

Q: A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32…

A:

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.