1. Absorbing Cerebrospinal Fluid [11] Cerebrospinal fluid is continually produced and reabsorbed by the body at a rate that depends on its current volume. A medical researcher finds that absorption occurs at a rate of 0.35 mL/min when the volume of fluid is 150 mL and at a rate of 0.14 mL/min when the volume is 50 mL. Answer the following questions: (a)  Suppose the absorption rate A, is a linear function of the volume V . Find the equation of the linear function using the information above and then sketch a graph of A (V )vs V .[7] (b)  State in your own words what does the slope of the graph that you calculated in part (a) above represent?[2] (c)  Find the A-intercept of the graph and what does it represent?[2]

Q: Wave mechanics are often employed for

A: Given,              ∂2u∂t2=16∂2u∂t2  for all  0≤x≤10 and t≥0.             ...(1)

Q: which of the following expressions is equivalent to: 3cot^2(t)/csc(t)   a. 3-3cos^2(t)/cos(t) b.…

A: This question is related to trignometry, We will solve it using trignometric identities.

Q: A 100-gal tank initially contains 25 gal of 50% salt solution. Fresh water is then poured into the…

A: (a) The problem belongs to the topic differential equation.

Q: Question 10 For the function g(x)=x²-2x+5, what is the best estimate for the instantaneous rate of…

A:

Q: 1. (a) What is related rates problems? Write down the necessity of related rates problems in…

A: The problems where two quantities are related to each other which can be used to find the rate at…

Q: The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres),…

A:

Q: (b) A 10 kL tank of water provides water for a small village. Water is drunk from the tank at a rate…

A:

Q: A 500 gallon tank currently holds 300 gallon of brine solution containing 150 pounds of dissolved…

A: Let A(t) denotes the amount of salt in pounds at time t and V(t) denotes the amount of gallons of…

Q: Let ya(t) and ye(t) be the amount of the pollutant at any time t in Tank A and Tank B, respectively.…

A: first solving for tank A . then we will solve for tank B.

Q: A five-gallon bucket is full of pure water. Suppose we begin by dumping salt into the bucket at a…

A:

Q: In a certain dynamic measurement application the input(x) – output(y) relationship is given by…

A: Given,y=1+1+xe-x∂yy×100=±2%         at x=3.8∂yy=0.02y=1+(1+3.8)e-3.8y=1.10737

Q: (10) The ifctime 7 of a device has pdf astsa+To fr(t) = To otherwise A. Determine R(t) and MTTF of…

A: Given The lifetime T of a device has pdf Find Determine R(t) and MTTF of the devices Determine the…

Q: Analysis 3: Based on the design of the antennas, the Standard Absorption Rate (SAR) of RF power by…

A: Consider the SAR function, SARt=2t+e0.1t+2 Where, t is in second. (1) We need to formulate a…

Q: Homing pigeons avoid flying over water. Suppose a homing pigeon is released on an island at point C,…

A: Here we have to find distance between point S and A.

Q: Two people on scooters just finished their conversation. One of them starts riding directly north at…

A: Given  dydt=15 m/sdxdt=12 m/s We have to find dzdt Using Pythagorean theorem we have z2=x2+y2 Now…

Q: The average rate of change of h(x) over the interval [a, b] is zero and b > a. Part A: What can we…

A: A) The average rate of change = change in outputchange in input…

Q: 24. A 30-gallon tank initially contains 15 gallons of salt water containing 6 pounds of salt.…

A: Given that dN(t)dt= Flux of salt in - Flux of salt out The salt flux into the tank is always C_in *…

Q: swer is correct for the cut-off grade and ore-grade of a deposit generating $4/t 30% recovery,…

A: The following solution is provided below:

Q: a) Determine the average rate of change in the size of the crowd for each half hour of the rally. b)…

A: Solution:

Q: 1. You have a shortage of drinkable water in your town and are trying to prepare safe drinking water…

A: Let S(t) be the salt in the tank at any moment of time. Initially at t=0, S=S0.

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.