Given,
Volume of tank after time t as:
For volume f(t) to be increasing or decreasing, rate of change of f(t) w.r.t. time must be positive or negative respectively.
And, for the rate of filling and draining to be increasing and decreasing, the second derivative of f(t) w.r.t. time must be positive and negative respectively.
Now,
Show all work and label answers (1) A mixing tank is filled and drained in gallons)...
Please show all work. Suppose there is a tank of 100 gallons of a salt mixture with concentration 0.25 pounds per rate of 2 gallons per minute. It is well mixed and then drained out at the rate of 2 gallons per minute. A) Write a differential equation, in terms of only A and t, that models this situation, where A is the amount of salt in tank after t minutes. Include the initial condition. DO NO1T SOLVE THE DE!...
Please show all work. Thank you! 2. Sections 4.3,4.5,4.6 Graphing:Consider the function f (x) = sin(2x) + cos(2x)on the interval [0, 1]. For this question, give your answers to parts a,b,c in interval notation. a. Find the intervals on which f is increasing or decreasing b. Find the local maximum and local minimum values of f c. Find the intervals of concavity d. Give the inflection points (if any) e. Sketch the graph of f. Be sure to label and...
show work 2. Let f(x) = x* – 18x²+4. a) Find the intervals on which f is increasing or decreasing. b) Find the local maximum and minimum values off. c) Find the intervals of concavity and the inflection points. d) Use the information from a-c to make a rough sketch of the graph.
show work 2. Let f(x)=x* - 18x+4. a) Find the intervals on which f is increasing or decreasing. b) Find the local maximum and minimum values of f. c) Find the intervals of concavity and the inflection points. d) Use the information from a-c to make a rough sketch of the graph.
A vertical cylindrical tank is being filled with water, while at the same time water is being drained as shown in Figure 1 below. Provide: Asketch of the analogous flow network using a capacitor symbol to indicate liquid a. volume storage. b. Let h liquid level height;t time; R 988.1(h)0 V 0.5+0.5cos(0.05t), the inlet flow rate; D 2.5, tank diameter; y 60; liquid specific weight; and ho 10, initial h Assume that the units are consistent and the exit pressure...
1) Given a tank initially contains 200 gallons of brine (salt mixed with water) in which 150 lbs of salt is dissolved. A salt solution consisting of 0.5×(1 + e^(-0.02t)) lb. of salt per gallon (where t is time in unit of minute) is flowing into the tank at a rate of 10 gal./min and the mixed solution is drained from tank at the same rate. Find the amount of the salt in the tank after 1 hour. (10 points)...
Please Show ALL Work 111. Use the guidelines to sketch the curve. 1. Find the domain 11. Find Intercepts Symmetry (Even or Odd Function) iv. Asymptotes V. Increasing/Decreasing Intervals vi. Local Extrema Concavity and Inflection Points viii. Sketch the Graph with all above information vii. b) y = 15-5%
please solve all and show steps thank you 1) Find the limit if it exists. x? - 7x+10 *+5 r + x - 30 a) lim tan x b) lim c) lim tan x In x x 0 2. Let f(x) = x° -18x' +4. a) Find the intervals on which f is increasing or decreasing, b) Find the local maximum and minimum values off. c) Find the intervals of concavity and the inflection points. d) Use the information from...
Please complete all parts (a-h.) and label them clearly. Thanks and I will rate. Tage 10 of 13 7. Let f(c) 2 - 1 1. Let (2) = 72 . Find or determine (a) the domain of f(x) (b) the x- and y-intercept of f(x) (c) the symmetry of f(x) (d) the intervals where f(x) is increasing or decreasing (e) the local maximum and minimum of f(x) (f) the intervals of concavity and inflection points of f(x) (g) the horizontal,...
1. A large mixing tank currently contains 100 gallons of water into which 5 pounds of sugar have been mixed. A tap will open pouring 10 gallons per minute of water into the tank at the same time sugar is poured into the tank at a rate of 1 pound per minute. Find the concentration (pounds per gallon) of sugar in the tank after 12 minutes. Is that a greater concentration than at the beginning? In which of the molecules...