A tank with capacity of 700 gal of water originally contains 200 gal of water with 100 lb of salt in solution. Water containing 1 lb of salt per gallon is entering at a rate of 3 gal/ min, and the mixture is allowed to flow out of the tank at a rate of 2 gal/ min. Let Q(t) lb. be the amount of salt in the tank, V(t) gal be the v
First order differential equation model: A ball with mass m kg is thrown upward with initial velocity 19 m/sec from the roof of a building 22 m high. Neglect air resistance. (a) Find the maximum height above the ground that the ball reaches. (b) Assuming that the ball misses the building on the way down find the time th
Consider the following Diff Eq: (x^2)(y'') + x(y') - 9y = 0. a) Solve the equation by seeking change of variables of the form x = e^x. b) Show that the DE with non-constant coefficients above becomes a Linear Ordinary Diff Eq with constant coefficents. c) Determine y by solving that Linear Ordinary Diff Eq. d) Find t
Note: all of the following _n denote n as a subscript. Suppose {f_n} from n = 0 to infinity, is a sequence of functions converging uniformly to a function f on an interval [a,b]. Also assume that the sequence has a uniform bound i.e. there exists M1 such that for all positive integers n, | f_n(x) | < = M1 for all x belonging
1: Given the situation described, identify the type of sampling involved. A student doing a report on fashion trends asks all her best friends their opinion on plaid clothing. - Random sampling - Systematic sampling - Convenience sampling - Cluster sampling - Stratified sampling 2: Scripps Hospital surveyed 10 patients
Find the values of a>0 and b>0 such that (a,b) is at distance 5 from (1,2) and the line passing through the points (a,b) and (1,4) is parallel with the line passing through the points (0,0) and (b,a).
Find the tangents and the normals at any point of the following curves: 1) y=1/x^2+2 (1,1/2) 2) y=6/(x^2+1)^2 (1,3/2)
Two ships are steaming away from a point O along routes that make a 120°angle. Ship A moves at 14 knots (nautical miles per hour; a nautical mile is 2000 yards). Ship B moves at 21 knots. How fast are the ships moving apart when OA = 5 and OB = 3 nautical miles?
Needed info: Whenever the Connecticut River reaches a level of 105 feet above sea level, two Northampton, Massachusetts flood control station operators begin a round the clock river watch. Every two hours they check the height of the river using a scale marked off in tenths of a foot, and record the data in a log book. In
5. Find the open intervals on which f(x) = x - log-base-4(x) is increasing or decreasing, and locate all relative extrema. 6. Find all relative extrema and points of inflection of y = x^2 log-base-3(x). 7. Find the limit of each of the following functions: Please refer to the attachment for details. 8. A farmer p
** Please see the attached file for the complete problem description ** A trainee is hired by a computer manufacturing company to learn to test a particular part of a personal computer after it comes off the assembly line. The learning curve for an average trainee is given by ...(a) How many computers can a trainee be expec
Let f:[a,b]--> R be continuous. Prove that the set f([a,b]) has both a least upper bound M and a greatest lower bound m and that there are points u,v in [a,b] such that f(u)=M, f(v)=m.
Research has indicated that the demand for heroin is given by the function q=100p^(-0.17) a) Find E b) Is the demand for heroin elastic or inelastic? Solve this problem, show all steps used to solve the equation, and explain the answer to receive credit for the solution.
Please show all work with explanations. Thank you for your help. 4. Find 6. Find the arc length of the graph of the function over the interval . 18. Solve the differential equation
A car salesman has two choices for his salary. Plan A: A salary of $100 per week plus a commission of 3% of gross sales Plan B: A salary of $75 per week plus a commission of 5% of gross sales For what gross sales is Plan B better? Any help is appreciated!
The quantity of watches demanded per month is related to the unit price by the equation: p = d(x) = 50/ (0.01x^2 + 1) (1 less than equal x less than equal 20) where p is measured in dollars and x is measured in units of a thousand. The supplier is willing to make x thousand watches available per month when the price
Evaluate the fundamental solution of the equation u^(4) - 2u'' + u. More in general, evaluate the fundamental solution of u^(4) - (m+1)u'' + mu, where m>=0. Please note that you are not solving the equation set equal to zero. Since you are looking for the fundamental solution you set the equation equal to the delta distributi
For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function. Explain your reasoning thoroughly. a. The time is takes to get to work as a function of speed at which you drive. b. The probability of getting into a car accident as a function of the speed a
Equation: x^2+9y^2-4x+54y+49=0 1. Identify the conic section represented by the equation. 2. Write the equation of the conic section in standard form. 3. Identify relevant key elements of your conic section such as center, focus/foci, directrix, radius, lengths of major and and or minor axes, equations of asymptotes
1. If f is continuous at x= a and g is differentiable at x=a then: Lim x->a f(x)g(x) = f(a)g(a) (if true explain why true, if false, explain and give an example of why it is false) 2. Let f(x) = 2/3x^3 + x^2 â?" 12x + . Find the values of x for which: A f prime (x) = -12 B f prime(x) =o C f prime (x) = 12 3
Hard Hat Construction's stock is currently selling at an equilibrium price of $30 per share. The firm has been experiencing a 6 percent annual growth rate. last years earnings per share, was $4.00, and the dividend payout ratio is 40 percent. The risk-free rate is 8 percent, and the market risk premium is 5 percent. If systemati
Consider function f(x) = -x^2 +2x and points P1 = (0, 0), P2 = (1, 1) and P3 = (2, 0). Find equations of: - secant lines to f through every pair of these points (3 pairs), and - tangent lines to f at each of these points.
The attached diagram shoes a lighthouse, L, 4.2 km from the nearest point, S, on a straight shoreline. The lighthouse beam rotates with a constant period of one complete rotation every 40 seconds. The beam makes an angle of theta with the line LS and the beam hits the shoreline a distance y km from S. At what rate is the beam
Please see attached Please show all work with explanations. Differential Equations 5. Solve the differential equation with the given initial conditions: 6. Solve the differential equation with the given initial conditions:
Let A be an n x n matrix. Let f(t; x0) be a solution to the initial value problem x' = Ax; x(0) = x0. Show that f(t2; f(t1; x0)) = f(t1 + t2; x0). Show by example that this is not true for a non-autonomous differential equation.
Please show all your work with helpful explanations. 1. Find the length of the arc of the curve y = x^(3/2) from x=1 to x=2. 2. Find the length of the arc of the curve y = ln(sec x) from x=0 to x=PI/4. What is the length of the curve from x=0 to x=PI/2? 5. Find the surface area of the cone formed by rotating the line y = ax
A) Evaluate â?«R^2 xy ? {[0,1]Ã?[0,1]} dm *(x, y), (or if you prefer, â?«[0,1]Ã?[0,1] xydm*(x, y)). b) Evaluate â?«R^2 xy ?{[0,1]Ã?[0,1]â?'Q^2} dm* (x, y) The original problem is sent as PDF file attachment below. It is number 4 on the list.
For the damped pendulum equation: x"+cx'+kx=0 assume k = 9. (a) Write down a solution to the equation. When does the solution type change as c varies? (b) Classify the equilibrium at the origin as a "sink", "source", "spiral sink", "spiral source", "center", or "saddle".
Please show all work. Explanations are very helpful. 1. Find the volume of the solid formed by rotating the ellipse (x/a)^2 + (y/b)^2 = 1 about the x axis. 12. The base of a solid is the region bounded by the parabola y = x^2 / 2 and the line y = 2. Each plane section of the solid perpendicular to the y axis is an
1. Show that the sequence x^2 (e^-nx) converges uniformly on [0, infinity). 2. Show that if a is greater than zero then the sequence (n^2 x^2 (e^-nx)) converges uniformly on the interval [a, infinity) but does not converge uniformly on the interval [0, infinity). For problem 2 text gives a hint that if n is sufficiently larg