1. A rancher wishes to fence in a rectangular corral enclosing 1300 sq yards and must divide it in half with a fence down the middle. If the perimeter fence costs $5 per yard and the fence down the middle costs $3 per yard, determine the dimensions of the corral so that the fencing cost will be as small as possible. 2. Find t
Please see the attached file for the fully formatted problems. 1. Graph . Using the formula for the area of a rectangle to find the function: . What is ? 2. Graph . Using the formula for the area of triangles (or trapezoids) to find the function: . (assume that ) What is ? 3. Based on the graph sketched to
Please show all work. Find a value for c so that f(x) is continuous for all x. c2-x2 if x<0 f(x)={ _______________ ccosx if x>0 use the four-step process to find a slopepredictor function m(x). Then write an equation for the line tangent to the curve at the point x = 8. 4
Use the Squeeze Law of limits to find the limit. limx => 0 x2sin210x Tell where h is continuous (Give your answer in interval form.) h(x) = (x-9)/|x-9| Tell where f is continuous. (Give your answer in interval form.) f(x) = 1/(sqrt[1 + sinx])
If you have not seen it yet, consider flying with Professor Goetz over Rio hills. His GPS recorded the this graph of the velocity function v(t) . Based on this graph estimate the total distance traveled during the glider flight from the take off to the landing on the beach. Explain in words how you do this estimate. Please s
Please see the attached file for the fully formatted problems. 2. Initial - boundary value problem; u -u =2x 0<x<1 t u(x,o)=sin( ) u(o,t)=t u (1,t)=1
Please see the attached file for the fully formatted problems. 18. (a) Find the general solution of (d^2y)/(dt^2) + 4(dy/dt) + 20y = 3 + 2cos2t (b) Discuss the long-term behavior of solutions of this equation.
Find the solution of the given initial-value problem. 12. (d^2)y/dt^2 + 7dy/dt + 10y = e^-2t, y(0) = y'(0) = 0.
Part a) Given the following predator prey model where x(t) is the predator population and y(t) is the prey population: dx/dt = - ax + bxy + (z1)*x dy/dt = cy - gxy +(z2)*y Here both z1 and z2 can be positive or negative; parameters a, b, c, g are all defined to be positive. Parameters z1 and z2 can r
An apartment complex has 240 units. When the monthly rent for each unit is $360, all units are occupied. Experience indicates that for each $16 per month increase in rent, 3 units will become vacant. Each rented apartment costs the owner of the complex $46 per month to maintain. What monthly rent should be charged to maximize pr
36. An automobile's suspension system consists essentially of large springs with damping. When the car hits a bump, the springs are compressed. It is reasonable to use a harmonic oscillator to model the up-and-down motion, where y(t) measures the amount the springs are stretched or compressed and v(t) is the vertical velocity of
In Exercises 21?28, consider harmonic oscillators with mass in, spring constant k, and damping coefficient b. (The values of these parameters match up with those in Exercises 13?20). For the values specified, (a) find the general solution of the second-order equation that models the motion of the oscillator; (b) find the parti
See the attached file. A perfectly flexible cable hangs over a frictionless peg as shown, with 8 feet of cable on one side of the peg and 12 feet on the other. The goal of this problem is to determine how long it takes the cable to slide off the peg, starting from rest. (a) At time t 0 what proportion of the whole cable is
If the total cost of manufacturing a commodity is dollars when x units are produced, for what value of x is the average cost the least? See the attached file.
The graph of f(x) = ln(x^2) has a. neither a relative minimum nor a point of inflection at x = 0 b. a relative minimum that is not an inflection point at x = 0 c. a relative maximum that is not an inflection point at x = 0 d. an inflection point that is not a relative minimum at x = 0. See the attached file.
What is the equation of the tangent line to f(x) = bar e^(x^2) at x = 2? Please see the attached file for the fully formatted problems.
Question 5 Suppose Anytown, USA has a fixed population of 200,000. On March 1, 3000 people have the flu. On June 1, 6000 people have it. If the rate of increase of the number N(t) who have the flu is proportional to the number who don't have it, how many will have the disease on September 1? Question 7 Suppose th
Eliminate the parameter. Find a retangular equation for the plane curve defined by the parametric equations. X=3t, y=t+7 Find a set of parametric equations for the rectangular equation. Y=2x-2
Consider the system (see attached file). Determine the transfer function of the system in terms of Laplace transform. Expand the transfer function by means of partial fractions and find your new state equations by means of inverse Laplace transform. Obtain the state-space representation of the system.
Suppose that A = R^2 with {(0,0)} removed and that f :A→ R is a uniform continuous mapping on A. a)Prove that there exists L an element of R so that lim f (x,y) = L [(x,y) → (0,0), (x,y) element of A]. b)Using L from part (a) prove that F(x,y) = { f(x,y) when (x,y) ≠ (0,0) and L when (x,y) = (0,0)}
1. A ladder 10 feet long rests against a vertical wall. If the top of the ladder slides down at a rate of 1 ft/sec how fast is the bottom of the ladder sliding away when the bottom of the ladder is 8 ft away from the wall? 2. Two people start from the same point. One runs west at 13 km/hr and the other walks north at 2 km/hr
22. Consider a harmonic oscillator with mass m = 1, spring constant k = 1, and damping coefficient b = 4. For the initial position y(O) = 2, find the initial velocity for which y(t) > 0 for all t and y(t) reaches 0.1 most quickly. [Hint: It helps to look at the phase plane first.] Differential Equations From Phase plane for
Please see attached file. Let f(x) = x, if x is a rational number, and f(x) = x^2 if x is an irrational number. For what values of a, if any, does lim(f(x)) as x --> a exist? Justify your answer. I know that the answer is 0 and 1, but why? Please explain. Thank you.
5. An object is moving along the straight line as follows. It starts at and then it moves to the right to . Then the objects moves to the left to , and finally to the right to stop at . Sketch a possible graph of the position function . Sketch a possible graph of the velocity (the instantaneous rate of change of ).
Use the limit definition of rate of change to calculate how quickly f(x) = x^2 is changing at x = -4.
Please see the attached file for the fully formatted problems. #1,#2,#3,#4,#5,#6,#7
Please see the attached file for the fully formatted problems. Properties of Linear Systems and the Linearity Principle
Question: Using a computer or calculator, apply Euler's method to sketch an approximation to the solution curve for the solution to the initial-value problem. 2(d^2y)/(dt^2) + (dy)/(dt) + 4y = 0, where (y_0, v_0) = (2,0). How does your choice of delta t affect your results?
Find the center of mass of a 3-D pyramid without using calculus.
Find the center of mass of a 4D pyramid (cube base) using calculus. Explanations, step-by-step procedure, diagram if possible.