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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).
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.
The equation has three distinct real roots. Approximate their locations by evaluating f at -2, -1, 0, 1, and 2.
Find the interval on which the function is increasing and decreasing. Sketch the graph of y = f(x), and identify any local maxima and minima.
Find the volume of the solid that is generated by rotating the region formed by the graphs of y = x2, y = 2, and x = 0 about the y-axis.
A tank, containing 300 gallons of pure water initially, is emptied out in the following fashion. A salt solution of concentration ½ lb of salt per gallon.
She has 51 bills consisting of $1, $5, and $10 bills. If the number of $5 bills is three times the number of $10 bils, find how many of each bill she has.
Find the upper and lower control limits for /x- and R-charts for the width of a chair seat when the sample grand mean.
Suppose that y1, y2 is a fundamental set of solutions. Prove that z1, z2, given by z1 = y1 + y2, z2 = y1 - y2, is also a fundamental set of solutions.
Consider a projectile of mass m which is shot vertically upward from the surface of the earth with initial velocity V.
An object moves along the x-axis with initial position x(0)=2. The velocity of the object at time t is greater than or equal to 0 is given by v(t)=sin((pi/3)t).
They need to know how much material will be required to construct the main support cables and what sort of cable they need to buy.
The Valve Division of Bendix, Inc, produces a small valve that is used by various companies as a component part in their production.
Suppose that the function f(x) and its first derivative have the following values at x = 0 and x = 1
Water is the most important substance on Earth. One reason for its usefulness is that it exists as a liquid over a wide range of temperatures.
Determine the (x,y) coordinates and the value of the parameter at the point(s) where the slope of the tangent line to the curve is 4.
A line goes through the origin and a point on the curve y = x2e-3x, for x>=0. Find the maximum slope of such a line. At what x-value does it occur?
As an epidemic spreads through a population, the number of infected people, I, is expressed as a function of the number of susceptible people.
The space between the supports must be 1000 feet; the height at the center of the arch needs to be 320 feet.
Both models are estimates of revenues for 2004-2008, with t = 4 corresponding to the year 2004.
What are the derivatives f’(0) and f’(1), and how do they relate to the slopes of the tangent lines to these points?
At what rate is revenue changing when 3,000 calculators are produced? Is revenue increasing or decreasing at this level of production?
Compute the derivative of the given function and find the equation of the line that is tangent to its graph for the specified value x = c.
The positions of two particles on the s-axis are s1=sin t and s2=sin(t+ p /3), with s1 and s2 in meters and t in seconds.
Are there any additional restrictions that you must impose on the parameters for this model to make sense?