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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?
Write the inequality that describes the production plan, if x represents the number of Turbo blowers and y represents the number of Tornado blowers.
There were two dates in a row on which the river rose and fell, then rose again during the course of the day.
Solve the differential equation with the given initial conditions: d2x / dt2 + dx/dt + x = 0, t = 0; x = 4/3 ; dx/dt = 3 - v3/ 3
For the given function f, the expression f(x+h)-f(x)/h can be simplified to the form Ax+Bh+C, where A, B and C are constants. Do it.
For any time t=8 the average velocity of the object on the time interval between 8 and t can be simplified into the form At+B, where A and B are constants.
Show that the standard matrix representation and the preceding matrix representation are similar. Show work.
Find the slope of the function's graph at the given point. Then find an equation for the line tangent to graph: f(x) = x^2 + 2, (-2,6)
Groups : Isomorphism and Homomorphism.Show that a group G is simple if and only if every nontrivial group homomorphism G -> G1 is one-to-one.
Find the values of a and b for the polynomial f(x) = 2x^3 + ax^2 - 4x + b, given that f(x) is divisible by x+1 and x-3. Write f(x) in a factorised form.
Conditions for Linear transformation.This chapter starts as follows rotations about the origin and all reflections