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A crocodile is stalking prey located 20 metres further upstream on the opposite bank of a river. Crocodiles travel at different speeds on land and in water. The time taken for the crocodile to reach its prey can be minimised if it swims to a particular point, P, x metres upstream on the other side of the river as shown in the diagram. The time taken, T, measured in tenths of a second, is given by T(x)= 5 √(36 + x2) + 4 (20 - x)
What is the minimum amount of time needed for the crocodile to catch its prey?
Find the set of fundamental solutions by using the differential operator method: [D2 - (2α - 1)D + α (α - l)y = 0, t ∈ (0, ∞); and determine the values of α, for which all solutions tend to zero as t→∞.
Explain why L'Hopital's Rule cannot be used to find the limit of Lim x→0 e^2x/x
A particle passes through the point P = (6, 5, -2) at time t = 4, moving with constant velocity v = i - 3j + 6k. Find parametric equations for the motion of the particle.
The hypotenuse of a right triangle is 26 cm. One of the legs is 14 cm longers than the other leg.
Derive the Euler-Lagrange Differential Equation (rigorously). Explain any theorems or results that you use in the derivation (e.g. don't just say "by the fundamental theorem of the calculus of variations" without telling what the fundamental theor..
for the data set shown below do they following. a compute the standard error the point estimate for sigma. b assuming
Solve the equation on the interval.
A study from a Colombian research center is about to publish a pilot study regarding a new coffee plant that they believe can reduce total cholesterol in humans. They gave increasing doses (cups of coffee) to a test patient over several weeks and ..
Describe a real world situation that could be modeled by a function that is increasing, then constant, then decreasing. What would be the difficulties associated with modeling this situation?
A rectangular poster has an area of 190 in. The height of the poster is 1 in less than twice its width. Find the dimensions of the poster.
Which of the following is not an ethical concern for the statistical researcher?
A reconnaissance airplane leaves its airport on the east coast of the United States and flies in a direction 85 degree. Because of bad weather, it returns to another airport 230 km due north of its home base.
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