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The velocity, v, with which air comes out depends on the radius, r, of your windpipe. If R is the normal (rest) radius of your windpipe, then for r R, the velocity is given by v = a(R - r)r2 , where a is a positive constant. What value of r maximizes the velocity? 4. The temperature change, T , in a patient generated by a dose, D of a particular drug is given by T = where C is a positive constant. (a) What dose maximizes the temperature change? DT (b) The sensitivity of the body, at dosage D, to the drug is defined to be . What dosage maximizes dD sensitivity?
The distance traveled by an object moving in a straight line is given by s=t^2-8t, where s is in feet and t is the time in seconds the object has been in motion. How long ( to the nearest tenth)
You have a wire that is 38 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What i..
A single-loop negative feedback system has a loop transfer function. Determine the range of the gain K for which the system is stable.
Let x be the length of the top of the rectangle (and thus also of the bottom of the rectangle and of the diameter of the circle) and y the length of the side of the rectangle.
Suppose that E is a normed linear space, and C is a subset. Prove that C is weakly bounded if and only if C is norm bounded. Conclude that weakly convergent sequences in E are bounded.
Find the volume of a frustum of a pyramid with square base of side 30, square top of side 15 and height 10.
A water storage tank has the shape of a cylinder with diameter 22 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 20 ft, what percentage of the total capacity is being used? (Round the answer to one..
Strontium 90 is a radioactive material that decays according to the function A(t)=Ae^(-.0244t), where A is the initial amount present and A is the amount present at time t (years). What is the half-life of strontium 90? The answer is 28.4 years. H..
A certain country taxes the first $16,000 of an individual's income at a rate of 15%, and all income over $16,000 is taxed at 20%. Find a piecewise-defined function T that specifies the total tax on an income of x dollars.
A cable 16 m long runs from the top of a utility pole to a point on the ground 4 m from the base of the pole. How tall is the utility pole, to the nearest tenth?
A shipment of 7 television sets contains 2 defective sets. A hotelmakes a random purchase of 3 of the sets. If x is the number ofdefective sets purchased by the hotel, find the probability distribution of X.
The practice's accounts receivable is $73,426 and the 90 day past due accounts are $18356.50. What % of the total accounts receivable is over 90 days?
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