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A bar of glass (k = 0.0036 cm2/sec, cp = 0.39 calories/cm3 °C) 20 cm long is initially at a temperature of 100°C and its ends are maintained at 0°C for t > 0. If the cross section of the bar has area 1 cm2, express the total amount of heat stored in the bar as a function of time, and then show that
(i) after five hours the amount of heat remaining in the bar is approximately 16.38% of the amount initially stored,
(ii) if the bar were made of steel (k = 0.128 cm2/sec, cp = 0.858 calories /cm3 °C), then the amount of heat initially stored in it is more than double the amount initially stored in the glass bar, and
(iii) it takes less than 13 minutes for the amount of heat remaining in the steel bar to equal the amount remaining in the glass bar at the end of five hours.
a certain radioactive isotope has a half life of approximately 1050 years. How many years will required for a given of the isotope to decay to 75% of that amount?
If the current demand is increasing by 1000 units per year and if the price remains fixed at $350 per unit, how much revenue will the manufacturer receive from the sale of the product over the next 5 years?
An isosceles triangle whose base is the interval from (0,0) to (c,0) has its vertex on the graph of f, where f(x)=12-x^2 for x is greater than or equal to 0 and f(x) is greater than or equal to 0.
Let G be a group (finite or infinite) and let a and b in G. Let o(a) represent the order of a. Suppose G is abelian and both a and b are of finite order. Show that ab is of finite order and o(ab) divides o(a)o(b).
R=6e^(12.77x) x is blood alcohol concentration and R, given as a percent, is the risk of having a car accident. What blood alcohol concentration corresponds to a 30% risk of a car accident?
The sum of the infinite series, 1/2^2 - 2/3^2 + 3/4^2 - 4/5^2 + ... is given as pi^2/12 - log 2 on pages 64-65 in the book "Summation of Series" by L. B. W. Jolley, 2nd ed., 1961, Dover Pubs. Inc. (the ^ symbol denotes exponentiation in the above ..
a survey is being planned to determine the mean amount of time corporation executives watch television. a pilot survey
the average number of calories in a 1.5 ounce chocolate bar is 225. Suppose the distribution of calories is approximately normal with standard deviation 10. Find the probability that a randomly selected chocolate bar will have less than 200 calori..
What is the cost at a fixed rate of producing a disk that costs $1.25 + fixed cost of $3000 and the revenue of one disk is $12?
1. show using algebra that the formula for a circle is a special case of the formula for an ellipse.2. show using
A tank contains 200 liters of fluid n which 30 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 4L/min; the well-mixed solution is pumped up at the same rate.
find the surface area obtained by rotating the curve 9x=y^2+18, 2 is less than or equal to x which is less than or equal to 6.
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