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1. Determine the volume of the solid generated by rotating function f(x) = √(64 - x2) about the x-axis on [6, 8].
2. Find the volume of the solid formed by rotating the region enclosed by y = e3x + 1, y = 0, x = 0, x = 0.4 about the x-axis.
3. Find the average value of the function f(x) = 5x2 on the interval 0 ≤ x ≤ 4.
4. Suppose you deposit $6000 at 7% interest compounded continuously. Find the average value of your account during the first 2 years.
5. If a cup of coffee has temperature 100oC in a room where the ambient air temperature is 24oC, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t) = 24 + 76e-t/50. What is the average temperature of the coffee during the first 28 minutes?
Let U be a uniform random variable on the interval (-pi/2, pi/2). Let X=sinU. Find the probability density function of X and calculate E(X) and var(X).
A small business buys a computer for $3700. After 4 years the value of the computer is expected to be $200. For accounting purposes the business uses linear depreciation to assess the value of the computer at a given time.
The value V (in millions of dollars) of a famous painting can be modeled by the equation V = 10ekt, where t represents the year, with t = 0 corresponding to 1980. In 2003, the same painting was sold for $50 million. Find the value of k.
f(x)=xlnx find f'(e), in other words, find the derivative of f at x=e
Find the amount of paint needed to paint a region that is the shape of a parabola...15 meters tall with a base of 10 meters if 1 liter of paint covers 10 square meters.
In how many ways can the six books be arranged on the shelf if books on the same subject matter are placed together?
Note the terms: 0% interest for ? number of years, the instant dollar discount, the retail price of the vehicle, and the interest rate of the loan. Given those figures, which is the better deal and why? Support your answer with calculations.
Use integer programming to establish whole numbers for the solution variables.
A table shows number of tickets and ticket cost, describe the pattern. How does the cost per ticket change as you buy more tickets?
1. what is the population parameter sample statistic and type of data for a given research study?2. what three facets
draw a digram of the info it provides or how to go about solving it???help plzz even if it isnt by 2marrow i would like to know how to do it thx
Find the x-intercept of L(x) as a way of estimating the x-intercept of f(x). Round the coefficients 3 decimal places.
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