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Question: At 1:00 pm one winter afternoon, there is a power failure at your house in Wisconsin, and your heat does not work without electricity. When the power goes out, it is 68°F in your house. At 10:00 pm, it is 57°F in the house, and you notice that it is 10°F outside.
(a) Assuming that the temperature, T, in your home obeys Newton's Law of Cooling, write the differential equation satisfied by T.
(b) Solve the differential equation to estimate the temperature in the house when you get up at 7:00 am the next morning. Should you worry about your water pipes freezing?
(c) What assumption did you make in part (a) about the temperature outside? Given this (probably incorrect) assumption, would you revise your estimate up or down? Why?
Determine whether the statement forms in logically equivalent. In each case, construct a truth table and include a sentence justifying your answer.
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In the days and weeks following the tragic events of September 22, 2001, some political leaders claimed that extraordinary times call for measures; in times of war, basic civil liberties and freedoms, such as privacyneed to be severely for the sak..
the american restaurant association collected information on the number of meals eaten outside the home per week by
f(x)= the square root of x^2+1 and [0,4] . Use the midpoint rule with 4 rectangles to approximate the area bounded by f(x) and the x axis.
Explain why f(x) is the only function with both these properties. [Assume g'(x) = g(x), and g(0) = 1, for some function g(x).
A picture measures 5 1/8 inch by 10 1/4 inch. The frame for the picture is 3/4 inch wide. What are the dimensions of the picture, including the frame?
Let f(x)=x^-3 (x-sinx) for x=0. How should f(0) be defined in order that f be continuous? Is it differentiable? Subject: Numerical Analysis: Mathematics of Scientific Computing
Describe it in words. A hyperbolic cylinder of two sheets on either side of the y-axis. A circular cylinder extended in the z-direction. A circular cylinder extended in the y-direction.
Draw all rooted trees on 5 vertices. The order and the place in which you write the vertices down on the page is unimportant. If you would like to label the vertices (as we did in the graph in Figure 6.10), that is fine, but don't give two differe..
What is the decimal notation for the fraction 1/4? How can you show that 1/4 = 25/100? How can you write 5/16 as a decimal? How would you write 1/9 as a decimal?
Determined how Jared should cut the sandwich into two shares s1 and s2. After Jared cuts which of the two shares should Karla choose and what is the values of this share.
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