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Chapter 1: Problem 46
Solve the following equations. $$\ln y=3$$
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Let \(S(n)=1+2+\cdots+n,\) where \(n\) is a positive integer. It can be shown that \(S(n)=n(n+1) / 2\) a. Make a table of \(S(n),\) for \(n=1,2, \ldots, 10\) b. How would you describe the domain of this function? c. What is the least value of \(n\) for which \(S(n)>1000 ?\)
The Earth is approximately circular in cross section, with a circumference at the equator of 24,882 miles. Suppose we use two ropes to create two concentric circles; one by wrapping a rope around the equator and then a second circle that is \(38 \mathrm{ft}\) longer than the first rope (see figure). How much space is between the ropes?
Consider the general quadratic function \(f(x)=a x^{2}+b x+c,\) with \(a \neq 0\) a. Find the coordinates of the vertex in terms of \(a, b,\) and \(c\) b. Find the conditions on \(a, b,\) and \(c\) that guarantee that the graph of \(f\) crosses the \(x\) -axis twice.
a. Find the linear function \(C=f(F)\) that gives the reading on the Celsius temperature scale corresponding to a reading on the Fahrenheit scale. Use the facts that \(C=0\) when \(F=32\) (freezing point) and \(C=100\) when \(F=212\) (boiling point). b. At what temperature are the Celsius and Fahrenheit readings equal?
Beginning with the graphs of \(y=\sin x\) or \(y=\cos x,\) use shifting and scaling transformations to sketch the graph of the following functions. Use a graphing utility only to check your work. $$q(x)=3.6 \cos (\pi x / 24)+2$$
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