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Chapter 4: Problem 7
Find a number \(y\) such that \(\ln y=4\).
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Find the two points where the circle of radius 2 centered at the origin intersects the circle of radius 3 centered at (3,0) .
Suppose a bank account that compounds interest continuously grows from \(\$ 100\) to \(\$ 110\) in two years. What annual interest rate is the bank paying?
The functions cosh and \(\sinh\) are defined by $$ \cosh x=\frac{e^{x}+e^{-x}}{2} \text { and } \sinh x=\frac{e^{x}-e^{-x}}{2} $$ for every real number \(x .\) For reasons that do not concern us here, these functions are called the hyperbolic cosine and hyperbolic sine; they are useful in engineering. Show that $$ \cosh (x+y)=\cosh x \cosh y+\sinh x \sinh y $$ for all real numbers \(x\) and \(y\).
Show that the area inside a circle with circumference \(c\) is \(\frac{c^{2}}{4 \pi}\).
Find six distinct points on the circle with center (2,3) and radius \(5 .\)
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