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Chapter 1: Problem 30
(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. $$(1,4),(8,4)$$
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Find the difference quotient and simplify your Answer: $$f(x)=\sqrt{5 x}, \quad \frac{f(x)-f(5)}{x-5}, \quad x \neq 5$$
The frequency of vibrations of a piano string varies directly as the square root of the tension on the string and inversely as the length of the string. The middle A string has a frequency of 440 vibrations per second. Find the frequency of a string that has 1.25 times as much tension and is 1.2 times as long.
Write a sentence using the variation terminology of this section to describe the formula. Area of a triangle: \(A=\frac{1}{2} b h\)
A balloon carrying a transmitter ascends vertically from a point 3000 feet from the receiving station. (a) Draw a diagram that gives a visual representation of the problem. Let \(h\) represent the height of the balloon and let \(d\) represent the distance between the balloon and the receiving station. (b) Write the height of the balloon as a function of \(d\) What is the domain of the function?
Find the difference quotient and simplify your Answer: $$f(x)=x^{2}-x+1, \quad \frac{f(2+h)-f(2)}{h}, \quad h \neq 0$$
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