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Chapter 1: Problem 53
Write a sentence using the variation terminology of this section to describe the formula. Area of a triangle: \(A=\frac{1}{2} b h\)
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Determine whether the statement is true or false. Justify your answer. A piecewise-defined function will always have at least one \(x\) -intercept or at least one \(y\) -intercept.
Graph each of the functions with a graphing utility. Determine whether the function is even, odd, or neither. $$\begin{aligned}&\begin{array}{ll}f(x)=x^{2}-x^{4} & g(x)=2 x^{3}+1 \\\h(x)=x^{5}-2 x^{3}+x & j(x)=2-x^{6}-x^{8}\end{array}\\\&k(x)=x^{5}-2 x^{4}+x-2 \quad p(x)=x^{9}+3 x^{5}-x^{3}+x \end{aligned}$$
Finding a Mathematical Model In Exercises \(41-50\), find a mathematical model for the verbal statement. \(z\) varies jointly as the square of \(x\) and the cube of \(y\)
Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring. The coiled spring of a toy supports the weight of a child. The spring is compressed a distance of 1.9 inches by the weight of a 25 -pound child. The toy will not work properly if its spring is compressed more than 3 inches. What is the maximum weight for which the toy will work properly?
Evaluate the function for the indicated values. \(g(x)=-7[x+4]+6\) (a) \(g\left(\frac{1}{8}\right)\) (b) \(g(9)\) (c) \(g(-4)\) (d) \(g\left(\frac{3}{2}\right)\)
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