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Magazine Problem 71
Find all real numbers a such that the given point is on the circle \(x^{2}+y^{2}=1\). $$ (a, 3 / 5) $$
Problem 72
Determine whether the graph of each function is symmetric about the y-axis or the origin. Indicate whether the function is even, odd, or neither. $$ f(x)=x^{6}-x^{4}+x^{2} $$
Problem 72
Find all real numbers a such that the given point is on the circle \(x^{2}+y^{2}=1\). $$ (a,-1 / 2) $$
Problem 72
Each of the following functions is invertible. Find the inverse using composition. $$ f(x)=\sqrt[3]{x-9} $$
Problem 73
Determine whether the graph of each function is symmetric about the y-axis or the origin. Indicate whether the function is even, odd, or neither. $$ f(x)=|x-2| $$
Problem 73
Find all real numbers a such that the given point is on the circle \(x^{2}+y^{2}=1\). $$ (-2 / 5, a) $$
Problem 74
Find all real numbers a such that the given point is on the circle \(x^{2}+y^{2}=1\). $$ (2 / 3, a) $$
Problem 74
Each of the following functions is invertible. Find the inverse using composition. $$ f(x)=-x^{3}+4 $$
Problem 74
Determine whether the graph of each function is symmetric about the y-axis or the origin. Indicate whether the function is even, odd, or neither. $$ f(x)=\left(x^{2}-2\right)^{3} $$
Problem 74
Compression Ratio The compression ratio \(C R\) for an engine is a function of the bore \(B\), the stroke \(S\), and the clearance volume \(V,\) where $$ C R=1+\frac{\pi B^{2} \cdot S}{4 V} $$ The clearance volume is the volume of air in the cylinder when the piston is at top dead center. Find a formula that expresses the clearance volume \(V\) as a function of \(C R, B,\) and \(S\).
