91Ó°ÊÓ

Sketch the set on a real number line. \(\left\\{x:\left|x^{2}+x\right|>x^{2}-x\right\\}\)

Sketch the given region. \(\left\\{(x, y): x^{2}+y^{2}=4, y>0, x>1\right\\}\)

In Exercises \(44-47,\) two functions \(f\) and \(g\) are given. Find constants \(h\) and \(k\) such that \(g(x)=f(x+h)+k .\) Describe the relationship between the plots of \(f\) and \(g\). \(f(x)=x^{2}, g(x)=x^{2}+2 x+5\)

Describe each set in Exercises \(44-47\) using interval notation and the notation \(\\{x: P(x)\\} .\) Use the symbol \(\cup\) where appropriate. The set of points with a distance from 2 that does not exceed 4

Use one or more of the basic trigonometric identities to derive the given identity. \(\tan (\theta+\pi)=\tan (\theta)\)

Sketch the line whose Cartesian equation is given. $$ y=(x-2) / 2+4 $$

Initially, a solution of salt water has total mass \(500 \mathrm{~kg}\) and is \(99 \%\) water. Over time, the water evaporates. Just for fun, estimate to within \(25 \mathrm{~kg}\) the mass of the solution at the time when water makes up \(98 \%\) of the solution. Find a formula for the total mass \(m(p)\) of the solution as a function of \(p\), the percentage contribution of water to the total mass. Exactly what is \(m(98)\) ? Graph \(m(p)\).

Two functions \(f\) and \(g\) are given. Find constants \(h\) and \(k\) such that \(g(x)=f(x+h)+k .\) Describe the relationship between the plots of \(f\) and \(g\). \(f(x)=3 x^{2}, g(x)=3 x^{2}+12 x\)

Sketch the line whose Cartesian equation is given. $$ y-2 x=4 $$

Use the identity \(\pi / 3+\pi / 4=7 \pi / 12\) to calculate the six trigonometric functions at \(7 \pi / 12\).