Chapter 11

Solve for the indicated variable. \(A=\pi r^{2}\) for \(r\)

Solve. \(t-\frac{48}{t}=8\)

Find the error in each, and correct the mistake. The solution to \(a x^{2}+b x+c=0(a \neq 0)\) can be found using the quadratic formula. $$x=-b \pm \frac{\sqrt{b^{2}-4 a c}}{2 a}$$

What is a perfect square trinomial? Give an example.

What are two methods that can be used to solve \(y^{2}-16=0 ?\) Solve the equation using both methods.

Solve each equation. $$(t+7)(t-6)=0$$

Solve for the indicated variable. \(V=\frac{1}{3} \pi r^{2} h\) for \(r\)

Solve. \(z+11=-\frac{24}{z}\)

Find the error in each, and correct the mistake. In order to solve \(5 n^{2}-3 n=1\) using the quadratic formula, a student substitutes \(a, b,\) and \(c\) into the formula in this way: \(a=5 \quad b=-3 \quad c=1\) $$n=\frac{-(-3) \pm \sqrt{(-3)^{2}-4(5)(1)}}{2(5)}$$

\(\ln 2 x^{2}-8 x+10,\) what is the a) quadratic term? b) linear term? c) constant?

Determine if each statement is true or false. Every real number is a complex number.

Solve each equation. $$3 z(2 z-9)=0$$

Solve for the indicated variable. \(a=\frac{v^{2}}{r}\) for \(v\)

Solve. \(\frac{2}{x}+\frac{6}{x-2}=-\frac{5}{2}\)

Determine if each statement is true or false. since \(i=\sqrt{-1},\) it follows that \(i^{2}=-1\)

Solve using the square root property. $$b^{2}=36$$

Solve each equation. $$u^{2}+15 u+44=0$$

Solve for the indicated variable. \(K=\frac{1}{2} I w^{2}\) for \(w\)

Solve. \(\frac{3}{y}-\frac{6}{y-1}=\frac{1}{2}\)

Find the error in each, and correct the mistake. The discriminant of \(3 z^{2}-4 z+1=0\) is $$ \begin{aligned} \sqrt{b^{2}-4 a c} &=\sqrt{(-4)^{2}-4(3)(1)} \\ &=\sqrt{16-12} \\ &=\sqrt{4} \\ &=2 \end{aligned} $$

What is the first thing you should do if you want to solve \(2 p^{2}-7 p=8\) by completing the square?

Determine if each statement is true or false. In the complex number \(-6+5 i,-6\) is the real part and \(5 i\) is the imaginary part.A

Solve using the square root property. $$h^{2}=64$$

Solve each equation. $$n^{2}+10 n-24=0$$

Solve for the indicated variable. \(E=\frac{I}{d^{2}}\) for \(d\)

Solve using the quadratic formula. $$x^{2}+4 x+3=0$$

Solve. \(1=\frac{2}{c}+\frac{1}{c-5}\)

Solve using the square root property. $$t^{2}=-25$$

Solve each equation. $$x^{2}=x+56$$

Solve for the indicated variable. \(L=\frac{2 U}{I^{2}}\) for \(I\)

Solve using the quadratic formula. $$v^{2}-8 v+7=0$$

Solve. \(\frac{2}{g}=1+\frac{g}{g+5}\)

Solve each equation. $$c^{2}+3 c=54$$

Solve using the square root property. $$s^{2}=-1$$

Solve for the indicated variable. \(F=\frac{k q_{1} q_{2}}{r^{2}}\) for \(r\)

Solve using the quadratic formula. $$3 t^{2}+t-10=0$$

Solve. \(\frac{3}{2 v+2}+\frac{1}{v}=\frac{3}{2}\)C

Solve each equation. $$1-100 w^{2}=0$$

Solve using the square root property. $$r^{2}-27=0$$

Solve for the indicated variable. \(E=\frac{k q}{r^{2}}\) for \(r\)

Solve using the quadratic formula. $$6 q^{2}+11 q+3=0$$

Solve. \(\frac{1}{b+3}+\frac{1}{b}=\frac{1}{3}\)

Solve each equation. $$9 j^{2}=49$$

Solve using the square root property. $$a^{2}-30=0$$

Solve using the quadratic formula. $$k^{2}+2=5 k$$

Solve. \(\frac{9}{n^{2}}=5+\frac{4}{n}\)

Solve. \(3-\frac{16}{a^{2}}=\frac{8}{a}\)

Solve using the quadratic formula. $$n^{2}=5-3 n$$

Solve each equation. $$19 a+20=-3 a^{2}$$

Solve using the square root property. $$v^{2}=\frac{121}{16}$$