Show that each system has infinitely many solutions.

$$\left\{ \begin{array} { l } { y = 2 x - 4 } \\ { 2 x - y - 4 = 0 } \end{array} \right.$$

Using context clues, write a definition for the underlined word in each sentence. With a partner, discuss which context clues helped you to determine the meaning of the word. Then, look up the word in a dictionary and confirm or correct your definition. It is important for cooks to keep their cupboards full of the $\underline{\text{staples}}$ they use every day.

In the United States, the birthrate B of unmarried women (births per 1000 unmarried women) for women whose age is a is modeled by the function $B(a)=-0.27 a^{2}+14.23 a-120.16.$ (a) What is the age of unmarried women with the highest birthrate? (b) What is the highest birthrate of unmarried women? (c) Evaluate and interpret B(40).

A helicopter 120 m from a person takes off vertically. Express the distance d from the person to the helicopter as a function of the height h of the helicopter. What are the domain and the range of d = f(h)?

Display a matrix A and an echelon form of A. Find bases for Col A and Nul A, and then state the dimensions of these subspaces.

$$A=\left[ \begin{array}{rrrr}{1} & {-3} & {2} & {-4} \\ {-3} & {9} & {-1} & {5} \\ {2} & {-6} & {4} & {-3} \\ {-4} & {12} & {2} & {7}\end{array}\right] \sim \left[ \begin{array}{rrrr}{1} & {-3} & {2} & {-4} \\ {0} & {0} & {5} & {-7} \\ {0} & {0} & {0} & {5} \\ {0} & {0} & {0} & {0}\end{array}\right]$$

A gas at a specified stagnation temperature and pressure is accelerated to $M_a = 2$ in a converging–diverging nozzle and to $M_a = 3$ in another nozzle. What can you say about the pressures at the threats of these two nozzles?

Use a truth table to prove the identity $A B C+A B C^{-}+A B^{-} C^{-}+A B^{-} C=A$

The motor of a table saw is rotating at 3450 rev/min. A pulley attached to the motor shaft drives a second pulley of half the diameter by means of a V-belt. A circular saw blade of diameter 0.208 m is mounted on the same rotating shaft as the second pulley. (a) The operator is careless and the blade catches and throws back a small piece of wood. This piece of wood moves with linear speed equal to the tangential speed of the rim of the blade. What is this speed? (b) Calculate the radial acceleration of points on the outer edge of the blade to see why sawdust doesn’t stick to its teeth.

Use the definition of the Laplace transform to find $\mathcal L \left\{ f(t) \right\}$ if

$$f(t)=\left\{\begin{array}{ll}{2-t,} & {0<t<2} \\ {0,} & {t>2}\end{array}\right.$$

Describe the benefits of physical activity for three different body systems.

For each sequence find $\frac { a _ { 2 } } { a _ { 1 } } , \frac { a _ { 3 } } { a _ { 2 } } , \frac { a _ { 4 } } { a _ { 3 } } ,$ and $\frac { a _ { 5 } } { a _ { 4 } }$ 3, 6, 12, 24, 48.

Describe the changes in elastic potential energy and kinetic energy that occur when a mass vibrates on a spring.

Find the derivative of function $g(x)=(\sin x)(\ln x)$

Find the indicated maximum and minimum values by the linear programming method of this section.The constraints are shown below the objective function.

$$\begin{array}{l}{\text { Maximum and }} \\ {\text { minimum } F :} \\ {F=x+3 y} \\ {x \geq 1, y \geq 2} \\ {y-x \leq 3} \\ {y+2 x \leq 8}\end{array}$$