Draw one line under each transitive verb and two lines under each intransitive verb. Draw three lines under each direct object and circle each indirect object. They painted scenes of daily Etruscan life on the walls.

A cylindrical container, with a volume of $4000 \mathrm{~cm}^3$, is being constructed to hold candies. The cost of the base and lid is $\$ 0.005 / \mathrm{cm}^2$, and the cost of the side walls is $\$ 0.0025 / \mathrm{cm}^2$. Determine the dimensions of the cheapest possible container.

Write each equation of the system in slope-intercept form. By comparing slopes and y-intercepts, determine whether the equations are consistent or inconsistent.

$$\left. \begin{array} { l } { 3 x = 4 y + 8 } \\ { 3 y = 4 x + 8 } \end{array} \right.$$

The three planes with equations 3x+y+7z+3 = 0, 4x-12y+4z-24 = 0, and x+2y+3z-4 = 0 do not simultaneously intersect.

(a). Considering the planes in pairs, determine the three lines of intersection.

(b). Show that these three lines are parallel.

The capillary rise of a fluid along the walls of the tube causes the fluid to rise a distance $h$. This effect depends upon the diameter $d$ of the tube, the surface tension $\sigma$, the density $\rho$ of the fluid, and the gravitational acceleration $g$. Find the relation between $h$ and these parameters.

Consider a person whose exposed surface area is $1.7 m^2,$ emissivity is 0.5, and surface temperature is $32^\circ C.$ Determine the rate of heat loss from that person by radiation in a large room having walls at a temperature of (a) 300 K and (b) 280 K.

Draw one line under each transitive verb and two lines under each intransitive verb. Draw three lines under each direct object and circle each indirect object. They buried their relatives with objects such as vases, statues, and jewelry.

A hollow cubical box is 0.30 m on an edge. This box is floating in a lake with one-third of its height beneath the surface. The walls of the box have a negligible thickness. Water is poured into the box. What is the depth of the water in the box at the instant the box begins to sink?

Jenna plans to paint the ceiling of a 15 foot-by-10 foot room, then mount crown molding along the upper edge of the walls. Jenna should buy enough paint to cover what area? What length of crown molding will she need?

Complete each of the following sentences by writing a pronoun that agrees with its antecedent.

Example 1. We need to repair these stone walls before one of $\underline{\color{#c34632}{them}}$ collapses.

Both Clarence and his brother keep ____________________ in good condition.

As a landscape architect, you are creating a patio. 128 cubic feet of concrete will be used to create the square patio floor. The length of the patio's side walls is 15.5 feet longer than the thickness of the floor. What proportions does the patio floor have?

A rectangular rug covers the floor in a living room. One of the walls in the same living room is painted blue. Are the rug and the blue wall parallel? Explain. • Can you visualize the rug and the wall as geometric figures? • What must be true for these geometric figures to be parallel?

Find equations for the lines that are tangent and normal to the level curve f(x, y) = c at the point

$$P_0.$$

Then sketch the lines and level curve together with

$$\nabla f \text { at } P _ { 0 }.$$

$$\frac { y ^ { 2 } } { 2 } - \frac { x ^ { 2 } } { 2 } = \frac { 3 } { 2 } , \quad P _ { 0 } ( 1,2 )$$

The wings of a certain beetle have a series of parallel lines across them. When normally incident 460-nm light is reflected from the wing, the wing appears bright when viewed at an angle of $51^{\circ} .$ How far apart are the lines?