A 12-kg piece of metal displaces 2 L of water when submerged. Show that its density is 6000 kg/m3. How does this compare with the density of water?

Suppose you balance a 2-kg ball on the tip of your finger, which has an area of 1 cm2. Show that the pressure on your finger is 20 N/cm2, or is 200 kPa.

On December 31 of the current year, Marris Corporation has one note receivable outstanding, a 120-day, 12%, $4,000.00 note dated November 16. Plan the adjustment on a work sheet. Label the adjustment (a).

Supply the missing amounts for each of the following companies:

$$\begin{matrix} \text{Company} & \text{Net Sales} & \text{Beginning Inventory } & \text{Net Purchases} & \text{Ending Inventory} & \text{Cost of Goods Sold} & \text{Gross Profit}\\ \text{Gerald} & \text{\$100,000 } & \text{\$21,000 } & \text{\$60,000} & \text{\$19,000 } & \text{(a)} & \text{(b)}\\ \text{Evans} & \text{137,000 } & \text{28,000} & \text{(c)} & \text{22,000 } & \text{(d)} & \text{41,000}\\ \text{Dunleavy} & \text{(e)} & \text{(f) } & \text{55,000 } & \text{21,000} & \text{60,000} & \text{32,000}\\ \text{Thomas} & \text{80,000} & \text{9,000} & \text{33,000} & \text{(g) } & \text{35,000} & \text{(h)}\\ \end{matrix}$$

Prepare the income statement for Gerald Company for the year ended December 31, 2012. Use the cost-of-goods-sold model to compute cost of goods sold. Gerald’s operating and other expenses for the year were $42,000. Ignore income tax.

Plot the point in polar coordinates and find the corresponding rectangular coordinates for the point. (-4, -3π/4)

A merchant in Kathmandu sells you a solid-gold, 1-kg statue for a very reasonable price. When you get home, you wonder whether you got a bargain, so you lower the statue into a container of water and measure the volume of displaced water. Show that for 1 kg of pure gold, the volume of water displaced is 51.8 cm3.

Determine whether each statement is true or false. If the statement is true, prove it. If the statement is false, give a counterexample. Assume that the functions $f$, $g$, and $h$ take on only positive values. $f(n)+g(n)=\Theta(h(n))$, where $h(n)=\max\{f(n),g(n)\}$

Which term applies to the relationship between two organisms of different species that live together, when both benefit from the relationship? a) commensalism b) sediment c) temperature d) water

A $1 \mathrm{~m}$ tall barrel is filled with water (with a weight density of $\left.10,000 \mathrm{~N} / \mathrm{m}^3\right)$. Show that the water pressure on the bottom of the barrel is $10,000 \mathrm{~N} / \mathrm{m}^2$ or, equivalently, $10 \mathrm{~kPa}$.

A 0.6 kg piece of metal displaces 1 liter of water when submerged. What is its density?

The density of a rock doesn’t change when it is submerged in water. Does your density change when you are submerged in water? Discuss and defend your answer.

To prove that $\exists x\forall yP(x,y)$ is true, show that for at least one $x\in X$, $P(x,y)$ is true for every $y\in Y$, where the domain of discourse is $X\times Y$.

At the surface of a freshwater lake the pressure is 105 kPa. (a) What is the pressure increase in going 35.0 m below the surface? (b) What is the approximate pressure decrease in going 35 m above the surface? Air at

$$20 ^ { \circ } \mathrm { C }$$

has density of 1.20

$$\mathrm { kg } / \mathrm { m } ^ { 3 }$$

.

A balloon that weighs 1 N is suspended in air, drifting neither up nor down. How much buoyant force acts on it? What happens if the buoyant force decreases? Increases?