Focal length Two thin lenses with focal lengths $p$ and $q$ and separated by a distance $d$ have their combined focal length given by the reciprocal of

$$\frac{1}{p}+\frac{1}{q}-\frac{d}{p q}$$

(a) Combine these fractions.

(b) Use the reciprocal of your answer in (a) to find the combined focal length.

Pie Bakery owns 60 percent of Slice Products Company's stock. During 20X8, Slice produced 100,000 bags of flour, which it sold to Pie Bakery for $900,000. On December 31, 20X8, Pie had 20,000 bags of flour purchased from Slice Products on hand. Slice prices its sales at cost plus 50 percent of cost for profit. Pie, which purchased all its flour from Slice in 20X8, had no inventory on hand on January 1, 20X8.

Pie Bakery reported income from its baking operations of$400,000, and Slice Products reported net income of $150,000 for 20X8.

Required

Give the worksheet consolidation entry or entries required to remove the effects of the inter-company sale in preparing consolidated statements at the end of 20X8.

A car is traveling at 80 feet per second (approximately 55 miles per hour) and slows down as it passes through a busy inter section. The car's velocity is shown in the following table.

$$\begin{array}{c|c|c|c|c|c|} \hline \text { Time since brakes applied (seconds) } & {0} & {3} & {6} & {9} & {12} \\ \hline \text { velocity (ft/sec) } & {80} & {62} & {47} & {32} & {22} \\ \hline \end{array}$$

Use a right sum to approximate the total distance the car has traveled over the 12 second interval.

A friend tells you that because he has just recovered from a cold, he now cannot get the flu. Is your friend right? Describe your answer.

By removing the biggest common factor, write in factored form.

$$65 y^{10}+35 y^6$$

Factor using factoring by grouping : $6 a^2-8 a-3 a+4$

Write as a natural logarithmic equation: a. $N=50 e^{2 t}$ b. $P=8.69 e^{-0.0541 t}$ c. $S=a^{2} e^{-k t}$

At what points, if any, does f assume local maximum or minimum values?

$$f^{\prime}(x)=1-\frac{4}{x^2}, \quad x \neq 0$$

a. Find the length of a $36^\circ$ arc of a circle whose radius is 6 cm.
b. Explain why you think that the arc in part (a) is longer or shorter in terms of centimeters if the radius had been 8 cm.
c. Find the arc length when the radius is increased to 8 cm.

If the sun expanded to a radius 100 times its present radius, what would its density be? (Hint: The volume of a sphere is $\frac{4}{3} \pi R^3.)$

Solve the following equations. $5 ^ { 3 x } = 29$

Find the simplified form for the reciprocal of $\frac{2}{x-1}-\frac{1}{3 x-2}$.

In the following sentence, identify the underlined pronouns by writing above each one PER for personal, REF for reflexive, INTEN for intensive, DEM for demonstrative, INTER for interrogative, REL for relative, or IND for indefinite.

$\underline{\text{Those}}$ are the pilots whom the general $\underline{\text{himself}}$ chose for the mission.

In each of the following sentence, identify the underlined pronouns by writing above each one PER for personal, REF for reflexive, INTEN for intensive, DEM for demonstrative, INTER for interrogative, REL for relative, or IND for indefinite.

Oh, $\underline{\text{this}}$ is $\underline{\text{some}}$ of that delicious tuna salad.