Gravity If an imaginary line segment is drawn between the centers of the earth and the moon, then the net gravitational force F acting on an object situated on this line segment is $F=\frac{-K}{x^{2}}+\frac{0.012 K}{(239-x)^{2}}$ where K>0 is a constant and x is the distance of the object from the center of the earth, measured in thousands of miles. How far from the center of the earth is the "dead spot' where no net gravitational force acts upon the object? (Express your answer to the nearest thousand miles.)

The ancient Babylonians knew how to solve quadratic equations. Here is a problem from a cuneiform tablet found in a Babylonian school dating back to about 2000 B.C. I have a reed, I know not its length. I broke from it one cubit, and it fit 60 times along the length of my field. I restored to the reed what I had broken off, and it fit 30 times along the width of my field. The area of my field is 375 square nindas. What was the original length of the reed? Solve this problem. Use the fact that 1 ninda = 12 cubits.

Describe tu pizza favorita.

The Russian ice breaker Yamal can move forward through 2.3-meter-thick ice at a speed of 5.5 kilometers per hour. Write and solve an equation to find the number of hours it will take to travel 82.5 kilometers through the ice.

Express the given quantity in terms of the indicated variable. The average of four quiz scores if each of the first three scores is 8; q = fourth quiz score

Find the exact value of the trigonometric function at the given real number. $\tan \frac{7 \pi}{6}$

Fill in each blank so that the resulting statement is true. The equation x+y=7 can be converted to a polar equation by replacing x with ____ and replacing y with ____.

A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given by the formula

$$P = \frac { 1 } { 10 } x ( 300 - x )$$

provided that

$$0 \leq x \leq 200$$

. How many ovens must be manufactured in a given week to generate a profit of $1250?

TexAm Petroleum, the giant oil company, holds reserves of oil and gas assets. At the end of 2012, assume the cost of TexAM Petroleum’s mineral assets totaled $234 billion, representing 13 billion barrels of oil in the ground. Which depreciation method is similar to the depletion method that TexAM Petroleum and other oil companies use to compute their annual depletion expense for the minerals removed from the ground? Suppose the company removed 800 million barrels of oil during 2013. Record this event. Show amounts in billions. Assume that, of the amount removed in (2), the company sold 200 million barrels. Make the cost of sales entry.

A factory is to be built on a lot measuring 180 ft by 240 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must the width of this lawn be, and what are the dimensions of the factory?

Express the given quantity in terms of the indicated variable.

A wire 360 in. long is cut into two pieces. One piece is formed into a square, and the other is formed into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)?

Wendy took a trip from Davenport to Omaha, a distance of 300 mi. She traveled part of the way by bus, which arrived at the train station just in time for Wendy to complete her journey by train. The bus averaged 40 mi/h, and the train averaged 60 mi/h. The entire trip took

$$5 \frac { 1 } { 2 } h$$

. How long did Wendy spend on the train?

A $19 \frac{1}{2}$-foot ladder leans against a building. The base of the ladder is $7 \frac{1}{2} \mathrm{ft}$ from the building. How high up the building does the ladder reach?