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Beranek Corp has $625,000 of assets (which equal total invested capital), and it uses no debt—it is financed only with common equity. The new CFO wants to employ enough debt to raise the total debt to total capital ratio to 40%, using the proceeds from borrowing to buy back common stock at its book value. How much must the firm borrow to achieve the target debt ratio?

An airplane flies at an altitude of 6  miles towards a point directly over an observer. Consider  and  as shown in the following figure. The speed of the plane is400 miles per hour. Find  when  miles. Round your answer to three decimal places. ​ ​

A ladder 20 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 2 feet per second. How fast is the top of the ladder moving down the wall when its base is 13 feet from the wall? Round your answer to two decimal places. ​ ​

Assume that  x  and  y  are both differentiable functions of  t  . Find  when  and  for the equation. ​

An airplane is flying in still air with an airspeed of 283  miles per hour. If it is climbing at an angle of 21 °, find the rate at which it is gaining altitude. Round your answer to four decimal places. ​

A petrol car is parked 40 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write  as a function of x. ​ ​

Find the derivative of the function. ​ . ​

A conical tank (with vertex down) is 12  feet across the top and 18  feet deep. If water is flowing into the tank at a rate of 18  cubic feet per minute, find the rate of change of the depth of the water when the water is 10  feet deep. ​

If the annual rate of inflation averages over the next  years, the approximate cost  of goods or cervices during any year in that decade is where  is the time in years and  is the present cost. The price of an oil change for your car is presently. Estimate the price years from now. Round your answer to two decimal places. ​

Suppose the table below shows the temperature at which a given liquid boils at selected pressures p (pounds per square inch). A model that approximates the data is . Find the rate of change of T with respect to p when . Round your answer to two decimal places. p 5 10 14.696 (1 atm) 20 30 40 60 80 100 T 327.43 404.29 448.84 485.71 536.18 573.59 629.02 670.61 704.38 ​