Red Valve Co. of Carnegie, Pennsylvania, makes a control pinch valve that provides accurate, repeatable control of abrasive and corrosive slurries, outlasting gate, plug, ball, and even satellite coated valves. How much can the company afford to spend now on new equipment in lieu of spending $75,000 four years from now? The company’s rate of return is 12% per year.

A family that won a $100,000 prize on America’s Funniest Home Videos decided to put one-half of the money in a college fund for their child who was responsible for the prize. If the fund earned interest at 6% per year, how much was in the account 14 years after it was started?

How much can Haydon Rheosystems, Inc., afford to spend now on an energy management system if the software will save the company $21,300 per year for the next 5 years? Use an interest rate of 10% per year.

One of the biggest vulnerabilities in a control system is network devices, such as Ethernet-based network switches that are located in unsecured locations and accessible to everyone. DeltaX switches, manufactured by Dahne Security, allow the user to automatically lock and unlock the port access to all switches in the network. The company is considering expanding its manufacturing lines now or doing it in 3 years. If the cost now would be $1.9 million, what equivalent amount could the company afford to spend in 3 years? The interest rate is 15% per year.

List the first five terms of the sequence. a1=2, a2=1, an+1=an-an-1

A waste-holding lagoon situated near the main plant receives sludge daily. When the lagoon is full, it is necessary to remove the sludge to a site located 8.2 kilometers from the main plant. Currently, when the lagoon is full, the sludge is removed by pump into a tank truck and hauled away. This process requires the use of a portable pump that initially costs $800 and has an 8-year life. The company pays a contract individual to operate the pump and oversee environmental and safety factors at a rate of$100 per day, plus the truck and driver must be rented for $200 per day. The company has the option to install a pump and pipeline to the remote site. The pump would have an initial cost of$1600 and a life of 10 years and will cost $3 per day to operate. The company’s MARR is 10% per year. (a) If the pipeline will cost$12 per meter to construct and will have a 10-year life, how many days per year must the lagoon require pumping to justify construction of the pipeline? (b) If the company expects to pump the lagoon once per week every week of the year, how much money can it afford to spend now on the 10-year life pipeline to just break even?

Structural unemployment is sometimes said to result from a mismatch between the job skills that employers want and the job skills that workers have. To explore this idea, consider an economy with two industries: auto manufacturing and aircraft manufacturing. a. If workers in these two industries require similar amounts of training, and if workers at the beginning of their careers could choose which industry to train for, what would you expect to happen to the wages in these two industries? How long would this process take? Explain. b. Suppose that one day the economy opens itself to international trade and, as a result, starts importing autos and exporting aircraft. What would happen to demand for labor in these two industries? c. Suppose that workers in one industry cannot be quickly retrained for the other. How would these shifts in demand affect equilibrium wages both in the short run and in the long run? d. If for some reason wages fail to adjust to the new equilibrium levels, what would occur?

The Moller Skycar M400 is a flying car known as a personal air vehicle (PAV) that is expected to be FAA-certified by December 31, 2011. The cost is $985,000, and a$100,000 deposit will hold one of the first 100 “cars.” Assume a buyer pays the $885,000 balance 3 years after making the$100,000 deposit. At an interest rate of 10% per year, what is the effective total cost of the PAV in year 3?

A manufacturer of off-road vehicles is considering the purchase of dual-axis inclinometers for installation in a new line of tractors. The distributor of the inclinometers is temporarily overstocked and is offering them at a 40% discount from the regular cost of $142. If the purchaser gets them now instead of 2 years from now, which is when they will be needed, what is the present worth of the savings per unit? The company would pay the regular price, if purchased in 2 years. Assume the interest rate is 10% per year.

Western Hydra Systems makes a panel milling machine with a 2.7-m-diameter milling head that emits low vibration and processes stress-relieved aluminum panels measuring up to 6000 mm long. The company wants to borrow money for a new production/warehouse facility. If the company offers to repay the loan with $60,000 in year 1 and amounts increasing by$10,000 each year through year 5, how much can the company borrow at an interest rate of 10% per year?

An object located at the origin and having mass M explodes into three pieces having masses M/4, M/3, and 5M/12. The pieces scatter on a horizontal frictionless xy-plane. The piece with mass M/4 files away with velocity 5.0 m/s at

$$37 ^ { \circ }$$

above the x-axis. The piece with mass M/3 has velocity 4.0 m/s directed at an angle of

$$45 ^ { \circ }$$

above the -x-axis. (a) What are the velocity components of the third piece? (b) Describe the motion of the CM of the system after the explosion.

Simplify the expression. -5(w + 3) - (w + 2)

For any triangle, show that $\cos \frac{C}{2}=\sqrt{\frac{s(s-c)}{a b}}$ where $s=\frac{1}{2}(a+b+c)$

Describe translations that transform the graph of f(x) = ∛x into the graph of the given function. h(x) = ∛x + 4