Luis is responsible for buying some specialized manufacturing equipment that has a purchase price of $10,000 and annual operating costs of$1000. The vendor is offering a special buyer incentive that provides free maintenance for the first four years. After that time, the maintenance is $500 per year over the 10-year life, and there is an overhaul expense in year 5 of$2000. The equipment has a salvage value of $1000. If the interest rate is 8%, what is the present value?

Annual maintenance costs for a particular section of highway pavement are $2500. The placement of a new surface would reduce the annual maintenance cost to$500 per year for the first 3 years and to $1000 per year for the next 7 years. After 10 years the annual maintenance would again be$2500. If maintenance costs are the only saving, what investment can be justified for the new surface? Assume interest at 5%.

Use spreadsheets to compare these situations after 10 years. total paid and total paid to the principal for a $300,000, 15-year mortgage with a 6.5% APR. total amount paid for a$2,600 monthly rent that has an annual increase of 2% after 10 years.

Give an example of a function f that is defined on a closed interval, and whose values at the endpoints have opposite signs, but for which the equation f(x)=0 has no solution in the interval.

Often environmentalists capture an endangered species and transport the species to a controlled environment where the species can produce offspring and regenerate its population. Suppose that six American bald eagles are captured, transported to Montana, and set free. Based on experience, the environmentalists expect the population to grow according to the model $P(t)=\frac{500}{1+82.33 e^{-0.162 t}}$ where t is measured in years. What is the population after 3 years?

Find and graph the solution set of each inequality.

$$x ^ { 2 } + 2 x \geq 0$$

You supervise an aging production line that constantly needs maintenance and new parts. Last month you spent $25,000 replacing a failed controller. Should the following plan be accepted if the interest rate is 15%? The net installed cost of the new line to replace the old line is$600,000 with a useful life of six years. In the first year its operating cost will be $100,000, and it will generate annual revenues of$300,000. Each year the operating cost will increase by $5000 and the revenues will fall by$15,000. After six years the equipment will have a value of $100,000 in the next re-building of the line

Show that for any fixed $\delta > 0$ (no matter how small),

$$\max\limits_{\delta\leq|x|<\infty} S(x,t)\to 0, \text{ as } t\to 0.$$

[This means that the tail of S(x, t) is “uniformly small”.]

Find the angle $\boldsymbol{\theta}$ between the vectors.

$$\begin{array}{l}{\mathbf{u}=\cos \left(\frac{\pi}{3}\right) \mathbf{i}+\sin \left(\frac{\pi}{3}\right) \mathbf{j}} \\ {\mathbf{v}=\cos \left(\frac{3 \pi}{4}\right) \mathbf{i}+\sin \left(\frac{3 \pi}{4}\right) \mathbf{j}}\end{array}$$

Write an equation for each sentence. Solve the equation. Seven multiplied by k is negative one hundred sixty-eight.

A machine costs $250,000 to purchase and will provide$60,000 a year in benefits. The company plans to use the machine for 12 years and then will sell the machine for scrap, receiving $15,000. The company interest rate is 10%. Should the machine be purchased?

Why might the rococo style have been disliked by the philosophes?

Sketch the graph of the equation using extrema, intercepts, symmetry, and asymptotes. y = 3x / (x-1)

Convert the degree measure to radians or the radian measure to degrees. 40°