Perform the indicated operation and, if possible, simplify.

$$\frac{a}{6 a-9 b}-\frac{b}{4 a-6 b}$$

Perform the indicated operation. Simplify, if possible.

$$\frac{x-2}{6}-\frac{x+1}{3}$$

Answer the following questions.

(a) On May 1, 2012, Goldberg Company sold some machinery to Newlin Company on an installment contract basis. The contract required five equal annual payments, with the first payment due on May 1, 2012. What present value concept is appropriate for this situation?

(b) On June 1, 2012, Seymour Inc. purchased a new machine that it does not have to pay for until May 1, 2014. The total payment on May 1, 2014, will include both principal and interest. Assuming interest at a 12% rate, the cost of the machine would be the total payment multiplied by what time value of money concept?

(c) Costner Inc. wishes to know how much money it will have available in 5 years if five equal amounts of $35,000 are invested, with the first amount invested immediately. What interest table is appropriate for this situation?

(d) Jane Hoffman invests in a “jumbo”$200,000, 3-year certificate of deposit at First Wisconsin Bank. What table would be used to determine the amount accumulated at the end of 3 years?

Perform the indicated operation and simplify the result.

$$(3 \sqrt{6})(4 \sqrt{3})$$

Verify that the indicated function is an explicit solution of the given differential equation. Give an interval of definition I for each solution.

$$\begin{array}{l} x^{2} y^{\prime \prime}+x y^{\prime}+y=\sec (\ln x) \\ y=\cos (\ln x) \ln (\cos (\ln x))+(\ln x) \sin (\ln x) \end{array}$$

The largest interval $I$ over which the explicit solutions $\phi_1(x) = \sqrt{25-x^2}$ and $\phi_2(x)=-\sqrt{25-x^2}$ of

$$\dfrac{dy}{dx} = \dfrac{x}{y}$$

are defined is the open interval $(-5, 5)$. Why can't the interval $I$ of definition be the closed interval $[- 5, 5]$?

For the following problem, write an equation for the inverse relation by interchanging the variables and solving for y in terms of x. Then plot the function and its inverse on the same screen, using function mode. Sketch the result, showing that the function and its inverse are reflections across the line y = x. Tell whether or not the inverse relation is a function.

$$y=-0.5 x^2-2$$

Let f(t) = t for $0 \leq t \leq 2$ and f(t) = 3 for $2<t \leq 4$. (a) Find an explicit expression for $F(x)=\int_{0}^{x} f(t) d t$ as a function of x. (b) Sketch F and determine where F is differentiable. (c) Find a formula for $F^{\prime}(x)$ wherever F is differentiable.

Consider the function f(x)=-x^2+4x-3. Find the average rate of change of the function from x1 to x2. Does the average rate of change seem to be approaching one value? If so, then state the value.

Name the operation you should perform first.

$$-4+3^3 \div 5$$

Maurice and Lester are twins who have just graduated from college. They have both been offered jobs where their take-home pay would be $2500 per month. Their parents have given Maurice and Lester two options for a graduation gift. Option 1: If they choose to pursue a graduate degree, their parents will give each of them a gift of$35,000. However, they must pay for their tuition and living expenses out of the gift. Option 2: If they choose to go directly into the workforce, their parents will give each of them a gift of $5000. Maurice decides to go to graduate school for 2 years. He locks in a tuition rate by paying$11,500 for the 2 years in advance, and he figures that his monthly expenses will be $1000. Lester decides to go straight into the workforce. Lester finds that after paying his rent, utilities, and other living expenses, he will be able to save$200 per month. Their parents deposit the appropriate amount of money in a money market account for each twin. The money market accounts are currently paying a nominal interest rate of 3 percent, compounded monthly. After Maurice withdraws $11,500 for tuition, how much money is left in his money market account?

When leukocytes are examined in a blood count, is it possible to tell B lymphocytes from T lymphocytes? Explain your answer.

For the following exercise, use the compound interest formula, $A(t)=P\left(1+\frac{r}{n}\right)^{n t}$.
Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded semi-annually, had an initial deposit of $\$ 9,000$ and was worth $\$ 13,373.53$ after 10 years.

New techniques have changed the cost function. For the new function

$$g ( p ) = \frac { 3.2 p + 1 } { 100 - p }$$

what percent of the pollutant can be removed for $50 million?