Describe the error in solving the equation. $\frac{1}{x+y}+\frac{1}{x-1}=\frac{2}{(x+1)(x-1)},$ $(x − 1) + (x + 1) = 2,$ $2x = 2,$ $x = 1$ The solution is x = 1.

Find $R_{\mathrm{IN}}$ in the given figure.

Find a solution of the given boundary-value problem. $y^{\prime \prime}+y=1, y(0)=0, y(1)=0$

Use a Karnaugh map to find the minimal sum-of-products form for the truth functions shown.

$$\begin{array}{|c|c|c|c|c|} \hline x_{1} & x_{2} & x_{3} & x_{4} & f\left(x_{1}, x_{2}, x_{3}, x_{4} )\right. \\ \hline 1 & 1 & 1 & 1 & 1 \\ \hline 1 & 1 & 1 & 0 & 1 \\ \hline 1 & 1 & 0 & 1 & 1 \\ \hline 1 & 1 & 0 & 0 & 1 \\ \hline 1 & 0 & 1 & 1 & 0 \\ \hline 1 & 0 & 1 & 0 & 1 \\ \hline 1 & 0 & 0 & 1 & 0 \\ \hline 1 & 0 & 0 & 0 & 1 \\ \hline 0 & 1 & 1 & 1 & 1 \\ \hline 0 & 1 & 1 & 0 & 1 \\ \hline 0 & 1 & 0 & 1 & 1 \\ \hline 0 & 1 & 0 & 0 & 1 \\ \hline 0 & 0 & 1 & 1 & 0 \\ \hline 0 & 0 & 1 & 0 & 0 \\ \hline 0 & 0 & 0 & 1 & 0 \\ \hline 0 & 0 & 0 & 0 & 0 \\ \hline \end{array}$$

Look at the following polynomial factorizations.

$$x^2-1=(x-1)(x+1)$$

,

$$x^3-1=(x-1)(x^2+x+1)$$

,

$$x^4-1=(x-1)(x^3+x^2+x+1)$$

. Factor

$$x^5-1$$

and

$$x^6-1$$

into the product of x-1 and another polynomial. Check your answers by multiplying.

What is the monthly payment for a 10-year, $20,000 loan at 4.625% APR? What is the total interest paid on this loan?

Ciana wants to take out a $7,500 loan with a 5.3% APR. She can afford to pay$128 per month for loan payments. What should be the length of her loan? Round to the nearest tenth of a year.

Identify each underlined verb by writing above it AV for action verb or LV for linking verb.

Example 1. I $\overset{\textit{\color{#c34632}{LV}}}{{\underline{\text{feel}}}\text{}}$ sleepy.

In Madrid, Jody $\underline{\text{stayed}}$ in a youth hostel.

Calculate the value of x in the figure shown.

Using trapezoids instead of rectangles. That is, on the subinterval $(1 /(n+1), 1 / n)$, let $a_n$ denote the area of the trapezoid having heights $y=1 /(n+1)$ at $x=1 /(n+1)$ and $y=1 / n$ at $x=1 / n$.

How do you decide to shade above or below a boundary line? What does this shading represent?

Find the truth value to be assigned to each conditional statement. If 1 x 1 = 1, then 1 x 1 x 1 = 1.

In exercise given below, determine the check matrix associated with the given generator matrix.

$$\left[\begin{array}{llllllll}1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 \\ 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1\end{array}\right]$$

Determine the water of hydration for the following hydrates and write the chemical formula.

Ni(NO$_{3}$)$_{2}$ $\sdot$ XH$_{2}$O is found to contain $37.2$% water.