If

$$\overrightarrow{\mathrm{AB}}=\left( \begin{array}{c}{-1} \\ {3} \\ {2}\end{array}\right), \overrightarrow{\mathrm{AC}}=\left( \begin{array}{c}{2} \\ {-1} \\ {4}\end{array}\right)$$

, and

$$\overrightarrow{\mathrm{BD}}=\left( \begin{array}{c}{0} \\ {2} \\ {-3}\end{array}\right)$$

, find: $\overrightarrow{\mathrm{CD}}$

Find the sum or difference. Write answers in standard form.

$$(-2+4 i)-(-4+4 i)$$

Why does Juliet ask Romeo not to swear by the moon?

Solve the equation of quadratic form.

$$t^{4}-13 t^{2}+36=0$$

$x=0$ is a regular singular point of the given differential equation. Show that the indicial roots of the singularity do not differ by an integer. Use the method of Frobenius to obtain two linearly independent series solutions about $x=0$. Form the general solution on the interval $(0, \infty)$. $2 x^{2} y^{\prime \prime}+3 x y^{\prime}+(2 x-1) y=0$

Explain why your weight would be less on the moon than on Earth even though your mass would not change.

Find cos A and cos B. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary.

There is a right triangle where $\overline{AC}=12$, $\overline{BC}=35$, $\overline{AB}=37$, and $\angle ACB = 90^\circ$.

Decompose the rectangle into two or three smaller rectangles to demonstrate the Distributive Property. Then write each in the form a(b+c)=ab+ac.

In earlier figure, ABC is a triangle in which $\angle \mathrm{ABC}<90^{\circ}$ and $\mathrm{AD} \perp \mathrm{BC}$. Prove that $\mathrm{AC}^2=\mathrm{AB}^2+\mathrm{BC}^2-2 \mathrm{BC} . \mathrm{BD}$.

True or false?

e. $\{1,2\} \subseteq\{2\}$

Calculate the escape velocity of the Moon from its mass and diameter.

Given that

$$\lim _{x \rightarrow c} f(x)=3, \quad \lim _{x \rightarrow c} g(x)=0, \quad \lim _{x \rightarrow c} h(x)=-2,$$

evaluate the limits that exist. If the limit does not exist, state how you know that.
(a ) $\lim\limits_{x \rightarrow c}[3 f(x)-2 h(x)]$.
(b ) $\lim\limits_{x \rightarrow c}[h(x)]^3$.
(c ) $\lim\limits_{x \rightarrow c} \frac{h(x)}{x-c}$.
(d ) $\lim\limits_{x \rightarrow c} \frac{g(x)}{h(x)}$.
(e ) $\lim\limits_{x \rightarrow c} \frac{4}{f(x)-h(x)}$.
(f ) $\lim\limits_{x \rightarrow c}[3+g(x)]^2$.

Write each expression as a complex number in standard form.

$$\frac{4+i}{3+5 i}$$

True or false?

a. $\{(3,4),(5,6)\}=\{(3,4),(6,5)\}$