Name a planet on which you would weigh less than on Earth.Name a planet on which you would weigh more than on Earth. Explain how you know.

Provide a concise definition of a stimulus:

State the property of real numbers being used. 2x(3 + y) = (3 + y)2x

Evaluate $\lim _{n \rightarrow \infty} n^{-2} \sum_{i=1}^{n} \sum_{j=1}^{n^{2}} \frac{1}{\sqrt{n^{2}+n i+j}}$.

Describe and correct the error in solving the equation

$$3 x ^ { 2 } - 7 x - 6 = 0$$

using the Quadratic Formula.

$$\left. \begin{array} { l } { x = \frac { - 7 \pm \sqrt { ( - 7 ) ^ { 2 } - 4 ( 3 ) ( - 6 ) } } { 2 ( 3 ) } } \\ { = \frac { - 7 \pm \sqrt { 121 } } { 6 } } \\ { x = \frac { 2 } { 3 } \text { and } x = - 3 } \end{array} \right.$$

Find $\mathbf{a} \times \mathbf{b}$.

$$\mathbf{a}=\mathbf{i}+\mathbf{j},\hspace{6pt} \mathbf{b}=2\mathbf{j}+3\mathbf{k}$$

Determine a scalar c so that the angle between $\mathbf{a}=\mathbf{i}+c \mathbf{j}$ and $\mathbf{b}=\mathbf{i}+\mathbf{j}$ is $45^{\circ}$.

Suppose you leave the solar system and arrive at a planet that has the same mass-to-volume ratio as Earth but has 10 times Earth's radius. What would you weigh on this planet compared with what you weigh on Earth?

You have a 0.30M solution of sodium sulfate. What volume (in mL) must be measured to give 0.0020 mol of sodium sulfate?

determine whether the statement is true or false. Justify your answer.

$$^4∑j=1 2^j = ^6∑j=32^j-^2$$

State the name of the property illustrated.

$$3 ( 2 + 5 ) = 3 ( 5 + 2 )$$

Find the dot product $\mathbf{v} \cdot \mathbf{w}$ and the angle between v and w. $\mathbf{v}=\mathbf{i}-3 \mathbf{j}, \mathbf{w}=-\mathbf{i}+\mathbf{j}$

At what points are the functions continuous? $y=\frac{x+2}{\cos x}$

Convert each of the following to polar form: a. $5+j 12$ c. $-8+j 15$ b. $9-j 6$ d. $-10-j 4$