Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs
(0, 1),(1, 1),(1, 2),(2, 0),(2, 2),(3, 0). Find reflexive, symmetric and transitive closure of R.

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution.

$$\begin{equation*}\begin{bmatrix}1&&-2&&0&&-4\\0&&0&&1&&3\\0&&0&&0&&0\end{bmatrix}\end{equation*}$$

Fill in the blanks with correct vocabulary or words. Adding a seed crystal may cause solute to crystallize from a(n) __________

Find the equation of the tangent to $y=\ln \left(x^{2}+3\right)$ at the point where x = 0.

For the problem. Draw a motion diagram, a force identification diagram, and a free body diagram. A person on a bridge throws a rock straight down toward the water. The rock has just been released.

Express f(f(x) as a single simplified fraction.

$$f ( x ) = ( 1 - x ) ^ { - 1 }$$

Write two numbers that, when multiplied, result in each product. 63

Multiply: 512 * 632

The table below lists motor vehicle fatalities by day of the week for a recent year (based on data from the Insurance Institute for Highway Safety). Use a 0.01 significance level to test the claim that auto fatalities occur on the different days of the week with the same frequency. Provide an explanation for the results.

$$\begin{matrix} \text{Day} & \text{Sun.} & \text{Mon.} & \text{Tues.} & \text{Wed.} & \text{Thurs.} & \text{Fri.} & \text{Sat.}\\ \text{Frequency} & \text{5304} & \text{4002} & \text{4082} & \text{4010} & \text{4268} & \text{5068} & \text{5985}\\ \end{matrix}$$

Suppose that

$$\mathbf { A } = \left[ \begin{array} { l l } { 0 } & { 1 } \\ { 1 } & { 0 } \end{array} \right].$$

Show that $\mathbf { A } ^ { 2 n } = \mathbf { I }$ and that $\mathbf { A } ^ { 2 n + 1 } = \mathbf { A }$ if $n$ is a positive integer. Conclude that

$$e ^ { \mathbf { A } t } = \mathbf { I } \cosh t + \mathbf { A } \sinh t$$

and apply this fact to find a general solution of $\mathbf { x } ^ { \prime } = \mathbf { A } \mathbf { x }$. Verify that it is equivalent to the general solution found by the eigenvalue method.

Of what colors does white light consist?

The table shows the specific heat of four metals. If 1,540 J of heat is transferred to 4 kg of each metal, which metal will increase in temperature by 1 K? "

$$\begin{matrix}\text{Specific Heat of Metals}\\\end{matrix}$$

" "

$$\begin{matrix}\text{Metal} & \mathrm{Specific Heat (J/(kg \cdot K))}\\\text{Silver} & \text{235}\\\text{Iron} & \text{450}\\\text{Copper} & \text{385}\\\text{Aluminum} & \text{903}\\\end{matrix}$$

" F. Silver G. Copper H. Iron J. Aluminum

Find the unit vector that has the same direction as the vector v.

$$\mathbf { v } = - 5 \mathbf { j }$$

Researchers found the demand for cheese in Mexico for a particular year can be estimated by the implicit equation

$$\ln q = D - 0.44 \ln p,$$

where $p$ represents the price of a unit of cheese and $D$ represents a constant that can be calculated uniquely for a particular year. Here $q$ represents the annual per capita cheese demand. (a) Use implicit differentiation to calculate and interpret the elasticity of demand. (Recall that elasticity of demand is $E = -(p/q) \cdot dq/dp.$) (b) Solve the equation for $q$, then calculate the elasticity of demand.