How did Christianity spread throughout the Roman Empire, and what were the consequences?

What factors enabled Christianity to spread throughout the Roman empire?

Find the minimum of $f(x, y, z)=4 x-2 y+3 z$ subject to the constraint $2 x^2+y^2-3 z=0$.

Express the equation of the given line in the form $A x+B y+C=0$. Then find the distance from the given point $P\left(x_1, y_1\right)$ to that line. Round answers to the nearest hundredth.

$$y=3 x+2 ; P(3,4)$$

Why did Christianity spread throughout the roman empire?

Selected September T-accounts for Kalgan Company follow.

$$\begin{array} {c} \textbf{Supplies}\\ \end{array}$$

$$\begin{array} {lr|lr} \hline \text{9/1 Bal.} & 1,720 & \text{9/30 Adj.} & \text{2,560}\\ \text{Sept. purchases} & \text{1,880}\\ \hline \textbf{Bal.} & \textbf{1,040}\\ \end{array}$$

$$\begin{array} {c} \textbf{Supplies Expense}\\ \end{array}$$

$$\begin{array} {lr|lr} \hline \text{9/30 Adj.} & 2,560 & \text{9/30 Closing} & \text{2,560}\\ \hline \textbf{Bal.} & \textbf{-}\\ \end{array}$$

$$\begin{array} {c} \textbf{Wages Payable}\\ \end{array}$$

$$\begin{array} {llr|lr} \hline && & \text{9/30 Adj.} & \text{1,280}\\ \hline &&& \textbf{Bal.} & \textbf{1,280}\\ \end{array}$$

$$\begin{array} {c} \textbf{Wages Expense}\\ \end{array}$$

$$\begin{array} {lr|lr} \hline \text{Sept. wages} & 7,880 & \text{9/30 Closing} & \text{9,160}\\ \text{9/30 Adj.} & \text{1,280}\\ \hline \textbf{Bal.} & \textbf{-}\\ \end{array}$$

1. In which of the accounts would a reversing entry be helpful? Why?

2. Prepare the appropriate reversing entry.

3. Prepare the journal entry to record a payment on October 25 for wages totaling $6,280. How much of this amount represents wages expense for October?

Find the total cost of each stock purchase.

Find the total cost of each stock purchase.

$$\begin{array}{|r|c|l|c|c|l|} \hline & \begin{array}{c} \text { Number of } \\ \text { Shares } \end{array} & {\begin{array}{c} \text { Name of } \\ \text { Stock } \end{array}} & \begin{array}{c} \text { Market } \\ \text { Price } \end{array} & \text { Commission } & \text { Total Cost } \\ \hline \mathbf{} & 35 & \text { Tolker } & 44.26 & 40.80 & \\ \hline \end{array}$$

Solve.

$$\log x+\log (2 x-1)=1$$

Acetylene $\left(\mathrm{C}_2 \mathrm{H}_2\right)$ can be made by reacting calcium carbide $\left(\mathrm{CaC}_2\right)$ with water. (This reaction was once employed in lamps used in cave exploration.)
What is the maximum amount of heat (in joules) that can be obtained from the combustion of acetylene, starting with $74.6 \mathrm{~g}$ of $\mathrm{CaC}_2$ ?

Graph $g(x)=x^2-9$. Give the minimum or maximum value and the axis of symmetry.

Show that the radius of curvature of the osculating circle of the parabola $y=a x^{2}+b x+c$ is a minimum at its vertex.

(Calculator required) Two dogs infected with a virus were admitted to a veterinary clinic, which holds a maximum of fifty dogs. The virus spread among the animals, and two days later ten dogs were infected.

(a) Assuming the logistic growth model for the spread of the virus dy/dt = ky(M-y), find the values of M and k, and find y as a function of t.

(b) If spread of the virus is not halted, after how many days will 25 dogs be infected?

Solve (log(7x)) log x = 5

Find the minimum or maximum value of the quadratic function.

$$f(x)=2 x^2+3 x-8$$