A chiral sample gives a rotation that is close to $180^{\circ}$. How can one tell whether this rotation is $+180^{\circ}$ or $-180^{\circ} ?$

Show that the set of irrational numbers is an uncountable set.

Abel and Family Perfumes wants to add one or more of four new products to its current line of colognes. Historically, Abel has used a 5-year project recovery period and a MARR of 20% per year. (a) Determine which of the four options the company should undertake on the basis of a present worth analysis, provided the total amount of investment capital available is $800,000. Use a hand solution, unless assigned otherwise. (b) What products are selected if the investment limit is increased to$900,000? Use a spreadsheet, unless assigned otherwise. (All cash flows are in $1000 units.)$ $$ \begin{matrix} \text{Product Line} & \text{R1} & \text{S2} & \text{T3} & \text{U4}\\ \hline \text{Investment, \$} & \text{$-200$} & \text{$-400$} & \text{$-500$} & \text{$-700$}\\ \text{M&O cost, \$/year} & \text{$-50$} & \text{$-200$} & \text{$-300$} & \text{$-400$}\\ \text{Revenue, \$/year} & \text{150} & \text{450} & \text{520} & \text{770}\\ \hline \end{matrix} $$ $

On a separate sheet of paper, answer the questions below. Make sure you read carefully and answer all parts of the questions. What can you deduce from the three different names for the rebellion of 1857 in India and the perspectives of the groups that use them?

Find the rotation–dilation matrix within the given matrix.

$$\left[\begin{array}{rr} 3 & 1 \\ -5 & 1 \end{array}\right]$$

Find the Errors. Locate as many as you can.

#include <iostream>
using namespace std;
struct ThreeVals
{
    int a, b, c;
};
int main()
{
    ThreeVals vals = {1, 2, 3};
    cout << vals << endl;
    return 0;
}

What are the properties that identify a rotation?

Find the time requested, to the nearest 0.1 year. The time it would take $6,000 to grow to$10,000 at 4.75% simple annual interest

Mayfield Corporation finished job no. 314 on June 1. On June 10, the company sold job no. 314 for $\$ 10,000$, cash. Total manufacturing costs allocated to this job at the time of the sale amounted to $\$ 6,500$.

a. Record the transfer of job no. 314 from Work in Process to Finished Goods on June 1.

Use a rotation matrix to rotate the vector

$$\left[\begin{array}{l} -2 \\ -3 \end{array}\right]$$

counterclockwise by the angle $\pi / 9.$

Solve the problem. Prove that $(\cosh (x)+\sinh (x))^{n}=\cosh (n x)+\sinh (n x)$.

Scientists think that the global population of tigers is falling exponentially. Estimates suggest that in 1970 there were 37 000 tigers but by 1980 the number had dropped to 22 000. (a) The number T of tigers n years after 1970 can be modelled by

$$T = k a ^ { n }$$

. (i) Write down the value of k. (ii) Show that a = 0.949 to three significant figures. (b) What does the model predict that the population will be in 2020? (c) When the population reaches 1000, the tiger population will be described as ‘near extinction’. In which year will this happen? In the year 2000 a worldwide ban on the sale of tiger products was implemented, and it is believed that by 2010 the population of tigers had recovered to 10 000. (d) If the recovery has been exponential, find a model of the form

$$T = k a ^ { m }$$

connecting the number of tigers (T) with the number of years after 2000 (m). (e) If each year since 2000 the rate of growth has been the same, find the percentage increase in the tiger population each year.

Solve each percent problem. What is 20% of 3?

Determine the appropriate rotation formulas to use so that the new equation contains no xy-term. $34 x^{2}-24 x y+41 y^{2}-25=0$