Is the elastic limit a limiting force or a limiting distance?

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 $1000 units.)$ $$ \begin{matrix} \text{Product Line} & \text{R1} & \text{S2} & \text{T3} & \text{U4}\\ \hline \text{Investment, \$} & \text{$-200$} & \text{$-400$} & \text{$-500$} & \text{$-700$}\\ \text{M&O cost, \$/year} & \text{$-50$} & \text{$-200$} & \text{$-300$} & \text{$-400$}\\ \text{Revenue, \$/year} & \text{150} & \text{450} & \text{520} & \text{770}\\ \hline \end{matrix} $$ $

Riley and Rhoda plan to buy several bags of dog food and a dog collar. Each bags of dog food costs $7, and the dog collar costs$5. a. Use the information above to write an expression for the amount of money they will spend if they buy b bags of food. b. Riley and Rhoda have $30. Use this information and the expression you wrote for Part (a) to write an inequality for finding the number of bags of food they could buy. c. Solve the inequality and graph the solutions. Check your answer in the original situation.

Find the distance from the

(b). origin to the plane $2=z-x$.

Find the complement of the following set.

The set {x|x is an integer strictly between 0 and 8} if U is the set of all integers.

In previous question, let the height h equal $6.00$ m and the speed v$_{boy}$ equal $2.00$ m/s. Assume that the food pack starts from rest.

(a) Tabulate and graph the speed–time graph.

(b) Tabulate and graph the acceleration–time graph. Let the range of time be from $0$ s to $5.00$ s and the time intervals be $0.500$ s.

Find the distance between the points. $(5,2),(-1,4)$

Find the number of positive outcomes in the sample space. Then list the possible outcomes. You flip a coin and draw a marble at random from a bag containing two purple marbles and one white marble.

Determine whether the statement is true or false. Use the following sets of numbers.

$N=$ set of natural numbers.

$Z=$ set of integers

$I=$ set of irrational numbers

$Q=$ set of rational numbers

$\mathbb{R}=$ set of real number

$$-1 \in Z$$

Find the distance between the points.

$$(6.2,5.4),(-3.7,1.8)$$

The Tethered Satellite discussed in this module is producing 5.00 kV, and a current of 10.0 A flows. (a) What magnetic drag force does this produce if the system is moving at 7.80 km/s? (b) How much kinetic energy is removed from the system in 1.00 h, neglecting any change in altitude or velocity during that time? (c) What is the change in velocity if the mass of the system is 100,000 kg? (d) Discuss the long term consequences (say, a week-long mission) on the space shuttle's orbit, noting what effect a decrease in velocity has and assessing the magnitude of the effect.

Let X={a, b, c}. Define a function S from $\mathcal{P}$(X) to the set of bit strings of length 3 as follows. Let Y$\subseteq$X. If a$\in$Y, set $s_1=0$; If a$\notin$Y, set $s_1=1$; If b$\in$Y, set $s_2=0$; If b$\notin$Y, set $s_2=1$; If c$\in$Y, set $s_3=0$; If c$\in$Y, set $s_3=1$. Define S(Y)=$s_1s_2s_3$.

Prove that S is onto.

Write each set in roster form and in set-builder notation. P is the set of natural numbers that are factors of 25.

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.