Sanja Maliyat

2022-04-08

450 cubic centimetres of wood is used to make a solid cylindrical ornament.

The radius of the base of the ornament is 5 centimetres. What is the height

of the cylindrical ornament?

1413 square metres of paint was used to paint a closed cylindrical tank of

radius 10 metres. What is the height of the cylindrical tank?

Vasquez

Expert2023-04-27Added 597 answers

**The amount of caffeine in the body after consumption follows an exponential decay model. After taking your coffee, 50% of caffeine is left in your body in about 6 hours. If you had 1 cup of coffee 9 hours ago how much caffeine is left in your system?**Show that the argument form with premises $(p\wedge t)\Rightarrow (r\vee s),\text{}q\Rightarrow (u\wedge t),\text{}u\Rightarrow p,$ and $urc{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}\ne rs$ and conclusion $q\Rightarrow r$ is valid by using rules of inferences.

$\begin{array}{|ccc|}\hline \text{Rule of Inference}& \text{Tautology (Deduction Theorem)}& \text{Name}\\ P& P\Rightarrow (P\vee Q)& \text{Addition}\\ \overline{\therefore P\vee Q}& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ P\wedge Q& (P\wedge Q)\Rightarrow P& \text{Simplification}\\ \therefore P& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ P& \left[\right(P)\wedge (Q\left)\right]\Rightarrow (P\wedge Q)& \text{Conjunction}\\ Q& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ \therefore \overline{P\wedge Q}& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ P& \left[\right(P)\wedge (P\Rightarrow Q\left)\right]\Rightarrow (P\wedge Q)& \text{Modus Ponens}\\ P\Rightarrow Q& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ \overline{\therefore Q}& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ \u231dQ& \left[\right(\u231dQ)\wedge (P\Rightarrow Q\left)\right]\Rightarrow \u231dP& \text{Modus Tollens}\\ P\Rightarrow Q& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ \overline{\therefore \u231dP}& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ P\Rightarrow Q& \left[\right(P\Rightarrow Q)\wedge (Q\Rightarrow R\left)\right]\Rightarrow (P\Rightarrow R)& \text{Hypothetical Syllogism (''chaining'')}\\ Q\Rightarrow R& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ \overline{\therefore \Rightarrow R}& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ P\vee Q& \left[\right(P\vee Q)\wedge (\u231dP\left)\right]\Rightarrow Q& \text{Disjunctive syllogism}\\ \u231dP& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ \overline{\therefore Q}& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ P\vee Q& \left[\right(P\vee Q)\wedge (\u231dP\vee R\left)\right]\Rightarrow (Q\vee R)& \text{Resolution}\\ \u231dP\vee R& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ \overline{\therefore Q\vee R}& \phantom{\rule{0ex}{0ex}}& \phantom{\rule{0ex}{0ex}}\\ \hline\end{array}$simplify (sinx/(1+sinx)) + ((1+sinx)/cosx)

*Explain the difference between a first and a second- order linear differential equation*4𝑦 ′′(𝑡) + 24𝑦 ′ (𝑡) + 37𝑦(𝑡) = 0 𝑦(𝜋) = 1, 𝑦 ′ (𝜋) = 0

How many arrangements of the letters ABCDEFGH contain BHFE?

Use Laplace transform to solve the following system of equations x' = 7x - 4y, x(0)= 1 y' = 8x - 5y, y(0)=3

Find an integer n such that Zn has the following properties:

a2 = a implies a = 0 or a = 1.

ab = 0 implies a = 0 or b = 0.

ab = ac and a 6= 0 imply b = c.

You will have to prove the properties hold in Zn for the n you choose.½+1/4