Answer:
32.008
Step-by-step explanation:

(a)
![f'(x) = \frac{d}{dx}[\frac{lnx}{x}]](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Cfrac%7Blnx%7D%7Bx%7D%5D)
Using the quotient rule:


For maximum, f'(x) = 0;


(b) <em>Deduce:
</em>

<em>
Soln:</em> Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)


, since ln(e) is simply equal to 1
Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.



Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:


, as required.
Answer: The answers are in the photo. (They are color-coded.)
Step-by-step explanation:
A monarchy, democracy, and communism are different ways to run a government.
A monarchy is usually ruled by someone of royalty, like a king or queen. Typically, they inherit all the power and get to make all the decisions, whether their people like it or not.
In a democracy, the people have many liberties and rights. They get to vote for candidates that represent them that could get elected as a president, minister, mayor, etc. Those elected have to listen to what their people want.
In communism, the government gets to make all the decisions whether it benefits the people or not. This is runned by a single-party, meaning no other parties are allowed to be developed or run.
Answer:
5/6 liters.
Step-by-step explanation:
Given that:
Amount of juice in a punch bowl = 2 * 1/2 liters
= 5/2 liters.
Part of juice drank by Liam from the bowl = 1/3
Amount of juice drank by Liam =
= 5/2 * 1/3 = 5\6 liters.
Answer:
yes
Step-by-step explanation:
x increases by 2, and y increases by 3 consistently