X=time of the third person it would take to fill the pool
We can suggest this equation:
6[(1/20) + (1/15) +(1/x)]=1
6[(3x+4x+60)/60x]=1
(7x+60)/10x=1
7x+60=10x
7x-10x=-60
-3x=-60
x=-60/-3
x=20
Answer: the third person alone would fill the pool in 20 hours .
(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.
There is no upper limit so, so x is greater than or equal to 24 (x ≥ 24)
Vertical angles ate those that ate directly across from each other and share the same vertex. An example of this would be angles 5 and 7. These types of angles are also congruent, so angles 5 and 7 could be your congruent pair or another set of vertical angles like 1 and 3. A linear pair is two angles that together are a line. Basically, they are next ro each other (divided only by another vector) and are supplementary, adding up to 180 degrees. An example of this in the image is angles 1 and 2.
