Math Is Fun Forum

length, width
l=1.5w
then how about the hight? Okay, set it as h.

then we know that 4(l+w+h)=6

so 2.5w+h=1.5

Now we wanna maximize V=1.5w w h    just under the condition of 2.5w+h=1.5.

The simplist way to do this is to gimmikly apply an inequality

We know that for a, b and c

and that

and that

the equality stands in previous two when a=b=c.

"abc" in the the second clause is more or like volume formula.

let's see 1.5w w h ....... a=1.5w, b=w, c=h--------wait! a and b can never be equal in this way, meaning we cannot find the very maximum point in this way.

However, there is another way, the smart way. Watch this:

a= b=1.25w and c=h.

Then
V= (1.5/1.25²) 1.25²w²h≤  (1.5/1.25²) ((2.5w+h)/3)^3

the equality stands when 1.25w=1.25w ( definately) =h

The maximum volume is then 1.5/12.5=0.12 when w=0.4 and h=0.5, and of cause, l=0.6:D

"mikau, your book should give you steps to produce such results"

I want to say the same words. The procedure you want is only routine, and your book should just contain it.

For sore throats......

It reminds me of a glass of hot brandy to cure cold in Sherlock Holmes.

Here are some basics in my replies

Ricky, you should distinguish between something intuitive and something logical.

You may not accept an intuitive perception, but you have to accept a logic one.

The 0 probability here either means possible or impossible, some chance or no chance at all. Not a third choice, only yes or no. That's how logic works.

If you just vaguously avoid talking about either case and try to ban the discussion, you are not reasoning but trying to make arbitary rules.

It will be a great pity for maths to be arbitary and illogical.

BTW:
1)A has no B.
2)A has some B.

Logically, if one in 1) and 2) is False, the other must be True.

This applies to any A and B(universal), such as  A=" the event occuring on some moment" , B= "probability"

I rather obey the universal rule of logic.

Yes, hence the probability is 0, meaning not any probability. If any, the sum of all the probabilities would be infinite.

How do you conceive not any probability? -I interpret it as no chance at all, impossible. No matter how many trials you have, you cannot make it happen once, otherwise the probability of the event cannot be 0.

Then why again and again these "impossible" things just happen in real life? -You get up every morning, Ricky.

[img]http://.......jpg[/img]

I didn't upload it, I linked an image from somewhere else

You've been so patient Janefairfax.

tan25 =
*120=
-15=
the answer

I mean, alcohol inside a chocolate, sometimes rum, sometimes vodka...

Okay, the final part.

Finding logs, roots and using LL shift.

C        1         3
LL3+   3         27

b       c
a       d

if you follow the a-b-c-d sequence find 3 first and slide to find 1 to match 3 below, then 3 on the right, last 27 as the result of 3^3

But if you follow the sequence of a-b-d-c, you get log[sub]3[/sub]27 in the end.

And if you follow the sequence of d-c-b-a, you get 27[sup]1/3[/sup] in the end.

That's how simple logs and roots work. Just keep in mind that the D-value represents the exponent to whom e or other can be raised to generate the value on LL , and C-value-pairs represents the ratio between the two exponents on D.

Thanks, glad you are one of my first readers.:)