The series of numbers is adding 5 and then subtracting 2
20+5=25
25-2=23
23+5=28
28-2=26
and so on. Do you understand?
If the length, breadth and height of the box is denoted by a, b and h respectively, then V=a×b×h =32, and so h=32/ab. Now we have to maximize the surface area (lateral and the bottom) A = (2ah+2bh)+ab =2h(a+b)+ab = [64(a+b)/ab]+ab =64[(1/b)+(1/a)]+ab.
We treat A as a function of the variables and b and equating its partial derivatives with respect to a and b to 0. This gives {-64/(a^2)}+b=0, which means b=64/a^2. Since A(a,b) is symmetric in a and b, partial differentiation with respect to b gives a=64/b^2, ==>a=64[(a^2)/64}^2 =(a^4)/64. From this we get a=0 or a^3=64, which has the only real solution a=4. From the above relations or by symmetry, we get b=0 or b=4. For a=0 or b=0, the value of V is 0 and so are inadmissible. For a=4=b, we get h=32/ab =32/16 = 2.
Therefore the box has length and breadth as 4 ft each and a height of 2 ft.
The symptoms of depression and suicide are very similar, because most of the people that are depressed sometimes think about doing something to harm themselves. Plus depression causes them to stop eating, starts to be non social etc. The same goes for those who are having thoughts of suicide or have already done it.
