write the above equation like (a-1)(b-1) + (c-1)(d-1) = 5... also, because of the first condition the second term is greater than or equal to the first term...and since they are all positive integers.....
can you work out the rest...?
there is a way of calculating the square root of any number (without using a calculator of course).
is there a similar way, or any way, in fact to calculate cube roots, fourth roots, etc. again without using a calculator??
there is something wrong in what u have written... first of all
log(a*b) = log(a) + log(b)...what u have used is log(a+b) = log(a) * log(b)..even after that u have written something wrong...check it once more...
anyway u don't need to use that...use the basic definition of logs...
if ln(a)...
conditions like:
x,y,z should be integers...or atleast x and y should be integers(if u want to accept decimal seconds). further 0<= x <12... 0<= y <60 and 0 <= z < 60...with these conditions u'll never get an appropriate answer
its not possible...one way of proving it is assume the time as xhrs, yhrs, and z secs...and put appropriate conditions on them... then find angles and solve...
the answer is 6, 1, 7, and 4
*just for knowledge, the number 6174(the answer) is called the Kaprekar Constant. If you do with this number, exactly as written above, then you always get the number back...
its not always necessary that there be a sigma bond for the formation of a pi bond. the C2 molecule(yes, such a molecule exists), consists of only two pi bonds, making a double bond. however, in most cases a double bond is made up of one sigma and one pi bond, but not in this case.
the centroid of a triangle has many 2:1 properties.
consider triangle ABC, with medians AD, BE, and CF.
1. Centroid G divides medians in the ratio 2:1, so that \frac{AG}{GD} = \frac{BG}{GE} = \frac{CG}{GF} = \frac {2}{1}
2. the centroid G divides the line joining the circumcentre O...
I don't know if there is a special place for fluids. so i'll post it here...
When a tube of small radius is placed in a liquid, the liquid rises or falls in the tube, due to adhesive and cohesive forces. also the height of the liquid in the tube is given by
h = \frac { 2 T...
well, there is a quick solution to your question hypermonkey2, though i do not know the proof...
the number of solutions to a_1x_1 + a_2x_2 + \dots + a_nx_n = p \ where \ b_i \leq x_i \leq c_i \mbox{for}\ 1 \leq i \leq n is given by the coefficient of t^n in the expression
\prod (...
Clearly, each term in the expansion of (a_{1} + a_{2} + \dots + a_{n})^y will have degree y.
Let an arbitary term be a_{1}^{p}a_{2}^{q}a_{3}^r\dots then according to the condition p+q+r...=y.
Thus, find the number of integer solutions of the above equation. that's your required number of...
the cable will be hanging down in the shape of a parabola...right??
if yes, then you get a really bad equation in natural logs and roots and stuff. but...it can be solved to get the the distance.