Common Sense and Science Rage!!!!!!!!!!!!!!!!!

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You should be good with this problem if you have solved some of my previous problems. ${S_n}$ is the space diagonal of a n dimensional cube with side length one. The extra number of minutes my group left the beaker on the burner today is the same as the the quantity z(will be defined later).x is the cosine of the angle between 2 3D vectors vector a and vector b.Vector a is defined as the following.Entry 1: $S_2$ .Entry 2 : $S_3$ .Entry 3 : $S_4$ .Vector b.Entry 1: $S_8$ .Entry 2: $S_{16}$ .Entry 3: $S_{32}$ . x in simplified form can be represented as $({\sqrt({n})*({\sqrt({m})}+{\sqrt({l})}+{o}))/{p}}$ , find $({n}+{m}+{l}+{o}+{p})/20=z$

The answer is 2.

1 solution

Aaryan Vaishya
Sep 25, 2019

X is the dot product of a and b divided by their magnitude. $S_n$ is $\\sqrt(n)$ (note that $S_{n}*S_{m}=S_{nm}$ ) shown in DEFINITELY NOT A COMMON SENSE PROBLEM .So the numerator of x is $S_16$ + $S_48$ + $S_128$ = 4(1+ ${\sqrt(3)}$ + ${2}{\sqrt(2)}$ ).The denominator is the magnitude of both vectors multiplied which is 3 *2sqrt(14)=6sqrt14.Just simplify and you will get n=7,m=2,l=6,o=4,p=21.The sum is 40 and the z,the extra number of minutes our group accidentally left the beaker on the burner is 2.

Common Sense and Science Rage!!!!!!!!!!!!!!!!!

The answer is 2.

1 solution

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