ab4=384a2b5=4608
Considering the second equation:
ab4⋅ab=4608ab=4608384=12
Considering the first equation:
ab4=384ab⋅b3=384b=3√38412=23√4
Substituting directly gives a=33√2
√8=√22⋅2=2√2√32=√42⋅2=4√2
So
√8+3√2+√32=2√2+3√2+4√2=9√2
By considering power of points at X,
2(2+7)=3(3+ED)ED=3
(√3x+√5)(√15x+2√30)=√45x2+√75x+2√90x+2√150=3x√5+5√3x+6√10x+10√6
f(f−1(x))=f(4)x=3⋅43+2=194
15÷4=15÷41=15×14=1×15×4=120
Everything outside on the surface of the cube is visible.
That means the taking away the outside layer, the inner 8 x 8 x 8 cube would not be visible.
Total number of visible 1 x 1 x 1 cubes = 10×10×10−8×8×8=488
First, we find f−1(x) in terms of a and b.
f(x)=ax+bx=af−1(x)+bf−1(x)=x−ba
Now,
g(x)=f−1(x)−35x−4=xa−(ba+3)
Comparing coefficients:
1a=5a=15
5b+3=4b=15
Therefore
5a+5b=5⋅15+5⋅15=2
Adding the 5 equations:
4(a + b + c + d + e) = 84
a + b + c + d + e = 21 --- (*)
Subtracting each equation from (*),
e = 21 - 14 = 7
d = 21 - 15 = 6
c = 21 - 17 = 4
b = 21 - 18 = 3
a = 21 - 20 = 1
abcde = 1(3)(4)(6)(7) = 504.
Using the definition:
cosB=610=ABBC
From this, we can conclude AB = 6.
By Pythagorean theorem, AC = 8.
tanC=ABAC=68=34