Calculating x, radius of the big inscribed green circle.
Radius, r of the bigger inscribed red circle is;
2(1-r)²=(2r)²
r²+2r-1=0
r = (√(2)-1) units.
Therefore radius, x of the big i...
Fruity Numbers Adventure.
In the sunny orchard, Anna finds a talking apple tree.
The apple tree says, 'Let's count my apples together! How many can you see?'
Anna counts, 'One, two, three,' and...
Paul Erdös (1913-1996).
Erdös lived a nomadic, possession-less life, moving from university to university, from colleague's spare room to conference hotel. He rarely published alone, preferring to...
Calculating Area Green.
Let z be the width of the ascribed rectangle.
Let y be the length of the ascribed rectangle.
½(az) = 22
a = 44/z cm.
½(by) = 48
b = 96/y cm.
c = y-44/z
c =...
Sir Mike Ambrose is the author of the question.
Calculating area red/area square.
Let the single side length of the ascribed square be 2 units.
Therefore;
Area square is;
2*2 = 4 sq...
Georg Cantor (1845-1918)
Of all the great mathematicians, Cantor most perfectly fulfils the (Hollywood) stereotype that a genius for maths and mental illness are somehow inextricable. Cantor's mos...
Kindly move the question right/left one time to review the solution.
Thank you nicely.
Let Alpha be x.
Calculating tanx.
Angle ABD = Angle ACD = y.
Let AB = AC = a.
Let AD = b.
b² = a²+10²-2a*10cosy
b² = a²+100-20acosy --- (1).
b² = a²+6²-2a*6cosy
b² = a²+36-12aco...
Calculating x.
tana = 30/40
a = atan(¾)°
Let y be each of the two equal lengths.
b² = y²+x²
b = √(y²+x²) units.
It implies;
y+b = 40
y+√(y²+x²) = 40
y²+x² = (40-y)²
x² = 1600-...
Banana the Frog-Chasing Pup.
Once upon a sunny street, there lived a dog named Banana. He was no ordinary pup; his love for bananas was unmatched. Every morning, he'd eagerly await the fruit truck...
