Ok. Length = L, Base = B
P = 2L + 2B
We know that B = 3L or L = B/3
so that's P = 2/3B + 2B = 2/3B + 6/3B = 8/3B
For the first;
For every four marbles, Izuku placed 2x more in the jar.
Sin(2θ)+sin(<span>θ)=0
use double angle formula: sin(2</span>θ)=2sin(θ)cos(<span>θ).
=>
2sin(</span>θ)cos(θ)+sin(<span>θ)=0
factor out sin(</span><span>θ)
sin(</span>θ)(2cos(<span>θ)+1)=0
by the zero product property,
sin(</span>θ)=0 ...........(a) or
(2cos(<span>θ)+1)=0.....(b)
Solution to (a): </span>θ=k(π<span>)
solution to (b): </span>θ=(2k+1)(π)+/-(π<span>)/3
for k=integer
For [0,2</span>π<span>), this translates to:
{0, 2</span>π/3,π,4π/3}
After 4 atmospheres the diver descends -132 feet because -33*4=-132
