Can you massage the parameters of these curves to make them match as closely as possible?
A weekly challenge concerning prime numbers.
Can you rotate a curve to make a volume of 1?
Suppose that we are told that four numbers $a, b, c, d$ lie between $-5$ and $5$. Suppose also that the numbers are constrained so that $$5< a+b < 10 \quad\mbox{ and }\quad -10< c+d < -5$$ Given this information, what can you deduce about these inequalities? $$ ?? < a+ b- c - d < ?? $$ $$ ?? < a- c < ?? $$ $$ ?? < a - c + d - b < ?? $$ $$ ?? < abcd < ?? $$ $$ ?? < \frac{|a|+|c|}{2}-\sqrt{|ac|} < ??$$