Artificial Stupidity

### Questions (51)

 37 Is it possible to have 2 different but equal size real number sets that have the same mean and standard deviation? 5 Distance from one vertex of a rectangular prism to the plane determined by three other vertices, without using vectors or calculus 5 Is there a simple pattern to memorize the sine of $0^\circ$, $15^\circ$, $30^\circ$, $45^\circ$, $60^\circ$, $75^\circ$, $90^\circ$? 4 How many $ax^2+bx+c=0$ with distinct pairs of rational roots can be made from integers $N=|ac|=|\alpha\beta|$ and $b=\alpha+\beta$? 4 A simpler approach to solve “how many k-permutations of aaabbccdef are there?”

### Reputation (1,479)

 +10 What is the minimum number of packs of each ingredient needed without left over? +10 Linear arrangement of 4 eagles, 3 horses and 5 dragons in which no two dragons get placed side by side +10 What is the difference between independent and mutually exclusive events? +2 Are “mutually exclusiveness” and “independency” orthogonal?

 8 Given that $x_0$ is a real root of $x^3+px + q = 0$, how can I show that $p^2 \geq 4x_0q$? 6 A lily pad doubles in area every second. After one minute, it fills the pond. How long would it take to quarter fill the pond ? 4 Is it possible to have two triangles with equal sides but with different angles? 3 How do I solve $\int\frac{\sqrt{x}}{\sqrt{x}-3}\,dx?$ 2 Simplify, equivalent for (p âˆ¨ ¬q) âˆ§ (¬p âˆ¨ ¬q)

### Tags (62)

 10 algebra-precalculus × 4 6 recreational-mathematics 8 polynomials × 4 5 calculus × 4 8 roots 4 geometry × 8 8 cubic-equations 4 triangles × 3 8 examples-counterexamples 3 integration × 2

### Bookmarks (2)

 82 General request for a book on mathematical history, for a VERY advanced reader. 7 Modern book on differential geometry?