Problem If you lend someone a dollar and get it back $5$ years later with a total of $2.0113571875$ dollars in principal and interest, what is the annual interest rate? $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$…

Problem Find the length of one side of a cube that is $1881676371789154860897069 \ cubic \ inches$. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution When $1881676371789154860897069$ is decomposed into prime factors, $$3^6×3607^3×3803^3=(3^2×3607×3803)^3.…

Problem What is the length of one side of a square inscribed in a triangle, of which the longest side is $21 \ inches$ and the perpendicular line from the vertex to the longest side is $8 \ inches$? $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$…

Problem Find the diameter of a circle inscribed in a triangle, of which sides have lengths of $21, \ 17$ and $10 \ inches$. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution Let…

Problem What is the side length of a square with an area of ​​$85000 ft^2$ ? $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution The prime factorization of $85000$ is:$$85000=2^3×5^4×17=2^2×5^4×(2×17),$$$$∴ \ \sqrt{85000}=2×5^2×\sqrt{2×17}≒291.547594742265.$$  …