Write the equation for the picture below x2 + (y-2)2 = 3
x² + (y+212= 6
x² + (y+212=9
x2 + (y-2)2 = 9

One side of a rectangle is 7 feet shorter than seven times the other side. find the length of the shorter side if we also know that the perimeter of the rectangle is 306 feet.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Hundred and tens tables to make 430 in five different ways