Y''+y'=3 hihihihihhihihihihihihih

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) = .

Graph the line with the given slope m and y-intercept b. m=-3,b=1

An unknown number x is at most 10. which graph best represents all the values of x? number line graph with closed circle on 10 and shading to the right. number line graph with open circle on 10 and shading to the right. number line graph with open circle on 10 and shading to the left. number line graph with closed circle on 10 and shading to the left.