If a 35 rope is cut into two sections with one section 6 times as long as the other section, how long is the shorther piece

Evaluate the expression for the given value of the variable 7a - 4a for a =8

Lucy is a dress maker. she sews \dfrac47 7 4 of a dress in \dfrac34 4 3 hour. lucy sews at a constant rate. at this rate, how many dresses does lucy sew in one hour? include fractions of dresses if applicable

Can someone me with #s 8, 9, and 11. with just one of the three also works. prove using only trig identities.