Answer the s below carefully. provide any relevant sketches. a) pick three points in the first quadrant with six distinct coordinates. b) find the equation for each side of the triangle. label them f. g and h. c) use three definite integrals to find the area of the triangle. d) verify your result from part (c) using a method other than calculus. ee e) verify your result from part (c) using heron's formula. f) suppose the three points are collinear. what is the area of the triangle? what property of integrals is demonstrated by this area formula? consider the following functions. complete the following parts very carefully (r-3)3+6- h(r)= sin(2na) v1+ cos(r r(r=

(50 ) mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.