Consider the vector field f(x, y)=(x^2+y^2)i+4xyj. compute the line integrals ∫c1 f⋅dr and ∫c2 f⋅dr, where c1 is parameterized by r(t)=ti+t^2j and c2 is parameterized by r(t)=ti+tj for 0 ≤ t ≤ 1. can you decide from your answers whether or not f is a gradient (conservative) vector field? ∫c1f⋅dr= ∫c2f⋅dr=

Jack has a piece of red ribbon that is two times as long as his piece of blue ribbon. he says that he can use two different equation to find out how long his piece of red ribbon is compared to his piece of blue ribbon is. is he correct? explain his reasoning

Samson is going shopping for sugar and butter to make three different kinds of cookies: lemon bars, peanut butter cookies, and sugar cookies. the recipe for lemon bars calls for 2 cups of flour, 2 cups of sugar, and 1 stick of butter. the peanut butter cookie recipe calls for 2 cups of flour, 4 cup of sugar and 2 stick of butter. the sugar cookie recipe calls for 1 cup of flour, 2 cups of sugar, and 2 sticks of butter. sampson has 13 cups of flour at home, and he buys 12 cups (6 pounds) of sugar and 10 sticks of butter. how many batches of each type of cookie can he make? samson can make batches of lemon bars, batches of peanut butter cookies, and batches of 09 cookies submit reset

In a right triangle δabc, the length of leg ac = 5 ft and the hypotenuse ab = 13 ft. find: b the length of the angle bisector of angle ∠a.