Consider f and c below. f(x, y) = x4y5i + x5y4j, c: r(t) = t3 − 2t, t3 + 2t , 0 ≤ t ≤ 1 (a) find a function f such that f = ∇f. f(x, y) = (b) use part (a) to evaluate c f · dr along the given curve c.

If 90° < θ < 180° and cotθ = -1/3, then cscθ =

Researchers were interested in whether relaxation training decreases the number of headaches a person experiences. they randomly assigned 20 participants to a control group or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training. which statistical analysis should be performed to answer the researchers' question?

X+ y = 5 ; x - y =3 solve using linear combination