Evaluate the line integral∫cf⋅dr, where f(x, y,z)=xi−4yj−zkf and c is given by the vector function r(t)=⟨sint, cost, t⟩, 0≤t≤3π/2.

Jessica and martha each have a bag of cookies with unequal quantities. they have 30 cookies total between the two of them. each of them ate 6 cookies from their bag. the product of the number of cookies left in each bag is not more than 80. how many more cookies will jessica have martha? if x represents the number of cookies jessica started with, complete the statements below. the inequality that describes the relationship between the number of cookies each one of them has is x^2 - x +224 > = 0.jessica has at least cookies more than martha.

Which of the following pairs of functions are inverses of each other? o a. f(x)=x72+8 and 96-9 = 7/x+2) =8 o b. f(x)= 6(x - 2)+3 and g(x) - *#2-3 o c. $4) = 5(2)-3 and 90- 4*: 73 o d. f(x) = 6)-12 and 910 – +12

The length of a field is 100 yards and its width is 75 yards. if 1 inch represents 25 yards, what would be the dimensions of the field drawn on a sheet of paper?