Use green's theorem to evaluate c f â· dr. (check the orientation of the curve before applying the theorem.) f(x, y) = x + 10y3, 10x2 + y c consists of the arc of the curve y = sin(x) from (0, 0) to (pi, 0) and the line segment from (pi, 0) to (0, 0)

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria. the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time. create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

Acomposition of transformations maps δxyz to δx"y"z". the first transformation for this composition is , and the second transformation is a 90° rotation about point x'.

Roderick wants to draw a circle for which the numerical value of the circumference is greater than the value of the area. which lengths could he use for the radius? check all that apply