The surface area S of a metal cylinder is given by S = 2r² + 2«rh where r is the radius and h is the height. The height can be cut to a relative accuracy of 3% but the radius can only be cut to a relative accuracy of 5%. Iif the cylinder is supposed to have a radius of 6 cm and a height of 10 cm, use differentials to estimate how bad the relative accuracy of the surface area can be. Don'tround anwe unie he inatructiona equest approimationa, or a part of checking your Ow work

Please circle the answer so that I can understand and separate the answer. Please, if you write by hand, write clearly so that I can understand, I appreciate you.

Elena was pouring coffee at a constant rate into a mug similar to the one shown in the figure. Counting the seconds to fill the mug with coffee, Elena calculated that she is pouring coffee at 25ml/sec. The mug has a height of 10 cm and it took Elena about 5 seconds to fill the mug to the brim. Sketch a graph of the depth of the coffee in the mug as a function of time. Account for the shape of the graph in terms of concavity. By looking at your graph, describe how the depth of the coffee in the mug is changing and answer the following: a) At first, the depth of the coffee in the mug is changing at a (Key words for your description: rate, faster, slower). I know that, because Then, the depth of the coffee is increasing at a b) Around second the mug is filling at the fastest rate. I estimate that, at that time, the depth of the coffee would be about cm. C) The inflection point of the function would be The inflection point is the point where d) The average rate of change of the depth of…

Differentiate the function P = 10e-0.8t %3D P'