(5 pts) If one wants to calculate π to an arbitrary number of decimal places, the best way to do this is to use a power series representation. In this problem we will derive a formula for this. (a) Find a power series representation of the function f(x) = tan−1 x. You can do this by noticing that tan−1 x = Z 1 1 + x 2 dx and integrating the power series representation of the right hand side term-byterm. Be sure to find the value of C. (b) Use the previous step to derive that π = 2√ 3 X[infinity] n

27 is what percent of 108? 27 is % of 108

Table which ratio is equivalent to 3: 7? 6: 7 3: 21 24: 56 15: 30

Astudent is determining the influence of different types of food on the growth rate of spiders. she feeds one group of spiders two caterpillars twice a week. the other group received similarly-sized beetles twice a week. she records the amount of time required for individuals to reach sexual maturity. her hypothesis is that the spiders feeding on caterpillars will have a faster growth rate because caterpillars have a higher protein content compared to beetles. in this experiment, what is the dependent variable? spiders assigned to different feeding groups. time required to reach sexual maturity number of prey items fed twice a week. growth rates of each group.