Find the area under one arch of a cycloid described by the parametric equations x = 3(20 - sin 20) and y = 3( i - cos 20). use 0 and π for the limiting values of θ . a. 27 π b. 36 π c. 18 π d. 9 π

Complete the table for different values of x in the polynomial expression -7x2 + 32x + 240. then, determine the optimal price that the taco truck should sell its tacos for. assume whole dollar amounts for the tacos.

What is the sum of the geometric series in which a1 = 7, r = 3, and an = 1,701? hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio

‼️‼️‼️‼️‼️the pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to the temperature of the gas. if the pressure is 6 pounds per square inch when the temperature is 440 f, find the pressure exerted when the temperature of the gas is 380°f. (show work)