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Consider the two functions yl : $2 7 3 and y2 : b on the interval [-a, a], if a = 9.1. What value does b have to be in order for the area between yl and y2 and [a, a], to equal 41.7? Round your answer to five decimal places. Consider the two functions $1 : y2 and 2:2 : b on the yinterval [a, a], if a = 11.6. What value does b have to be in order for the area between 331 and $2 and [a, a], to equal 81? Round your answer to five decimal places. Consider two functions y1 = f(x) and y2 = g(x), and that y1 / y2 except where they intersect. If these two functions intersect at 214 places, how many different integrals do you need to find the total area enclosed by the two curves?A DNA sequence consists of a string of elements called nucleotides, in a defined order. Suppose the DNA sequence of a virus is 17 nucleotides long. If each nucleotide can be either a G, T, C, or A, how many different sequences are possible?A palindrome is a word, such as "radar" reads the same forward and backward. How many different 11-letter palindromes are possible if they do not need to be real words and there are only 6 letters in the alphabet? Ajar contains 12 differently coloured balls. If you remove all the balls, one at a time, how many colour sequences are possible? a. 12! b. 12 c.(12-1)! d. 12"12 e.1 Ajar contains 29 differently coloured balls. If you remove two balls, one at a time, how many different colour sequences are possible? a. 29!/2! b. 29! c. 29!/(29 - 2)! d. 29 e. 291/((29 - 2)'.2!)