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Chapter 11: Q. 72 (page 774)
The sum of two numbers is , and the difference of their
squares is . Find the numbers.
The required numbers are,.
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If a system of equations has no solution, it is said to be _______.
With a tail wind, a small Piper aircraft can fly 600 miles in 3 hours. Against this same wind, the Piper can fly the same distance in 4 hours. Find the average wind speed and the average airspeed of the Piper.
In Problems , solve each equation.
.
Cryptography; One method of encryption is to use a matrix to encrypt the message and then use the corresponding inverse matrix to decode the message. The encrypted matrix, , is obtained by multiplying the message matrix, , by a key matrix, . The original message can be retrieved by multiplying the encrypted matrix by the inverse of the key matrix. That is, and .
(a) Given the key matrix , find its inverse, . [Note: This key matrix is known as the Fibonacci encryption matrix.]
(b) Use your result from part (a) to decode the encrypted matrix
(c) Each entry in your result for part (b) represents the position of a letter in the English alphabet (and so on). What is the original message?
In Problems , use a graphing utility to solve each system of equations. Express the solution(s) rounded to two decimal places.
role="math" localid="1646895844686"
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