We have encoded a message by assigning the numbers 1 - 26 to the letters a - z of the alphabet, respectively, and assigning 27 to a blank space. We have further encoded it by using an encoding matrix. Decode this message by finding the inverse of the encoding matrix and multiplying it times the coded message.The encoding matrix is A = 
and the encoded message is 29, 63, 28, 72, 10, 21, 41, 96, 29, 67.
Fill in the blank(s) with the appropriate word(s).
explain it
Mathematics
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Rewrite the given integral so that it fits the form 
, and identify u, du, and n.
A. 
; u = 1 + cos x, du = sin x dx, n = 
B. -
; u = cos x, du = -sin x dx, n = 
C. -
; u = 1 + cos x, du = -sin x dx, n = 
D. 
; u = sin x, du = (1 + cos x)1/2 dx, n = 1
Mathematics
Provide an appropriate response. The length of a rectangle is 3 times the width. The difference between the length and width is 12 inches. What is the length?
A. 6 inches B. 18 inches C. 4 inches D. 9 inches
Mathematics
Graph the circle.x2 + (y - 1)2 = 4
A. 
B. 
C. 
D. 
Mathematics
Find the exact value of the logarithmic expression.log71
A. 1
B. 7
C. 
D. 0
Mathematics