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Oduvanchick [21]
3 years ago
9

Find a vector a with representation given by the directed line segment AB. Draw AB and the equivlent representation starting the

origin. A(2,1), B(0,6)
Mathematics
1 answer:
chubhunter [2.5K]3 years ago
5 0

Answer:

AB = (-2, 5)

Step-by-step explanation:

The vector V is of the form, V = (B1 - A1, B2 - A2)

A = (2, 1);  B = (0, 6)

V = (0 - 2, 6 - 1)

V = (-2, 5)

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<h2>Problem 6:</h2><h2>a)</h2>

a(0) = 1  \:  \:  \:  \:  \:  \: b(0) = 2 \:  \:  \:  \:  \: c(0) = 3 \\ a(1) = b(0) + c(0) = 2 + 3 = 5 \\ b(1) = a(0) + c(0) = 1 + 3 = 4 \\ c(1) = a(0) + b(0) = 1 + 2 = 3 \\  \\ a(2) = b(1) + c(1) = 4 + 3 = 7 \\ b(2) = a(1) + c(1) = 5 + 3 = 8 \\ c(2) = a(1) + b(1) = 5 + 4 = 9

a(3) = b(2) + c(2) =  8 + 9 = 17\\ b(3) = a(2) + c(2) =7 + 9 = 16  \\ c(3) = a(2) + b(2) = 7 + 8 = 15 \\  \\ a(4) = b(3) + c(3) = 16  + 15 = 31 \\ b(4) = a(3) + c(3) = 17 + 15 = 32 \\ c(4) = a(3) + b(3) = 17 + 16 = 33

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a(7) = 128 + 129 = 257 \\ b(7) = 127 + 129 = 256 \\c (7) = 127 + 128 = 255 \\  \\ a(8) = 256 + 255 = 511 \\ b(8) = 257 + 255 = 512 \\ c(8) = 257 + 256 = 513

a(9) = 512 + 513 = 1025 \\ b(9) = 511 + 513 = 1024 \\ c(9) = 511 + 512 = 1023 \\  \\ a(10) = 1024 + 1023 = 2047 \\ b(10) = 1025  + 1023 = 2048 \\ c(10) = 1025 + 1024 = 2049

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a(n) + b(n) + c(n) =   \\  2(a(n - 1) + b(n - 1) + c(n - 1)) \\   6 \times 2 {}^{n }

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6 \times 2 {}^{n}  > 100 \: 000 \\ 2 {}^{n}  >  \frac{100 \: 000}{6}  \\ n >  log {}^{2} ( \frac{100 \: 000}{6} )  \\ n > 14.02468 \\ n = 15

<h2 />
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