FUNDAMENTALS OF MATERIALS SCIENCE AND E
5th Edition
ISBN: 9781119571803
Author: Callister
Publisher: WILEY
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Question
Chapter 10.21, Problem 4QP
To determine
The
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The input reactance of an infinitesimal linear dipole of length A/60 and radius a=A/200
is given by
Xin = – 120
[In(€/a) — 1]
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Assuming the wire of the dipole is copper with a conductivity of 5.7 x 10' S/m,
determine at f = 1 GHz the
(a) loss resistance
(b) radiation resistance
(c) radiation efficiency
(d) VSWR when the antenna is connected to a 50-ohm line
Example
Solve the octic polynomial
2x⁸-9x⁷+20x⁶-33x⁵+46x⁴-66x³+80x²-72x+32=0
Solution
Divide by x⁴
2x⁴-9x³+20x²-33x+46-66/x + 80/x² - 72/x³ + 32/x⁴=0
Combine and bring terms
2(x⁴+16/x⁴) - 9(x³+8/x³) +20(x²+4/x²)-33(x+2/x) + 46= 0
Let use substitution
Let x+2/x =u
(x+2/x)²= u²
x²+2x*2/x + 4/x² = u²
x²+4/x²= u²-4
(x+2/x)³= x³+8/x³+3x*2/x(x+2/x)
u³= x³+8/x²+6u
x³+8/x³= u³-6u
(x²+4/x²)²= x⁴+2x²*4/x² + 16/x⁴
(u²-4)²= x⁴+16/x⁴ + 8
x⁴+16/x⁴ = (u²-4)²-8
x⁴+16/x⁴ = u⁴-8u²+8
2(u⁴-8u²+8)-9(u³-6u)+20(u²-4)-33u+46=0
Expand and simplify
2u⁴-9u³+4u²+21u-18=0
After checking
(u-1)(u-2) Are factors
Then
2u²-3u-9=0
u=3, u=-3/2
Assignment question
Solve the octic polynomial
2s⁸+s⁷+2s⁶-31s⁴-16s³-32s²-160=0 using the above example question, please explain in detail
please explain each method used, thank you
Chapter 10 Solutions
FUNDAMENTALS OF MATERIALS SCIENCE AND E
Ch. 10.21 - Prob. 1QPCh. 10.21 - Prob. 2QPCh. 10.21 - Prob. 3QPCh. 10.21 - Prob. 4QPCh. 10.21 - Prob. 5QPCh. 10.21 - Prob. 6QPCh. 10.21 - Prob. 7QPCh. 10.21 - Prob. 8QPCh. 10.21 - Prob. 9QPCh. 10.21 - Prob. 10QP
Ch. 10.21 - Prob. 11QPCh. 10.21 - Prob. 12QPCh. 10.21 - Prob. 13QPCh. 10.21 - Prob. 14QPCh. 10.21 - Prob. 15QPCh. 10.21 - Prob. 16QPCh. 10.21 - Prob. 17QPCh. 10.21 - Prob. 18QPCh. 10.21 - Prob. 19QPCh. 10.21 - Prob. 20QPCh. 10.21 - Prob. 21QPCh. 10.21 - Prob. 22QPCh. 10.21 - Prob. 23QPCh. 10.21 - Prob. 24QPCh. 10.21 - Prob. 25QPCh. 10.21 - Prob. 26QPCh. 10.21 - Prob. 27QPCh. 10.21 - Prob. 28QPCh. 10.21 - Prob. 29QPCh. 10.21 - Prob. 30QPCh. 10.21 - Prob. 31QPCh. 10.21 - Prob. 32QPCh. 10.21 - Prob. 33QPCh. 10.21 - Prob. 34QPCh. 10.21 - Prob. 35QPCh. 10.21 - Prob. 36QPCh. 10.21 - Prob. 37QPCh. 10.21 - Prob. 38QPCh. 10.21 - Prob. 39QPCh. 10.21 - Prob. 40QPCh. 10.21 - Prob. 41QPCh. 10.21 - Prob. 42QPCh. 10.21 - Prob. 43QPCh. 10.21 - Prob. 44QPCh. 10.21 - Prob. 45QPCh. 10.21 - Prob. 46QPCh. 10.21 - Prob. 47QPCh. 10.21 - Prob. 48QPCh. 10.21 - Prob. 49QPCh. 10.21 - Prob. 50QPCh. 10.21 - Prob. 51QPCh. 10.21 - Prob. 52QPCh. 10.21 - Prob. 53QPCh. 10.21 - Prob. 54QPCh. 10.21 - Prob. 55QPCh. 10.21 - Prob. 56QPCh. 10.21 - Prob. 57QPCh. 10.21 - Prob. 58QPCh. 10.21 - Prob. 59QPCh. 10.21 - Prob. 60QPCh. 10.21 - Prob. 61QPCh. 10.21 - Prob. 62QPCh. 10.21 - Prob. 63QPCh. 10.21 - Prob. 64QPCh. 10.21 - Prob. 65QPCh. 10.21 - Prob. 66QPCh. 10.21 - Prob. 67QPCh. 10.21 - Prob. 68QPCh. 10.21 - Prob. 69QPCh. 10.21 - Prob. 70QPCh. 10.21 - Prob. 71QPCh. 10.21 - Prob. 72QPCh. 10.21 - Prob. 73QPCh. 10.21 - Prob. 74QPCh. 10.21 - Prob. 75QPCh. 10.21 - Prob. 76QPCh. 10.21 - Prob. 77QPCh. 10.21 - Prob. 78QPCh. 10.21 - Prob. 79QPCh. 10.21 - Prob. 80QPCh. 10.21 - Prob. 81QPCh. 10.21 - Prob. 82QPCh. 10.21 - Prob. 83QPCh. 10.21 - Prob. 84QPCh. 10.21 - Prob. 1FEQPCh. 10.21 - Prob. 2FEQPCh. 10.21 - Prob. 3FEQPCh. 10.21 - Prob. 4FEQP
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