Introductory Mathematics for Engineering Applications
Introductory Mathematics for Engineering Applications
1st Edition
ISBN: 9781118141809
Author: Nathan Klingbeil
Publisher: WILEY
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Chapter 9, Problem 14P

The cross section of an airfoil is described by the shaded area that is bounded by a cubic equation y ( x ) = x 3 + 9 x , as shown in Fig. P9.14.

  1. Given the above equation for y ( x ) , determine the height h and width b of the fin.
  2. Determine the area of the cooling of the fin by integration with respect to x .
  3. Determine the x-coordinate of the centroid by integration with respect to x .
  4. Determine the y-coordinate of the centroid by integration with respect to x .

Chapter 9, Problem 14P, The cross section of an airfoil is described by the shaded area that is bounded by a cubic equation

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1. 2. Show that the following are not logically equivalent by finding a counterexample: (p^q) →r and (db) V (d←d) Show that the following is not a contradiction by finding a counterexample: (pV-q) AqA (pv¬q Vr) 3. Here is a purported proof that (pq) ^ (q → p) = F: (db) v (bd) = (db) v (bd) =(qVp) A (g→p) = (¬¬q V ¬p) ^ (q→ p) (db) V (db) = =¬(a→p)^(a→p) = (gp) ^¬(a → p) =F (a) Show that (pq) ^ (q→p) and F are not logically equivalent by finding a counterex- ample. (b) Identify the error(s) in this proof and justify why they are errors. Justify the other steps with their corresponding laws of propositional logic.
5 Show by multiplying matrices that the following equation represents an ellipse: 5 - -7 I (x)(3)()=30. y) 7 7)

Chapter 9 Solutions

Introductory Mathematics for Engineering Applications

Ch. 9 - Repeat the problem P9-10 if the shaded area of the...Ch. 9 - Repeat the problem P9-10 if the shaded area of the...Ch. 9 - Repeat the problem P9-10 if the geomectry of a...Ch. 9 - The cross section of an airfoil is described by...Ch. 9 - The geometry of a decorative heat-sink fin of...Ch. 9 - The geometry of a gear tooth is approximated by...Ch. 9 - A cantilever beam is subjected to a quadratic...Ch. 9 - A simply supported beam is subjected to a...Ch. 9 - Determine the velocity v(t) and the position y(t)...Ch. 9 - A particle starts from rest at a position x(0)=0....Ch. 9 - The acceleration of an automobile is measured as...Ch. 9 - A vehicle starting from rest at position x(0)=0 is...Ch. 9 - A vehicle starting from rest at position x(0)=0 is...Ch. 9 - A vehicle starting from rest at position x(0)=0 is...Ch. 9 - The current flowing in a resistor is given by...Ch. 9 - The RLC circuit shown in Fig,. P9.26 has R=10,...Ch. 9 - An input voltage vin=10sin(10t)V is applied to an...Ch. 9 - Repeat problem P9-27 if vin=10e10tV.Ch. 9 - Repeat problem P9-27 if vin=10(1cos(100t))V.Ch. 9 - An input voltage vin=5cos(20t)V is applied to an...Ch. 9 - A current i(t)=10e10tmA is applied to a 100F...Ch. 9 - For the circuit shown in Fig. P9.32, the voltage...Ch. 9 - The sawtooth current i(t) shown in Fig. 9.33 is...Ch. 9 - The sawtooth voltage v(t) shown in Fig. 9.34 is...Ch. 9 - A current i(t) is applied to a capacitor of...Ch. 9 - A biomedical engineer is evaluating an...Ch. 9 - A biomedical engineer measures the velocity...Ch. 9 - A civil engineer designs a building overhung to...Ch. 9 - A building overhang is subjected to a parabolic...

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