Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 77, Problem 11A
To determine
(a)
Sketch the rectangular solid for the given views.
To determine
(b)
The angle of rotation
To determine
(c)
The angle of tilt
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sketch stability
x= -4x + 2xy - 8
y° =
4 y 2 - x²
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Q/Given H (x,y) = x² + y² - y² Find the Hamiltonian
System and prove it is first integral-
Q2) A: Find the region where ODEs has no limit cycle:
x = y + x³
y=x+y+y³
6
Chapter 77 Solutions
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- Q3)A: Given H(x,y)=x2-x+ y²as a first integral of an ODEs, find this ODES corresponding to H(x,y) and show the phase portrait by using Hartman theorem and by drawing graph of H(x,y)-e. Discuss the stability of critical points of the corresponding ODEs.arrow_forwardQ/ Write Example is First integral but not Conservation system.arrow_forwardQ/ solve the system X° = -4X +2XY-8 y°= 2 4y² - x2arrow_forward
- Q4: Discuss the stability critical point of the ODES x + sin(x) = 0 and draw phase portrait.arrow_forwardUsing Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates). HINT: Pay closeattention to both the 1’s and the 0’s of the function.arrow_forwardRecall the RSA encryption/decryption system. The following questions are based on RSA. Suppose n (=15) is the product of the two prime numbers 3 and 5.1. Find an encryption key e for for the pair (e, n)2. Find a decryption key d for for the pair (d, n)3. Given the plaintext message x = 3, find the ciphertext y = x^(e) (where x^e is the message x encoded with encryption key e)4. Given the ciphertext message y (which you found in previous part), Show that the original message x = 3 can be recovered using (d, n)arrow_forward
- Theorem 1: A number n ∈ N is divisible by 3 if and only if when n is writtenin base 10 the sum of its digits is divisible by 3. As an example, 132 is divisible by 3 and 1 + 3 + 2 is divisible by 3.1. Prove Theorem 1 2. Using Theorem 1 construct an NFA over the alphabet Σ = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}which recognizes the language {w ∈ Σ^(∗)| w = 3k, k ∈ N}.arrow_forwardRecall the RSA encryption/decryption system. The following questions are based on RSA. Suppose n (=15) is the product of the two prime numbers 3 and 5.1. Find an encryption key e for for the pair (e, n)2. Find a decryption key d for for the pair (d, n)3. Given the plaintext message x = 3, find the ciphertext y = x^(e) (where x^e is the message x encoded with encryption key e)4. Given the ciphertext message y (which you found in previous part), Show that the original message x = 3 can be recovered using (d, n)arrow_forwardFind the sum of products expansion of the function F(x, y, z) = ¯x · y + x · z in two ways: (i) using a table; and (ii) using Boolean identities.arrow_forward
- Give both a machine-level description (i.e., step-by-step description in words) and a state-diagram for a Turing machine that accepts all words over the alphabet {a, b} where the number of a’s is greater than or equal to the number of b’s.arrow_forwardCompute (7^ (25)) mod 11 via the algorithm for modular exponentiation.arrow_forwardProve that the sum of the degrees in the interior angles of any convex polygon with n ≥ 3 sides is (n − 2) · 180. For the base case, you must prove that a triangle has angles summing to 180 degrees. You are permitted to use thefact when two parallel lines are cut by a transversal that corresponding angles are equal.arrow_forward
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