Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 30.1, Problem 1E
Program Plan Intro
To multiply the polynomials
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Two points on line 1 are given as (x1, y1) and (x2,y2) and on line 2 as (x3, y3) and (x4, y4), as shown in Figure 3.8a and b.The intersecting point of the two lines can be found by solving the following linearequations:(y1 - y2)x - (x1 - x2)y = (y1 - y2)x1 - (x1 - x2)y1(y3 - y4)x - (x3 - x4)y = (y3 - y4)x3 - (x3 - x4)y3This linear equation can be solved using Cramer’s rule . If the equation has no solutions, the two lines are parallel (see Figure).
Write a program that prompts the user to enter four points and displays the intersectingpoint. Here are sample runs:
Using Matlab, code the following:The paper cup has Radius R2 = l.5(R1), height (h), volume V = 716 cm3
,and surface area (S). The height, volume, and surface area of the cup are given by:
V =πh(R1^2+R2^2+R1R2)/3
S = π R1^2+ π (R1+R2)√(R2 − R1)^2 + h^2
Determine R1, R2, and S of the paper cups with heights h = 8, 10, 12, 14, and 16 cm.
• Method 1: Simulate Equations without using a for loop.
• Method 2: Simulate Equations using a for loop.
Display results to the screen tabulated Hint: You may need to transpose the vectors before printing to the screen.
Simplify the following Boolean expressions, using four-variable K-maps: x′z+w′xy′+w(x′y+xy′)
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- Design an algorithm to find the real roots of a quadratic equation of the form ax2 +1bx + 1c = 0, where a, b, and c are real numbers, and a is nonzero.arrow_forwardUsing Matlab, code the following:The paper cup has a bottom radius R1, top radius R2 = l.5(R1), height (h), volume V = 716 cm3 ,and surface area (S). The height, volume, and surface area of the cup are given by: V =πh(R1^2+R2^2+R1R2)/3, S = π R1^2+ π (R1+R2)√((R2 − R1)^2 + h^2). Determine R1, R2, and S of the paper cups with heights h = 8, 10, 12, 14, and 16 cm. • Method 1: Simulate Equations without using a for loop. • Method 2: Simulate Equations using a for loop. Display results to the screen tabulated Hint: You may need to transpose the vectors before printing to the screen.arrow_forwardWrite pseudocode for an algorithm for finding the real roots of equation ax2 + bx + c for arbitrary real coefficients a, b, and c. (You may assume the availability of the square root function sqrt(x).)arrow_forward
- 1. Show that xy' + yz' + x'z = x'y + y'z + xz'arrow_forwardFind the first three examples of an odd number x>0 and an even number y>0 such that x − y = 7.arrow_forwardAdd the polynomials A(x) = x4 + x3 + x2 + 1 and B(x) = x2 + 1 in GF(25) using the irreducible polynomial P(x) = x4 + 1. Give the answer in binary representation and show your calculations.arrow_forward
- Given an arithmetic equation consisting of positive integers,+,-,* and/ (no parentheses), compute the result.EXAMPLEInput:2*3+5/6*3+15Output: 23.5arrow_forwardSimplify the following expressions according to the commutative law: a. A⋅B + B⋅A + C⋅D⋅E + C⋅D⋅E + E⋅C⋅D b. A⋅B+A⋅C+B⋅A c. (L⋅M⋅N) (A⋅B) (C⋅D⋅E) (M⋅N⋅L) d. F⋅(K + R) + S⋅V + W⋅X + V⋅S + X⋅W + (R + K)⋅Farrow_forwardUse the following K-Map to create an equation ~y~z ~yz yz y~z ~w~x 1 1 ~wx 1 1 1 Wx 1 1 w~x 1 1 1arrow_forward
- The equations given below are the mathematical models of the three mixed tanks that are connected in series. Solve the following equations using MATLAB programme using numerical methods and plot the graphics (C, t) for all tanks. Data: Q=constant= 300 L/min, V= constant= 50 000 L, t=0; C=Co, Differential equations : dCA1 / dt = -0.006 CA1 (CA1 - CA2 ) = 167 (dCA2 /dt) d CA3 /dt = 0.006 (CA2 - CA3 )arrow_forwardSimplify the following Boolean function , using three- variable maps: a) F(x,y,z) = Σ (0,2,6,7) b) F(A,B,C ) = Σ (0,2,3,4,6) c) F(a,b,c) = Σ (0,1,2,3,7) d) F(x,y,z) = Σ (3,5,6,7)arrow_forwardLet A = {c, n, b}, B = {x, y} and C = {0, 1}. Find A)A X B X C B)C X B X A C)B X C X Carrow_forward
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