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Basic Algebra

Cryptography: RSA Problem - Public and Private Keys

Fill in the blank choose public or private. Alice chooses two large prime numbers p and q. She finds their product m = pq, which is _____. She also finds n= (p-1)(q-1) which is _____. She chooses e which is _____and finds d=_____. The number e is public or private. and the number d is public or private. When Bo

Sides of a Cube Problem

Eight small cubes are put together to form one large cube. All six sides of the larger cube are painted, the paint is allowed to dry, and then the cube is taken apart. a) How many of the small cubes will have paint on just one side? On two sides, On three sides? On no sides? b) Complete the following table, assuming in turn

Least Common Multilpes

A. Find the LCM (Least common multiple) (84, 108). Show how you obtained your answer. B. Suppose LCM (18,A) = 72. What are the possible values, if any, for A? Explain your answer.

Equivalence and Simplification

A. Show that 693/858 and 42/52 are equivalent in THREE different ways. B. Simplify 3^5 X 24^3 divide by 12^3 X (6^3)^2 ^ means exponent.

Algebra : Graphing Functions

Please see the attached file for the fully formatted problems. Can you please assist me with the problems listed below? P. 237 1. a) #6, b) #18 2. a) #22, b) #24 3. a) #32, b) #46 P.253 4. a) #1, b) #2, c) #3. d_ #4 5. a) #10, b) #12 6. a) # 28, b) #30 7. P.260, Matched Problem 1 P.271 8. # 2 - 22 (Eve

Algebraic simplification problem after a u-substitution derivation

The attached file contains a function that needs to have the first order derivative taken. I took the derivative, but I am making a mistake in the algebra simplification of the result. Would you please take a look. I am working on a dynamic programming problem, and one part of it requires that I take the derivative of the

Linear Congruences: Example Problems

Find the solutions of (1) 153x is congruent to 6 (mod 12) (2) x + 1 is congruent to 3 (mod 7) (3) 8x is congruent to 6 (mod 422) (4) 363x is congruent to 345 (mod 624).

Intervals Real Numbers

Please see the attached file for full problem description Find ten real numbers in the closed interval [0,1] such that for each value m from 2 to 10, the numbers lie so that there is one of them in each of the open intervals [Note that these conditions for m = 1,2......,10 all have to hold simultaneously for your

Proving that an equality is false.

I have two sets of 64 numbers (1.1 to 7.4). Both number sets are created using the same equation for values of i from 0 to 63. m = 1.1 + ( i * 0.1 ) n = 1.1 + ( i * 0.1 ) I am trying to understand if the following equality is false in all cases except when the terms in each expression are equal (e.g. m^-12 = n^-12 and

Quadratic equation Matrix Function

The graph of the quadratic equation x^T Ax = [0,0,1]x, where A = [ 1/(alpha^2) 0 0 ] [ 0 -1/(beta^2) 0 ] [ 0 0 0 ] is a(n): A. ellipse B. hyperbola C. elliptic paraboloid D. parabolic cone E. hyperbolic paraboloid

Inner Products for Unit Vectors

Let f1, f2, f3 be unit vectors in R3 such that < f1, f2 >= 1/2. Give a necessary and sufficient relationship between x =< f1, f3 > and y =< f2, f3 >. Please be sure to be rigorous and as detailed as possible.

Algebra with Indices

Given that S=(R+D)^(1/3) and T=(R-D)^(1/3) where D= square root(R^2+Q^3), show that ST=-Q

Square Root Functions Explained

Hi, can someone please explain to me how sqrt (square root of)128 becomes 8sqrt2 ; or sqrt68 becomes 2sqrt17? ; or sqrt45 becomes 3sqrt5? Thank you

Simplifying Expression Function

Simplify the following expressions: a. 3x-2/2x2+x-3 Divide by 9x-6/2x-2 b.(108)1/2- (48)1/2+ (192)1/2 (should be exponent 1/2) c. (20x3+3x2-4x+5)/(4x2+3x-7) (should be exponent 3 and 2,2).