1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any 2 terms? b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? d)
A commutative ring is called a local ring if it has a unique maximal ideal. Prove that if R is a local ring with maximal ideal M then every element of R-M is a unit. Prove conversely that if R is commutative ring with one in which the set of nonunits forms an ideal M, then R is a local ring with unique maximal ideal M.
1. Prove that gcd (a, lcm[b, c]) = lcm[gcd(a,b), gcd(a,c)]. 2. Find the simultaneous solutions of the following congruences: 2x ≡ 1(mod 5) 3x ≡ 9 (mod 6) 4x ≡ 1 (mod 7) 5x ≡ 9 (mod 11)
Fibonacci posed the following problem: Suppose that rabbits live forever and that every month each pair produces a new pair which becomes productive at age 2 months. If we start with one newborn pair, how many pairs of rabbits will we have in the nth month? Show that the answer is fn, where {fn} is the Fibonacci sequence defined
Indicate whether each system is independent, inconsistent or dependent 4 ( 1-x) + y = 3 3 (1-y) - 4x = -=4y 1/3x - 1/6y = 1/3 1/6x + 1/4y= 0
Indicate whether each system is independent, inconsistent or independent x-5y= 4 4x + 8y = -5
Factor 4z^2 + 16z + 15.
Factor 25-9z^2
See attached file for full problem description. 1) An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of th
Solve for x. Your answer should be in the simplest form fraction. 3x + 2/3 = 1/6x - 3/2
Solve for x: -6 (x - 9) = 7x + 1 - 4 (-8x + 8) Please try to get the answer in the simplest form possible.
Write each expression in the form a + bi, where a and b are real numbers. (3-5i) - (2-7i)
Rational Exponents. -25^(-3/2)
Find the root. See attached file for full problem description.
Solve for R. (distance, rate, & time). See attached file for full problem description.
b/3=-3/4
Equation w/ two solutions. (a+4)/2 = (a+4)/a
Soving Equation: X+2-2 square root X+2=0
The line through (-4,6) that is parallel to y=5x The line through (3,5) that is parallel to the x-axis
10 34 ___ = _______ x x + 12
Factoring Quadratic Equations How do you factor z^2 - z - 30?
A/y + 1/3 = B/y
1/a + 1/b = 1/f for a P1V1 P2V2 ______ = ______ for P2 (note: the 2 is a tiny #2 below the P) T1 T2
Three problems 5/x + 6/x =12 a-1/a^2-4 = 1/a-2 = a+4/a+2 z/z+1 - 1/z+2 = 2z+5/z^2 + 3z +2
Please address the following question: Convert each rational expression into an equivalent rational expression with the LCD as the denominator. y x ___ , _____ 4x 6y
How do you do these type of problems? 2.4=3(m+4) 5(1-2w)+8w=15 If 3(x+1)=7 what is the value of 3x
Please complete the following: Solve the following equation for Z. (4z - 5)/2 - (z + 9)/4 = 4 Simplify the answer as much as possible.
The final velocity, V, of an object is given by the equation - See attached file for full problem description.
The centripetal force F acting on a mass M traveling along a circular path of radius R at a velocity V is given by...See attached file for full problem description.
Solve the following equation for X. Write your answer as a fraction in simplest form. 7(x-3)=-3x+2-3(-2x+7)