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Given
A=(-1/2+isqrt(3)/2)^n
1. Show that A is real for any natural n
2. Show that for n=3K where K is a natural number, A=2
What is the solution of the system of equations?
Tom has five times as many marbles as Jim. together they have 42 marbles. how many marbles does each has?
Graph the basic function using a solid line and the transformed function using a dotted line.
Suppose that you have student loan of $80,000 with an APR of 7% for 30 years. If you decide to pay off the loan in 20 years instead of 30.
Find the point of equilibrium of the given demand and supply equations. (Hint: The point of equilibrium is the price p and the number of units x that satisfy both the demand and the supply equations.)
A shipping company is shipping cargo by truckloads. The number of miles per gallon the truck averages goes down as the weight of each load goes up.
How can we picture real numbers "mod 2 pi" as something that goes round in a ring? How is that related to trigonometry? Can we make a function from "real numbers mod 2 pi" to the rotations around the origin of the Cartesian plan so that this functi..
A box whose volumeis 80cubic cm has length,width,height in the ratio 1:2:5 if each of the length,width,height is increased by 2cm how many cubic centimeters will the volume be increased?
During a marathon, Kim our champion cyclist is having struggles. At the halfway checkpoint she is behind the leader, Allison by 10 miles. Kim still has a lot of energy left and pacing herself at a constant 15 miles per hour.
the electric current in a in a circuit with a battery of voltage e a resistance r and an inductance l is i er1-e-rtl
For an integer n, define the graph Tn as follows: Vertices are 2-element subsets of {1,2,...,n}. Two vertices are adjacent if they have one element in common.
Need detail on this problem.I= {4m+6n I m, n E Z} closest to (and including) 0. Show that the set I is closed under addition and multiplication. Use part (a) to find an mEZ such that I=mZ.
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