Suppose that n straight lines in the plane are positioned so that no two are parallel an no three pass throught the same point. Show that they divide the plane into 1/2(n^2 + n + 2) distinct regions.
A mapping %:A->B is called a constant map if there exists b.(b not) belonging to B such that %(a) = b. for all a belonging to A. Show that a mapping %:A->B is constant if and only if %$=% for all $:A->A
I know the formula Rate x Time = Distance. However, I have a question where I am asked to find the time and not the distance? Can you give me some basic information about how to calculate the time using this formula or is there a different formula that I should be using? Thanks.
Karen can row a boat 10 kilometers per hour in still water. In a river where the current is 5 kilometers per hour, it takes her 4 hours longer to row a given distance upstream than to travel the same distance downstream. Find how long it takes her to row upstream, how long to row downstream, and how many kilometers she rows?
What if you want to calculate the number of miles a car travelling 30 mph goes in 120 minutes? How do I calculate this and with what formula?
What is the relationship between rate, time and distance? Say a car is traveling at 30 mph, how far will it go in 2 hours?
I will use parentheses for absolute value signs. I need help to solve these two equations. 1. 3(s) - 2 >7 and 2. 6 - (2 - p) < 4
Solve for the following scenario: The product of 2 consecutive positive odd numbers is 195. Find the numbers.
What must be added to each of the following expressions to obtain a perfect square? a) x^2 + 5x b) a^2 + 2ka c) c^2 - 4c
Find the equation in x whose roots are 2 and -3/4.
Solve the following quadratic equations by factorization: a) x^2 - 5x = 0 b) 6t^2 = t(t-4) c) a^2 + 9a = 0
1/X - X+1/8 = X - 1/4X . These are fractions.
Simplify y2 /X2 - 4y2 + y/2x + 4y When I have 2 after the y and the x it means squared. These are fractions, in case it is not clear.
It is a description of how to apply Mathematical Induction in proving theorem or statement. Application of mathematical Induction : F 2n+1 - Fn Fn+2 = (-1) n
Application of Mathematical Induction Application of Mathematical Induction Fibonacci Numbers :- The Fibonacci numbers are numbers that has the following properties. If Fn represents the nth Fibonacci number, F1 = 1, F2 =1, F3 =2, F4=3, F5 = 5 etc. We can find the Fibonacci number
Find the intensity I of an earthquake measuring R on the Richter scale (let Io=1). (a) Chile in 1906, R=8.6 (b) Los Angeles in 1971, R=6.7
Endangered Species: A conservation organization releases 100 animals of an endangered species into a game preserve. The organization believes that the preserve has a carrying capacity of 1000 animals and that the growth of the herd will follow the logistic curve. p(t)=1000/1+9e^-0.1656t where t is measured in months (a)
Radioactive Decay: Carbon 14 dating assumes that the carbon dioxide on earth today has the same radioactive content as it did centuries ago. If this is true, the amount of carbon 14 absorbed by a tree that grew several centuries ago should be the same as the amount of carbon 14 absorbed by a tree growing today. A peice of anc
The population P of a city is P=240,360e^0.012t where t=0 represents 2000. According to this model, when will the population reach 275,000?
The number of trees per acre N of a certain species is approximated by the model N=68(10^-0.04x), 5 <_ x <_ 40 (<_ = less than or = to) Where x is the average diameter of the trees (in inches) three feet above the ground. Use the model to approximate the average diameter of the trees in a test plot when N=21.
Let G be a finite nonabelian group of order 27 where all the elements have order 3. Prove that there is exactly one such group G and give a complete description.
Please see the attached file for the fully formatted problems. 5. Find an irreducible polynomial f(x) over the field Z3 with Z3[x]/(f(x)) = F243. Note that 243 = 3^5 . Please explain your reasoning and solution in as much detail as possible. Thank You.
Five problems are "solved for x".
Prove that (n + 1)!>2^(n+3) for n>=3 Hint: try using mathematical induction
Compute the discriminants and the Galois groups of the polynomials x3 + 27x − 4 x4 − 5
Describe all subgroups of S5 which are Galois groups of irreducible polynomials of degree 5.
Find an irreducible polynomial defining the extension Q(3^1/2, 5^1/2).
Let K be obtained as a field Q(alpha) where alpha is a root of P(x) = x3 −3. Find an irreducible polynomial which defines the splitting field of P(x).
NUMBER OF FARMS. The number N of farms in the United States has declined continually since 1950. In 1950 there were 5,647,800 farms, and in 1995 that number had decreased to 2,071,520. Assuming that the number of farms decreased according to the exponential model: A). Find the value of k, and write an exponential function
Please see the attached file for the fully formatted problem. Show the existence of an extension of Fq of order l for any prime l.