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Basic Algebra

Cyclic Groups - Modern Algebra

(a) Let F = { (matrix with first row; a 0, second row is 0 a) : a is an element of R Show that F is a field and that F ~= R (b) Give the definition of a cyclic group Prove that every subgroup H of a cyclic group G =<a> is itself cyclic

Looking for the value of x.

If x times 5 gives the same result as x less than 5, what is the value of x? (A)5 (B)6 (C)4/5 (D)5/6 (E) -5/4

Bacterial growth word problem using logarithms.

The number of bacteria N in a culture is given by the model N=250e^kt, where t is the time in hours, with t=0, corresponding to the time when N=250. When t=10, there are 280 bacteria. How long does it take the population to double in size? To triple in size?

male enrollment of a college in an algebraic word problem.

A state college has a total freshman enrollment of 2,200 students, of whom 42% are male. If the remainder of the total school enrolment of 6,800 students is divided evenly between male and female, determine the total male enrollment in the school.

Algebra Word Problem: Percent Increase

A start-up firm's sales increased by 350% from its first year of operation to its third year total of $1.68 million. What were its total sales in its first year of operation?

Number Magic Algebraic Explanation

Pick a number from 1 to 9 (0<x<10). Multiply it by 2. Then add 3 to the result. Now multiply this number by 50, then add 1853 and subtract the year of you birth. You now should have a 3 digit number. The first digit is the number you picked above, and the last 2 digits are your age after your birthday this year (2003). How is t

Square Roots Multiplied

Square root of 100 plus the square root of 200 plus the square root of 300 multiplied by the square root of 400 equals ?


Solve for X:LOG2X=8 Write as a single logarithm:5LNX-1N(X+1)

Elementary School Math: Single Digit Division

This is a day to day problem which can be taken mathematically: There are 23 school buses each carrying 41 kids and teachers on a picnic to the Niagara Falls. How many total number of people are going in this trip? Mathematically, the problem is 41 X 23 = ?

Investigating trios.

Q. Three whole numbers, greater then zero can be used to form a trio. example: (1,2,2) is a trio whose sum is 1+2+2=5 And (2,1,2) is a different trio whose sum is also 5 How many trios can you find with a sum of 5?

Point of Intersection of Line

The equations of two lines are 4x-5y = -15 and y = 4/5x -6 Which of the following describes their point of intersection? A) (5,-2) B) (-5,1) C) (10,-5) D) (No intersection)

Least Squares to Measure Wavefronts

1)We wish to measure a wavefront u(x,y) on a 3X3 grid (see the attached file). The sensor how ever provides us only with differences between grid points. There is sensor noise, so the difference measurements may not be consistent. Number the grid points linearly and set up a set of linear equations (matrix form) relating the

Polynomials Real Values

Solve, find the solution set, solve for the real values - see attachment Solve for x: x + 1 - x > 1 2 5 a. { x _ x > 5 } 3 b. { x _ x > 3 } c. { x _ x > - 4 } 3 d. { x _ -2 < x < 5 } Find the solution set for x = 2 + __1___ 1 + x

solve logarithmic equations.

Lnx+ln(x+2)=4 3^x=45 x=log17 96 I did not know how to put the 17 lower than the log lnx for x=e^x f(6) for x^2+3x-2/x^2-6x=f(x)