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Let delta=sqrt(-3) and R=Z[delta]. This is not the ring of integers in the imaginary quadratic number field Q[delta]. Let A be the ideal (2,1+delta).
Let y = f(x) describe the speed y of an automobile after x minutes if the cruise control is set at 60 miles per hour.
Under what condition is there a solution to the simultaneous vector equations alpha*x+beta*y = a and x ^ y = b, for the vectors x and y.
The relation between the cost of a certain gem and its weight is linear. In looking at two gems, we find that one of the gems weighs 0.2 carats.
An aerobics instructor says she drinks one cup (8 ounces) of water before she starts her classes and then she drinks 10 ounces every 10 minutes.
In solving the equation (x + 1)(x - 2) = 4, Eric stated that the solution would be x + 1 = 4 => x = 3 or (x - 2) = 4 => x = 6.
Identify the key components of the graph (minimum or maximum, vertex, roots) and give a brief description of what each represents.
Different pets need to have different areas. For example, a horse needs more space than a dog. Determine an area that is appropriate for your pet.
Let a_n from n=0 to infinity be a sequence of real numbers which converge to 0, i.e. lim n-->infinity a_n=0.
Find an arithmetic sequence that gives the amount depreciated each year by each method.
Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where a does not equal 0, may have how many solutions?
You are choosing between two health clubs. Club A offers membership for a fee of $50 plus a monthly fee of $25.
You are doubling a receipe that calls for 3/4 of a cup of milk. How much milk will you need?
Assume the operator R(theta) transforms a vector v (in two-dimensional real space) by swinging it around counterclockwise through an angle theta.
Begin by solving the linear equation for Y. This will put the equation in slope-intercept form.
The equation of a line is given below. Find the slope of a line that is Parallel to the line with the given equation.
How would you explain the performance of synthetic division to someone else? Use the problem (2x3 - 3x2 - 11x + 7)/(x + 3) to support your explanation.
Multiply and Simplify (7+6i)(2+9i) Write the answer in the form a+bi, where a and b are real numbers.
The positive integers are classified into two types, A and B; a number is A if and only if it is the sum of two (distincts) A numbers.
A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.9 x 10^2 µm.
One day's discharge at its mouth, 5.6 trillion gallons, could apply to all of country X's households for four months.
Write the equation of the line through each indicated point with the indicated slope. Write the final answer in the form Y=mx+b
He carries 9 different CD players, 7 different receivers, 10 different kinds of speakers. Assume that a sound system consists of one of each.
Population growth in Ethiopia: In 2006, the estimated population in Ethiopia was 75 million people with a relative growth rate of 2.3%.
The two NCAA stadiums with the largest capacities are beaver Stadium (Penn State) and Michigan Stadium (Univ. of Michigan).