Questions in Section Algebra II

Find the foci, eccentricity and the directrices of the given ellipse 2x^2+ y^2-4y+3=0.

A hardware store makes a mixed bag of 42 items using screws, bolts, and washers. The cost of screws are $3.00 each, bolts cost$2.00 each, and washers are $1.50 each. The mixture calls for four times as many screws than bolts. The total cost of the mixture is$102.00. How much of each item did the store use?

Find x_1, x_2 and x_3.

Three equations are given.

x_1+x_2+x_3 = 2

x_1^2+x_2^2+x_3^2=6

x_1^3+x_2^3+x_3^3= 8

Thank you.

The sum of two numbers is 59 and the difference is 3. What are the numbers?

Solve sqrt(k-7)-sqrt(k-3)=2.

Show that the polynomial x^8-x^7+x^2-x+15 has no real root.

Given the equation y=x^2-6x+8.

1. For what values of x is y>=0?
2. What is the maximum and minimum values of y?

Find the amount of an annuity if \$800/month is paid into it for a period of 20 years earning interest at the rate of 7%/year compounded continuously.

Solve the following equation for x: e^(-2x)-3e^(-x)=-2.

Simplify ((cot^2(theta))/(csc^2(theta))+(tan^2(theta))/(sec^2(theta)))/(sin(theta)+cot(theta)cos(theta))^2.