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`

Please find its answer by another method instead of hit and trial.

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`.

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