Sender: Troy
Subject: Extra Credit Problems
Date: 14 Apr 99 13:56:16 -0500

My teacher has given me 5 extra point questions. I have figured out two, but i need a little assistance with 3 others, could you help me with:

  1. A stablehand agreed to work for 1 year. At the end of that time, she was to receive $240 and one horse. After 7 months she quit the job, but still received the horse and $100. What was the value of the horse?

  2. If the roots of x2 + bx + c are pi and square root 2, then find "b" and "c."

  3. Solve for "x" (square root x +(square root x +(square root x +(square root x +...))))= 5. All of the subsequent square root x are under the first radical. I figured the following:

  4. A parabolic arc is 30 feet wide at its base and 15 feet high. How many feet wide it it ten feet above the base? I used similar triangles to conclude that the relationship was x= 10 30 15. Therefore, x = 20 ft. Right?

Hi Troy

Here are a few ideas.

For problem number 1 the stablehand is to receive $240 at the end of 1 year so that is $20 per month. Thus at the end of 7 months she is owed 7x$20 = $140 and seven twelths of a horse. Since she only received $100 in cash she must have used $40 to buy the remaining five twelths of the horse.

For 2. if the roots of x2 + bx + c are pi and the square root of 2 then (x - pi) and (x - the square root of 2) are factors of x2 + bx + c. Multiply (x - pi) by (x - the square root of 2) to try to determine b and c.

I don't think that you can use similar triangles in 4. You need somehow to use the fact that the curve is a parabola. Draw the parabola in the plane with the y-axis as the axis of symetry and the vertex at (0,15). Now can you determine the equation of the parabola to solve your problem?

I hope this helps

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