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Maths Homework - Assignment 3

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Maths Homework 110 - Assignment 3

1. Solve the following equations for x.
a. (x - 1)2 – (x2 - 1) = 2 - 2x
b. (x – 1) / 4 + (2x + 3) / -1 = 0
c. 4 / (x + 2) + 1 / (x – 2) = 4 / (x2 – 4)
d. |6 x – 5| = 25
f. (x – a) / (x – b) = (b – x) / (a – x)

2. Solve the following equations by factoring if possible. If not, solve by completing the square.
a. x (2x -13) = - 6
b. x2 – x – 5 = 0
c. 12x2 + 32 x + 5 = 0
d. 6 + 6 x2 = 5x

3. Solve the following equations for x.
a. (2x)/ (x2 – 1) – 1/ (x +3) = 0
b. 3 x2 – 6x – 3/ (x +1) (x – 2) (x -3) + (5 - 2x)/(x2 – 5x + 6) = 0

4. The average of three numbers is 42. The first two numbers differ by 1, and the average of the second and third number is 47. What are the three numbers?

5. You deposit $2000 at 8% and $3000 at 9% annual simple interest. What additional amount would you need to invest at 12% to yield an overall return of 10% after one year?

6. A student in a chemistry laboratory has two acid solutions available to her. The first solution is 10% acid and the second is 35% acid. Assuming the percentages are by volume, how many mL of each solution should she mix to obtain 200 mL of a 25% acid solution?

7. A 100 lb pumpkin consists of 99% water by weight. Suppose the pumpkin is placed outdoor for drying. How much water, in terms of weight, has to be evaporated if the pumpkin consists of 98% water after drying?

8. If the sides of a square are doubled, the area increases by 147 cm2. Find the sides of the original square.

9. Consider the quadratic equation x2 + bx + c = 0, where c is nonzero.
(a) If one root is three times the other, show that b2/c = 16/3.
(b) If one root is n times the other, show that b2/c = (n + 1)2/n.
(c) Use the result in part (b) to verify the result in part (a).

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