# Math

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MTH133

Units 3-5 – Individual Project – B

Name:

1) Solve algebraically. Trial and error is not an appropriate method of solution. You must show all your work.

Learn how to type math roots and fractions by clicking on the link in the assignment list. Alternately, you may type as cuberoot(x) and show raising to the nth power as ^n, like x 3 is typed x^3.

a)

Answer: x = 216

Show your work here: 3x = 2 + 4 = 6  x = 6³ = 216

b)

Answer: x = 25

Show your work here: x = 1252/3 = (5³)2/3 = 5² = 25

c)

Answer: x = -26/3

Show your work here:

(2x - 1)/(x + 2) = 3 - ¼ = 11/4  4(2x - 1) = 11(x + 2)  3x = -26  x = -26/3

2) a) Show the steps that you would take to solve the following algebraically:

Show your work here:

(a) Take the LCD in the LHS and combine the terms: [4(x – 2) – x]/(x – 2)

(b) Simplify the LHS: (3x – 8)/(x – 2)

(c) Solve the equation for x: 3x – 8 = -2 [provided x ≠ 2]

 3x = 6  x = 2

 The given equation has no solution.

b) What potential solution did you obtain? Explain why this is this not a solution.

Answer:

x = 2 is a potential solution. But this is not a solution because this will make the denominators zero.

3) The volume of a cube is given by V = s3, where s is the length of a side. Find the length of a side of a cube if the volume is 500 cm3. Round the answer to three decimal places.

Answer: 7.937 cm

Show your work here: s = V^(1/3) = 500^(1/3) = 7.937

4) Suppose that N= models the number of cases of an infection, in millions, of a disease x years from now.

a) How many cases of the infection will there be 9 years from now?

Answer: 6 million cases

Show your work here: N = Ö9 + 3 = 6 million

b) In how many years will there be 5 million cases?

Answer: 4 years

Show your work here: 5 = Öx + 3  Öx = 2  x = 4

5) Consider the function .

a) Find h, the x-coordinate of the vertex of this...