# Unit 3 – Individual Project – A Essays

Name: Terri Woodard

MTH133

Unit 3 – Individual Project – A

Name: Terri Woodard

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 = 2

Show your work here:

à

à

à

à x = 2

b)

Answer: x = 9

Show your work here:

à

à

à x = 9

c)

Answer: x = 9/11

Show your work here:

à

à 4 (3x – 2) = (x + 1) [Multiplying both side by 4*(x + 1)]

à 12x – 8 = x + 1

à 11x = 9

à x = 9/11

2) Solve algebraically and check your potential solutions:

Answer: x = 2 and – 1

Show your work here:

à

à x + 2 = x2

à x2 – x – 2 = 0

à x2 + x – 2x – 2 = 0

à x (x +1) –2(x + 1) = 0

à (x + 1)(x – 2) = 0

à x = 2 and –1

For x = 2, we have to take value of as + 2 and for x = –1, we have to take value of as –1 for satisfying the equation.

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 800 cm3. Round the answer to three decimal places.

Answer: the length of a side of a cube is 9.283 cm.

Show your work here:

V = s3

à 800 = s3

à s = 8001/3

à s = 9.283 cm

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

Show your work here:

à

à

à

à

à

à 7(x – 6) [multiplying both side by (x -6)]

à x = 6

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

Answer: Potential solution got from above equation solution is x = 6.

This is not a solution for the above given equation because of the two facts:

1. We had multiplied equation by (x – 6) for getting solution.

2. When we put x = 6 in above equation we get (or ), which is undefined (left part of the equation 0/0)

5) For the following function, C computes a value, where if you add millions of dollars to the value, the result is the cost of implementing a city recycling project when x , as a percent (not its decimal equivalent), citizens participate.

a) Using this model, determine the cost if 60% of the citizens participate?

Answer: The cost of participating of 40% of the citizens is $1 million.

Show your work here:

à

à

à

b) Using this model, find the percentage of participation that can be expected if $5 million is spent on this recycling project? Set up an equation and solve algebraically. Round to the nearest whole percent.

Answer: 77 percent of participation can be excepted if $5 million is spent.

Show your work here:

à

à

à

à x ≈ 77

6) a) If , fill in the following table for x = 0, 1, 2, 3, 4. Round to three decimal places where necessary.

x

y

0

2

1

1, 3

2

0.586, 3.414

3

0.268, 3.732

4

0, 4

Show your work here:

For x= 0, = = 2

For x= 1, = = 1+ 2 and – 1 + 2 = 3 and 1

For x= 2, = = 1.414+ 2 and – 1.414 + 2 = 3.414 and 0.586

For x= 3, = = 1.732+ 2 and – 1.732 + 2 = 3.732 and 0.268

For x= 4, = = 2 + 2 and -2 + 2 = 4 and 0

b) Explain why no negative values are chosen as values to substitute in for x.

Answer: If we take negative value for x , then value for y become imaginary value, since we have to take square root of negative number. Therefore, there will be no negative value for x means that the solution for the equation will exist in only first and fourth quadrant of x and y co-ordinates.

c) Graph in MS Excel and paste your graph here.

Answer:

7) 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 16 years from now?

Answer: There will be approximately 6 millions cases after 16 years from now.

Show your work here:

N=

à N=

à N=

à N=

b) In how many years will there be 7 million cases?

Answer: After approximately 25 years there will 7 millions cases.

Show your work here:

N =

à 7 =

à

à x = 25