Download MTH133 - JustAnswer

Name:
MTH133
Unit 3 – Individual Project – A
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 3 x as cuberoot(x) and show raising
to the nth power as ^n, like x 3 is typed x^3.
a)
3
x 53
Answer: 512
Show your work here:
Add 5 to each side:
Cuberoot(x) = 8
Take each side cubed:
X = 8^3
X = 512
b)
3
x2
 27
Answer: 9
Show your work here:
Raise each side to the 2/3 power:
X^(3/2)^(2/3) = 27^(2/3)
X = 27^2/3
Cuberoot of 27:
X = 3^2
X=9
c)
3
3x  2
1
4
x 1
Answer: 9/11
Show your work here:
Multiply through by x+1:
3(x+1)/4 = (x+1) – (3x-2)
Simplify:
3x/4 + ¾ = -2x+3
Multiply by 4:
3x + 3 = -8x + 12
Add 8x:
11x + 3 = 12
Subtract 3:
11x = 9
Divide:
X = 9/11
2)
Solve algebraically and check your potential solutions:
x2  x0
Answer: 2
Show your work here:
Add x:
Sqrt(x+2) = x
Square both sides:
X+2 = x^2
Move to one side:
X^2 – x – 2 = 0
Factor:
(x-2)(x+1) = 0
X = 2 or -1
Check:
Sqrt(2+2) – 2 = sqrt(4) – 2 = 2-2 = 0, yes
Sqrt(-1+2) – (-1) = sqrt(1) + 1 = 1+1 = 2, NO
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 cm 3. Round the
answer to three decimal places.
Answer: 9.283 cm
Show your work here:
800 = s^3
Cuberoot of each side:
S = cuberoot(800)
S = 9.283
4)
a)
Show the steps that you would take to solve the following
algebraically: 5 
2
10  2 x

x6
x6
Show your work here:
Multiply through by x-6:
5(x-6) – 2 = 10-2x
Distribute the left:
5x-30 – 2 = 10-2x
Combine:
5x-32 = 10-2x
Add 2x:
7x-32 = 10
Add 32:
7x = 42
Divide:
X=6
b)
What potential solution did you obtain? Explain why this is not a
solution.
Answer: The potential solution is x = 6. However, that is not a valid
solution, because when x is 6, the denominator of the fractions are equal
to 0. That makes them undefined.
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.
C ( x) 
a)
1.5 x
100  x
Using this model, determine the cost if 60% of the citizens participate?
Answer: $2.25 million
Show your work here:
Plug in x = 60:
1.5*60 / 100-60
= 90/40
= 9/4
= 2.25
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%
Show your work here:
Set C = 5:
5 = 1.5x / (100-x)
Multiply by 100-x:
5(100-x) = 1.5x
500 – 5x = 1.5x
Add 5x:
6.5x = 500
Divide:
X = 76.923
Rounds to 77%
6)
a)
If y  x  2 , fill in the following table for x = 0, 1, 2, 3, 4. Round to
three decimal places where necessary.
x
0
1
2
3
4
y
2
3
3.414
3.732
4
Show your work here:
Sqrt(0) + 2 = 0 + 2 = 2
Sqrt(1) + 2 = 1 + 2 = 3
Sqrt(2) + 2 = 1.414 + 2 = 3.414
Sqrt(3) + 2 = 1.732 + 2 = 3.732
Sqrt(4) + 2 = 2 + 2 = 4
b)
Explain why no negative values are chosen as values to substitute
in for x.
Answer: You cannot take the square root of a negative number, since it is
not part of sqrt’s domain. Therefore, we do not pick negative numbers.
c)
Graph in MS Excel and paste your graph here.
Answer:
7)
Suppose that N= x  2 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: 6 million
Show your work here:
Plug in x = 16:
Sqrt(16) + 2
=4+2
=6
b)
In how many years will there be 7 million cases?
Answer: 25 years from now
Show your work here:
Set N = 7:
7 = sqrt(x) + 2
Subtract 2:
5 = sqrt(x)
Square it:
X = 5^2
X = 25