#$&*
course mth158
resubmission
001. `* 1
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Question: * R.1.26 \ was R.1.14 (was R.1.6) Of the numbers in the set {-sqrt(2), pi + sqrt(2), 1 / 2 + 10.3} which are counting numbers, which are rational numbers, which are irrational numbers and which are real numbers?
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Your solution:
Counting numbers: none
Rational numbers: 10.3
Irrational numbers: {-sqrt(2), pi + sqrt(2),
Real Numbers: ˝, 10.3
The reason these numbers are placed in these catagories is because a counting number or a natural number is defined by the numbers in the set 1,2,3,4…
Rational numbers are defined as a number that can be expressed as a quotient a/b of two integers. 10.3 can also be expressed as a fraction. 10 1/3
Irrational numbers are defined as a decimal that neither repeats nor terminates. These occur naturally.
Real numbers are numbers that represent a quality upon a continuum.
002. `* 2
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Question: * R.2.46 (was R.2.36) Evaluate for x = -2, and y = 3 the expression (2x - 3) / y and explain how you got your result.
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Your solution:
Since x=-2 and y =3 then you plug x and y into the equation respectively which gives you
(2*-2-3)/3 = (you use the order of operations or PEMDAS to complete the equation)
first mutiply within the parentheses (-4-3)/3 then complete what is inside the parentheses -7/3 and that is your answer when x=-2 and y =3 the equation = -7/3
003. `* 3
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Question: * R.3.16 \ 12 (was R.3.6) What is the hypotenuse of a right triangle with legs 14 and 48 and how did you get your result?
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Your solution:
The equation for a right triangle is a^2 + b^2 = c^2 and for this the legs are a and b so
14^2+48^2 = c^2
196 +2304 = c^2
2498= c^2
sqart 2498 = c
c = 49.97
because the hypotenuse is always the “leg” that is diagnol from the 90 degree angle.
005. `* 4
* R.4.36 (was R.5.30). What is the single polynomial that is equal to 8 ( 4 x^3 - 3 x^2 - 1 ) - 6 ( 4 x^3 + 8 x - 2 )?
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Your solution:
First you must distribute the 8 and the -6 into the equation so
8 ( 4 x^3 - 3 x^2 - 1 ) - 6 ( 4 x^3 + 8 x - 2 ) becomes because you must also distribute the negative in the negative 6
32x^3 -24x^2 -8 - 24x^3 -48x +12= then you combine like terms
8x^3 -24x^2 -48x +4 is your final answer
006. `* 6
R.5.22 (was R.6.18). What do you get when you factor 36 x^2 - 9 and how did you get your result?
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Your solution:
.first you take 9 out of 36 x^2 - 9 this gives you
9(4x^2-1) you continue to factor this and you get 9(2x-1) (2x+1)
007. `* 7
* R.7.10 (was R.7.6). Show how you reduced (x^2 + 4 x + 4) / (x^4 - 16) to lowest terms.
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Your solution:
First you need to factor (x^2 + 4 x + 4) / (x^4 - 16) =(x+2) (x+2)/(x^2-4)(x^2-4)
Now (x^2-4)(x^2-4) can be factored further so this = (x+2) (x-2) (x+2)(x-2)
The factored problem looks like =(x+2) (x+2)/ (x+2) (x-2) (x+2)(x-2)
The numerator cancels out with 2 terms from the denominator and so the final answer = 1/(x-2)^2
008. `* 8
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Question: * R.8.12. Simplify the cube root of 54
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Your solution:
The cube root of 54 = cube root 9 *6 = 3 sqart 6
In order to simplify the cube root of a number you use what multiplies into the number in order to simplify the cube root to either a squart or a natural number
@& The square root of 54 would be 3 sqrt(6), but not the cube root.*@
010. `* 10
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Question: * 1.1.20 (was 1.1.12). Explain, step by step, how you solved the equation 5y + 6 = -18 - y
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Your solution:
5y + 6 = -18 - y
first you combine like terms which is 5y and -y and 6 and -18
this = 6y = -24 you then divide -24 by 6
your final answer should be -4
if you plug the -4 back into the equation as y you can check your work.
5*-4 +6 = -14
-18- - 4 = -14
thus, -4 is the correct answer
011. `* 11
* 1.2.13 \ 5. Explain, step by step, how you solved the equation z^2 - z - 6 = 0 using factoring.
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Your solution:
To use factoring to solve this equation you first find the common factors in the equation. z^2 - z - 6 = 0 = (z+3) (z-2) you then set both (z+3) (z-2) to 0 (z+3) = 0 then z = -3
(z-2) = 0 z = 2 the solution set is (-3,2)
012. `* 12
* 1.4.12 (was 1.4.6). Explain how you found the real solutions of the equation (1-2x)^(1/3) - 1 = 0
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Your solution:
Since the equation is to the power 1/3 you square both sides in order to give yourself whole numbers
( (1-2x)^(1/3) - 1 = 0 )^2 = 1 - 2x - 1 = 0
you then have to add 1 to the side with 0
1-2x = 1 you then subtract 1
-2x = 0
since 0 divided by 2 = 0 then the answer is 0 when plugged back in 0 = 0
013. `* 13
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Question: * 1.5.34 (was 1.5.24). How did you write the interval [0, 1) using an inequality with x? Describe your illustration using the number line.
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Your solution:
0 is less than or equal to x is less than or equal to 1
on the number line the part between 0 and 1 would be shaded because the answer is either 0 or 1 or in between.
014. `* 14
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Question: * 1.6.12 (was 1.6.6). Explain how you found the real solutions of the equation | 1 - 2 z | + 6 = 9.
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Your solution:
With the absolute value lines you have to set your equation to both negative and positive to get your solution.
First we need to subtract 6 from the original equation so
| 1 - 2 z | = 3 then we set 1 - 2z to both 3 and -3
1-2z = 3 or 1 - 2z = -3
-2z = 2 -2z = - 4
z = - 1 z = 2
the solution set is (-1,2)
015. `* 15
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Question: * 1.7.20 (was 1.2.30). Explain how you set up and solved an equation for the problem. Include your equation and the reasoning you used to develop the equation. Problem (note that this statement is for instructor reference; the full statement was in your text) million to lend at 19% or 16%, max lent at 16% to average 18%.
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Your solution:
If you multiply 1 million by 18 %, 16% and 19 % you get
180,000
160,000
190,000 respectively and this means that if you gave everyone a loan at 16% you would be 20,000 short of your quota. IF you gave everyone a loan at 19% you would be 10,000 over your quota so this means that your equation should be
x = money loaned out at 16%
then 180,000 - x = money loaned out at 19%
.16x +.19(1,000,000) - x = 180,000
160,000x + 190,000 - x = 180,000 combine like terms
159999x + 190,000 = 180,000
159999x = -10,000
x = - 6 % which means 6 % of the loans must be at 19%
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Question: * 2.3.34 / 30 (was 2.3.24). Slope 4/3, point (-3,2)
Give the three points you found on this line and explain how you obtained them.
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Your solution:
Because we know that the slope = 4/3 which is rise over run it will increase by 4 for y and 3 for x
-3 + 4 = 1 and 2 + 3 = 5 one new point is (1,5)
1 + 4 = 5 and 5 + 3 = 8 second new point is (5, 8)
5+4 = 9 and 8 + 3 = 11 last new point = (9,11)
019. `* 19
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Question: * 2.4.10 (was 2.4.30). (0,1) and (2,3) on diameter **** What are the center, radius and equation of the indicated circle?
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Your solution:
Since the center can be determined from the points it is (1,2)
The radius is the distance from (1,2) (0,1) =
Squart (0-1)^2 + (2-1) ^2 = squart 1 + 1 = sqart 2
Equation = (x -2)^2 + (y-1)^2 = 2
020. `* 20
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Question: * 4.2.8 / 2.6.8 (was 2.5.6). graph like basic stretched cubic centered around (20,20)
How well does the graph appear to indicate a linear relation?
Describe any significant deviation of the data from its best-fit linear approximation.
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Your solution:
The graph appears to fit the linear relation
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@& You appear to have submitted the first question from each of a number of Queries.
For the most part your work looks good, as it did when you originally submitted these.
However you need to submit the entire document, inserting your work without deleted anything.
Be sure you've seen all the notes I've posted with your previous submissions. Many of those notes are repetitive, but you need to read them all to be sure you don't miss anything.*@