course Mth 158
I e-mailed you yesterday about taking my first test and was wondering if you are recieving my e-mails, or perhaps you have not had a chance to respond. I was just making sure my e-mail is working because I e-mailed you at least twice about trying to get the Query program to work and you never responded. Thanks.
Assignment 9, Chapter R Review
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List the numbers in the set that are a) Natural numbers b)Integers c)Rational numbers d)Irrational numbers e)Real numbers
1.A= {-10, 0.65, 1.343434…, square root of 7, 1/9}
a)natural numbers- none b)Integers- -10 c)Rational numbers- -10, 0.65, 1.343434, 1/9
d)Irrational- square root of 7 e) real numbers- -10, 0.65, 1.343434, square root of 7, 1/9
Evaluate each expression
3. –6+4*(8-3)= -6+4*5= -6+20= 14 6.5/18 / 11/27= 5/18*27/11= 135/198= 15/22
Use the Distributive Property to remove the parentheses.
9. 4(x-3)= 4x-12
Graph the numbers x on the real number line
12. x less than or equal to 5 , the line starts at 5 and goes towards the left
Evaluate each expression if x=-5 and y=7
15. 4x/x+y= 4(-5)/-5+7= -20/2=-10 18. 2x^2y^-2= 2(5)^2(7)^-2= 2*(25)*(49)= 2450
Determine the domain of the variable.
21. 3/ x-6= Domain= {x/x not equal to 6}
Simplify each expression. All exponents must be positive. Assume that x > 0 and y > 0, when they appear.
24. square root of 75= square root of 25*3= 5 square root of 3
27. 5 square root of 8 – 2 square root of 32= 5 square root of 4*2 – 2 square root of 16*2= 10 square root of 2 – 8 square root of 2= 2 square root of 2
30. (x^2 y^2 / x^-1)^2= x^4 y^4 / x^1= x^3 y^4
33. Use a calculator to evaluate (1.5)^4= 5.0625
36. Write 3.275*10^5 as an integer= 327,500
Perform the indicated operation.
39. (2x+1) (3x-5)= 6x^2-10x+3x-5= 6x^2-7x-5
42. (5x+2) (5x+2)= 25x^2+10x+10x+4= 25x^2+10x+4
Find the quotient and remainder.
45. 3x^3-x^2+x+4 divided by x-3 = _3x^2+8x+25
x-3 / 3x^3-x^2+x+4
- 3x^3-9x^2
8x^2+x+4
- 8x^2-24x
25x+4
- 25x+79= 79 Answer: 3x^2+8x+25
Factor each polynomial completely (over the integers). If the polynomial cannot be factored, say it is prime.
51. x^2+5x-14= (x+7) (x-2)
54. 6x^2+x-2= (3x+2) (2x-1)
57. 8x^3+1= (2x^3+1^3= (2x+1) ((2x)^2-(2x) (1)+1^2)= (2x+1) (4x^2-2x+1)
60. 2x^3+3x^2+2x+3= x^2(2x+3)+(2x+3)= (2x+3) (x^2+1)= (2x+3) (x+1) (x-1)
63. 9x^2+1= prime
66. 4x^2+12x+9= (2x+3) (2x+3)
Perform the indicated operation and simplify. Leave your answer in factored form.
69. 9x^2-1 / x^2-9= 9x^2-1 / x^2-9 * 3x-9 / 9x^2+6x+1= (3x+1) (3x-1) / (x-3) (x+3) * 3(x-3) / (3x+1)^2= 3(3x-1) / x+3 (3x+1)
72. x / x+1 – 2x / x+2= x/x+1 * x+2/x+2 – x+1/x+1 * 2x/x+2= x^2+2x-2x^2+2x/ (x+1) (x+2)= -x^2+4x/ (x+1) (x+2)
75. x^2-1/x^2-5x+6 / x+1/x-2= x^2-1/x^2-5x+6 * x-2/x+1= (x-1) (x+1)/ (x-3) (x-2) * x-2/x+1= x-1/ x-3
Simplify each expression.
78. square root of 2x, square root of 5xy^3/ square root of 10y , x is greater than or equal to 0 and y is greater than y
square root of 2x, square root of 5xy^3/ square root of 10y * square root of 10y/ square root of 10y= square root of 2x * square root of 5xy^3 * square root of 10y/ square root of 100y^2= square root of 2x * square root of 5xy^3 * square root of 10y/ 10y
Rationalize the denominator of each expression
81. 4/ square root of 5= 4/ square root of 5 * square root of 5/ square root of 5= 4 square root of 5 / square root of 25= 4 square root of 5/ 5
84. –4/ 1+ square root of 3= -4/ 1 + square root of 3 * 1- square root of 3/ 1- square root of 3= -4+ square root of 3/ 1- square root of 9= -4+ square root of 3/ 1-3= -4+square root of 3/ -2= 2+ square root of 3
Write each expression as a single quotient in which only positive exponents and / or radicals appear.
87. (2+x^2)^1/2+x*1/2(2+x^2)^-1/2*2x= (2+x^2)^1/2+ 2x^2/ 2(2+x^2)^1/2= (2+x^2)^1/2+ x^2/(2+x^2)^1/2= (2+x^2)^1/2+(2+x^2)^1/2+x^2/ (2+x^2)^1/2= 2+x^2+x^2/ (2+x^2)^1/2= 2+2x^2/ (2+x^2)^1/2= 2(1+x^2)/ (2+x^2)^1/2
90. (x^2+4)^1/2*2x-x^2*1/2(x^2+4)^-1/2*2x / x^2+4= (x^2+4)^1/2*4x-x^2/ 2(x^2+4)^1/2 / x^2+4= 2(x^2+4)^1/2(x^2+4)^1/2*4x-x^2/ 2(x^2+4)^1/2 / x^2+4= 2(x^2+4)*4x^2-x^2/ 2(x^2+4)^1/2 / x^2+4= 2x^2+8*3x^2/ 2(x^2+4)^1/2 / x^2+4= 6x^4+8/ 2(x^2+4)^1/2 / x^2+4= 6x^4+8/ 2(x^2+4)^1/2 * 1/ x^2+4= 6x^4+8/ 2(x^2+4)^3/2= 2(3x^4+4)/ 2(x^2+4)^3/2= 3x^4+4/ x^2+4^3/2
Factor each expression
93. 3(x^2+4)^4/3+x*4(x^2+4)^1/3*2x= (x^2+4)^1/3 [3(x^2+4)+8x^2]= (x^2+4)^1/3 (11x^2+12) 96. Find the hypotenuse of a right triangle whose legs are of lengths 5 and 8. a^2+b^2=c^2….5^2+8^2=c^2……..25+64=c^2…….Answer: aprox. 9.43
99.Quaterly Corporate Earnings: In the first quarter of its fiscal year, a company posted earnings of $1.20 per share. During the second and third quarters, it posted losses of $0.75 per share and $0.30 per share, respectively. In the fourth quarter, it earned a modest $0.20 per share. What were the annual earnings per share of this company?
1.20-0.75-0.30+0.20=$0.35 per share
102. A statue with a circular base of radius 3 feet is enclosed by a circular pond as shown in the illustration. What is the surface area of the pond? How much fence is required to enclose the pond?
Surface area of pond= pi*r^2= pi*5^2=pi*25= 78.5
How much fence is required is by taking the area of the circular base in the pond and the area of the pond. The area of the circular base in the pond is 28.3 feet, when using the formula pi*r^2, and substituting 3 feet in for r, and squaring it. The area of the pool is 12.6 feet, when using the formula pi*r^2, and substituting 5 feet in for r, and squaring it. Adding the two areas together you get 154.7 feet, the amount of fence needed to enclose the pond.
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Your formatting is not such that I can easily read the details. I could scan your work more accurately if you would use correct 'typewriter' notation (e.g., being sure to group numerators and denominators, etc.). Also since it's easier to scan down a page than across, you should not put multiply problems on a single line, and a multi-step problem should usually be done with each step on its own line. A statement like 'square root of 10y' should be written sqrt(10y).
I have in any case looked at a good portion of your work and see no overall difficulties. Let me know if you have specific questions.