Quiz 1 - JustAnswer



MTH/209 COLLEGE MATHEMATICS II

Week Four σ INDIVIDUAL HW ASSIGNMENT TWO

Name:      

Instructions:

1. Please type your name in the appropriate space above.

2. You may use the “Equation Editor and Graphing Tool” link from the Course Outline at the left of your rEsource page (the “Materials” link on the toolbars near the top of your pages) to download software, OR for many of the problems, you may just type using Word’s top toolbars (from the “Insert” tab above) or use the drawing tools at Word.

3. Write your solution and show supporting work; be sure to show all necessary computations, graphs, etc.

a. You can click on the “File” menu (top left above) or “Office” button (top left above) to save changes as you make them, and then return to the document.

b. Save the HW in a separate file as a Word Doc file. Just name it Ind-HW (number – your name). For example: Ind-HW-1-Jones. Many students make a new folder on their desktops and save their files there. If you want to do this, then this saved file can be moved directly to the new folder. (A complete sequence such as the following could be used: At your desktop, right-click the mouse . . . “New” . . . “Folder” . . . name it and then open it . . . now, back at this document, “File” menu or “Office” button at top left . . . “Save As” . . . “browse” to find your desktop’s folder . . .)

c. Submit your completed assignment through the “Assignments” feature.

Remember that this week’s Individual HW Assignment (worth 7 points) is due by day 6 (which is next Sunday). However, try to complete it as soon as possible so that you won’t be pressed for time. Remember that the software at “Assignments” electronically keeps up with postings’ date/time of submission (and uses Phoenix time).

Be sure to show all necessary computations BELOW each exercise. (You can just hit “Enter” below each given exercise in order to add more spaces in which to work.)

From Ch. 6:

1) Section 6.1, Exercise 44

Which numbers cannot be used in place of the variable in each rational expression?

44 a^2-b^2/ a-b

Set the bottom to 0:

a-b = 0

a = b

So a cannot equal b.

2) Section 6.2, Exercise 24

3/ a^2 + a * 2a+2/6

Multiply the top: 3(2a+2) = 6a+6

Multiply the bottom: (a^2+a)(6) = 6a^2 + 6a

Clear all the 6’s and put it together:

a+1

a^2+a

3) Section 6.3, Exercise 20 Build each rational expression into an equivalent rational expression with the indicated denominator

-7yt/3x= blank/18xyt

Cross multiply:

3x? = -126xy^2t^2

Divide by 3x:

? = -42y^2t^2

(4) Section 6.4, Exercise 40 Perform the indicated operation. Reduce each answer to lowest terms.

[Hint for # 40: Think of 2y as (2y)/(1).]

y/4 =2y

Cross multiply:

8y = y

So y = 0

(5) Section 6.4, Exercise 56

[Hint for # 56: The LCD is (x+1)(x-1).]

3/x+1 + 2/x-1

Get LCD:

3(x-1)/LCD + 2(x+1)/LCD

= (3x∓3+2x+2)/LCD

= (5x+5)/(x^2-1)

(6) Section 6.6, Exercise 30

x/3= 4/x+1

Cross multiply:

x(x+1) = 12

x^2 + x = 12

x^2 + x – 12 = 0

(x+4)(x-3)= 0

So:

X = -4, 3

From Ch. 9:

(7) Section 9.1, Exercise 48 ( below is a screen shot with exercise 48. I don’t know how to write the question?).

[pic]

= sqrt(9*2)

= sqrt(9) * sqrt(2)

= 3 sqrt 2

(8) Section 9.2, Exercise 16 Evaluate each expression. 16. 16 ^1/2

Sqrt(16)

= sqrt(4*4)

= 4

(9) Section 9.3, Exercise 6 Once again here is a screen shot only exercise 6.

[pic]

= 1sqrt5 – 3sqrt5

= (1-3) sqrt 5

= -2 sqrt 5

(10) Section 9.3, Exercise 36 Another screen shot only exercise 36.

[pic]

Multiply:

-12 sqrt 20

Simplify:

-12 sqrt(4*5)

= -12 sqrt(4) * sqrt(5)

= -24 sqrt 5

(11) Section 9.5, Exercise 16 The Even-Root Property- Find all real solutions to each equation.

16. a^2-40=0

Add 40:

a^2 = 40

Square root:

a = +/- sqrt(40)

a = +/- sqrt(4*10)

a = +/- 2 sqrt 10

a = 2 sqrt 10, -2 sqrt 10

From Ch. 10:

(12) Section 10.2, Exercise 10 Solve each equation by using the quadratic formula

10. x^2 + 4x +3 =0

x = (-b +/- sqrt(b^2-4ac)) / (2a)

x = (-4 +/- sqrt(4^2-4*1*3)) / 2

x = (-4 +/- sqrt(4)) / 2

x = (-4 +/- 2) / 2

x = -2 +/- 1

x = -3, -1

Section 6.4: Exercise 90

90. Barn painting. Melanie can paint a certain barn by herself in x days. Her helper Melissa can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for x =5.

Melanie's rate = 1/x

Melissa's rate = 1/(2x)

 

Combined rate = 1/x + 1/(2x)

= 2/2x + 1/2x

= 3/(2x)

 

Total time = 1/rate

= 2x/3

 

With x = 5:

2*5/3 = 10/3 days = 80 hours

Section 9.5 Exercise 116 (I ONLY NEED THE WORK FOR 116)

116. Orbit of Venus. If the average radius of the orbit of Venus is 0.723 AU, then how many years does it take for Venus to complete one orbit of the sun? Use the information in Exercise 115.

Kepler says:

T^2 = R^3

 

Plug in the value of A:

T^2 = 0.723^3

 

Square root:

T = sqrt(0.723^3)

T = about 0.6147626 years

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