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Sandhya_sharma, Master's Degree
Category: Math Homework
Satisfied Customers: 3710
Experience:  I hold M.Sc and M.Phil degrees in math and have several years of teaching experience.
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# Math problem help

Math problem help
Hi,

Thanks
Customer: replied 4 years ago.

Ok thanks. I have two questions that I am stuck on.

c and d are defined as

c={w|w<2}

d={w|w is greater than or equal sign to 7}

and

The Lewis family and the Cook family each used their sprinklers last summer. The
water output rate for the Lewis family's sprinkler was
per hour. The water output rate for the Cook family's sprinkler was
per hour. The families used their sprinklers for a combined total of hours, resulting in a total water output of
.
How long was each sprinkler used?

Hi,

Questions didn't appear completely..Numbers didn't appear..

Thanks
Customer: replied 4 years ago.

C and D are defined as

C={w|w<2}

D={w|w the greater than or equal to symbol 7

Write in interval notation.

2. The Lewis family and the Cook family each used their sprinklers last summer. The
water output rate for the Lewis family's sprinkler was 35 L
per hour. The water output rate for the Cook family's sprinkler was 20 L
per hour. The families used their sprinklers for a combined total of 35 hours, resulting in a total water output of 1000 L.
How long was each sprinkler used? By the Cook family? By the Lewis family?

Customer: replied 4 years ago.

What I just sent. There are two questions.

Thanks, XXXXX XXXXX received two questions. I will send answers in 10 minutes.

Thanks
Customer: replied 4 years ago.
Ok thanks.
C and D are defined as
C={w|w<2}
D={w|w the greater than or equal to symbol 7
Write in interval notation.

C={w|w<2}

In interval notation: (-∞, 2)

D={w|w the greater than or equal to symbol 7

In interval notation: [7, ∞)

2. The Lewis family and the Cook family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was 35 L per hour. The water output rate for the Cook family's sprinkler was 20 L
per hour. The families used their sprinklers for a combined total of 35 hours, resulting in a total water output of 1000 L. How long was each sprinkler used? By the Cook family? By the Lewis family?

Solution:
Let Cook family used sprinkler for x hours and Lewis family used for y hours.
The families used their sprinklers for a combined total of 35 hours.
x+y = 35

The water output rate for the Cook family's sprinkler was 20 L per hour. The water output rate for the Lewis family's sprinkler was 35 L per hour.
Total water output of 1000 L.
20x + 35y = 1000

System of equations will be

x+y = 35---------------(i)
20x + 35y = 1000-------(ii)

from (i)

x = 35-y
substitute it in (ii)

20(35-y) + 35y = 1000
700 - 20y + 35y = 1000
700 + 15y = 1000
15y = 300
y = 300/15 = 20

x = 35-y = 35 - 20 = 15

Cook family used sprinkler for 15 hours and Lewis family used for 20 hours

I hope it will help.

Thanks

Sandhya_sharma, Master's Degree
Category: Math Homework
Satisfied Customers: 3710
Experience: I hold M.Sc and M.Phil degrees in math and have several years of teaching experience.
Customer: replied 4 years ago.
Wow you are good. Thank you.
You are most welcome!

Feel free to request me for future questions by writing " For Sandhya".

Customer: replied 4 years ago.
Hi you did a great job earlier. I wanted to know how much is it for 10 problems like the ones done earlier?
Hi,

Sorry for replying late. I was away.

You can decide affordable price for 10 questions by yourself and send questions. Feel free to request me for future questions by writing " For Sandhya".

Customer: replied 4 years ago.
Ok I have to get my questions together. How late will you be on tonight? Will you be on this weekend too? If so what time? I am eastern time zone.
Okay, Thanks

yeah I will remain online tonight. I am available during weekend as well. I am mostly available during your evening and morning time.

I will wait for your questions.

Thanks
Customer: replied 4 years ago.

Hi I have 4 problems that I cant seem to get right?

Hi,

Please post your problems here. I will be happy to assist you.

Thanks
Customer: replied 4 years ago.

Ok thanks again.

1.Graph the solution below and write its solution.

2x+y=4

y=1/3x-3

2.Solve the compound inequality, and graph on the number line.

2x+4 less than or equal to sign -4 or 2x+3 greater than or equal to 5

3. Solve the compound inequality, write the solution in interval notation

4w+5>25 or 3w+1 greater than or equal sign 4

4. Two mechanics worked on a car. The first mechanic worked for 5 hours and the second mechanic worked for 15 hours. Together they charged a total of \$1825. What was the rate charged per hour by each mechanic if the sum of the two rates was \$185 per hour?

Also I wanted to know if an equation is always true does it have a unique solution or an infinite solution?

I will post solutions within 30 minutes.

Thanks again.
Customer: replied 4 years ago.
Ok great.

Hi,

http://www.sendspace.com/file/hjgzev

I hope it will help you. I will be happy to assist you in future.

Thanks again

Customer: replied 4 years ago.
Ok I installed and looked for the download and I do no not see it?

No, you dont need to install anything..

Let me know.

Thanks

Let me know if you are able to download otherwise I will paste solutions here.

Thanks
Customer: replied 4 years ago.

okay..Here are the solutions

1.Graph the solution below and write its solution.
2x+y=4
y=1/3x-3

Take Equation 2x+y=4
----------------------

Put x = 0
2x+y=4
0+y= 4
y = 4

Put x = 2
2x+y=4
2(2)+y= 4
4 + y = 4
y =0

Points will be (0, 4) and (2,0)

Take Equation y=1/3x-3

----------------------
Put x = 0
y=1/3x-3
y=1/3(0)-3
y = -3

Put x = 9
y=1/3x-3
y=1/3(9)-3
y = 3-3
y =0

Points will be (0, -3) and (9,0)

Use these points to plot each line

From the graph, we can note that solution is (3, -2).
Answer: x = 3, y = -2
In ordered pair: (3, -2)

2. Solve the compound inequality, and graph on the number line.
2x+4 ≤ -4 or 2x+3 ≥ 5

2x+4 ≤ -4
2x + 4 + (-4) ≤ -4 + (-4)
2x ≤ -8
Divide by 2
x ≤ -4

2x+3 ≥ 5
2x+3 + (-3)≥ 5+ (-3)
2x ≥ 2
Divide by 2
x ≥ 1

Since there is or between two inequalities so solution will be union of solutions of both inequalities.
In interval notation: (-∞, -4] U [1, ∞)
Graph is shown below:

3. Solve the compound inequality, write the solution in interval notation
4w+5>25 or 3w+1 ≥ 4

4w+5>25
4w+5+(-5)>25+(-5)
4w > 20
Divide by 4
w > 5

3w+1 ≥ 4
3w+1 + (-1)≥ 4+ (-1)
3w ≥ 3
Divide by 3
w ≥ 1

Since there is or between two inequalities so solution will be union of solutions of both inequalities.
Solution will be w ≥ 1.
In interval notation: [1, ∞).

4. Two mechanics worked on a car. The first mechanic worked for 5
hours and the second mechanic worked for 15 hours. Together they charged a
total of \$1825. What was the rate charged per hour by each mechanic if the sum
of the two rates was \$185 per hour?

Solution:

Let x be the rate of first mechanic and y be the rate of second
mechanic

Sum of the two rates was \$185 per hour

x + y = 185

The first mechanic worked for 5 hours and the second mechanic
worked for 15 hours. Together they charged a total of \$1825

5x + 15y = 1825

System of equations will be

x + y = 185-------------(i)

5x + 15y = 1825-------(ii)

From first equation, we will get

x = 185-y

substitute it in (ii)

5(185-y) + 15y = 1825

925 - 5y + 15y = 1825

10y = 1825-925

10y = 900

y = 90

x = 185-y = 185-90 = 95

Rate charged by first mechanic: \$95

Rate charged by second mechanic: \$90

Also I wanted to know if an equation is always true does it have a
unique solution or an infinite solution?

If an equation is always true, it will have infinite number of
solutions.

Example:

2(x-1) = (2x-1) - 1

Sandhya_sharma, Master's Degree
Category: Math Homework
Satisfied Customers: 3710
Experience: I hold M.Sc and M.Phil degrees in math and have several years of teaching experience.
Customer: replied 4 years ago.
Hi I need help with my math assignment. I dont get it.
Hi,

Thanks
Customer: replied 4 years ago.
• Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2 (www.sailing.com). For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function

 a) Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5 feet. b) Solve this formula for d. c) The accompanying graph shows C in terms of d for the Tartan 4100 (b = 13.5). For what displacement is the Tartan 4100 safe for ocean sailing?
• Page 606
• Sailboat speed. The sail area-displacement ratio S provides a measure of the sail power available to drive a boat. For a boat with a displacement of d pounds and a sail area of A square feet S is determined by the function

 a) Find S to the nearest tenth for the Tartan 4100, which has a sail area of 810 square feet and a displacement of 23,245 pounds. b) Write d in terms of A and S.
• Hi,

Thanks
Customer: replied 4 years ago.

I am technology challenged. I can type the formula.

103. 4d^-1/3b

Whats on the graph for 103 is the formula 54d^-1/3b. I guess that is for c for problem 103.

Hi,

Thanks

Customer: replied 4 years ago.

Ok thank you. Were you able to see c for

Customer: replied 4 years ago.

Ok thank you. Were you able to see c for 103?

Sorry here it is:

C = 54d^(-1/3)

To be considered safe for ocean sailing, the capsize screening value C should be less than 2

54d^(-1/3)<2
54/d^(1/3) < 2

54/2 < d^(1/3)

27 < d^(1/3)

27^3 < d

19683 19683

d should be greater than 19683.

I hope it will help.

Thanks
Customer: replied 4 years ago.
Ok great thank you so much. Also I wanted help understanding this problem that I have to turn in today its a^1/2 over a^2. My answer is a^1 or a. I just want to make sure I have it right before i turn it in.

Some parts didn't appear for part (c). here it is again:

C = 54d^(-1/3)

To be considered safe for ocean sailing, the capsize screening value C should be less than 2

54d^(-1/3)<2
54/d^(1/3) < 2

54/2 < d^(1/3)

27 < d^(1/3)

27^3 < d

19683 < d

OR

d >19683

d should be greater than 19683.

(a^(1/2)) / a^2

= 1/(a^(2 - 1/2)

= 1/a^(3/2)

Sandhya_sharma, Master's Degree
Category: Math Homework
Satisfied Customers: 3710
Experience: I hold M.Sc and M.Phil degrees in math and have several years of teaching experience.
Customer: replied 4 years ago.
Oh ok. I am glad I asked. Thank you so much again.
You are most welcome!
Please feel free to request me for future questions.

Thanks
Customer: replied 4 years ago.
Hi I need help with a few math problems please?

Please start a new thread and you can request me by writing my name "Sandhya". You can post your questions there.

Thanks

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