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Good morning or good afternoon, Need to see if you can do…

Good morning or good afternoon, Need...
Good morning or good afternoon,
Need to see if you can do 4 different question for me:
word problem
1. While finding the amount of seed needed to plant his three square wheat field, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and that the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kilometers, then what is the area of each field?
(show how the problem is solved )

2. How is the following problem solved using factorization?
The sum of the squares of two consecutive integers is 13. Find the integers.
(need to show how the problem is solved and worked out.)

3. write and solve a problem that address the solution of rational equations.

4. Write and solve a problem that address the simplification of rational expressions.

Would like to have these as soon as you can get to them, please let me know if you can do them for me, not saying that you can not do them, but you know what I mean.

Thanks,
Nena
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Answered in 16 minutes by:
6/24/2010
Scott
Scott, MIT Graduate
Category: Math Homework
Satisfied Customers: 17,710
Experience: Over 13,000 accepts & 100% feedback in the old math category
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Hi there,

 

1. While finding the amount of seed needed to plant his three square wheat field, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and that the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kilometers, then what is the area of each field? (show how the problem is solved )

Call the lengths:

x, x+1, and x+3

Set up an equation:

x^2 + (x+1)^2 + (x+3)^2 = 38

Expand the terms:

x^2 + x^2 + 2x + 1 + x^2 + 6x + 9 = 38

Simplify:

3x^2 + 8x + 10 = 38

3x^2 + 8x - 28 = 0

Factor:

(x-2)(3x+14) = 0

So:

x = 2 or -14/3

It can't be negative, so x = 2.

The lengths are 2, 3, 5

The areas are:

4 sq km, 9 sq km, 25 sq km

 

2. How is the following problem solved using factorization? The sum of the squares of two consecutive integers is 13. Find the integers. (need to show how the problem is solved and worked out.)

The numbers are x and x+1:

x^2 + (x+1)^2 = 13

Simplify:

x^2 + x^2 + 2x + 1 = 13

2x^2 + 2x - 12 = 0

x^2 + x - 6 = 0

Factor:

(x+3)(x-2) = 0

So:

x = -3 or 2

There are two pairs of solutions:

-3 and -2

2 and 3

 

3. write and solve a problem that address the solution of rational equations.

3/x - x/3 = 0

 

Solution:

Multiply through by x:

3 - x^2/3 = 0

Multiply by 3:

9 - x^2 = 0

Add x^2:

x^2 = 9

So:

x = +/- sqrt(9)

x = 3 or -3

 

4. Write and solve a problem that address the simplification of rational expressions.

(3m^2 + 3m)/(9m^2 + 3m)

We can simplify by canceling out 3m from all the terms:

(m + 1) / (3m + 1)

 

Let me know if you have any questions,
Scott

Scott
Scott, MIT Graduate
Category: Math Homework
Satisfied Customers: 17,710
Experience: Over 13,000 accepts & 100% feedback in the old math category
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Scott and 87 other Math Homework Specialists are ready to help you
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Customer reply replied 8 years ago

Thanks a million, will talk to you later, will need some help later on.

 

Thanks,

Nena

Sure thing! Don't forget to put "For Scott" if you want to be sure to get me. I only answered this because I clicked on it before anyone else -- it was first come first serve :)

Thanks again,

-Scott

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