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trapecia [35]
2 years ago
10

The back of Tom's property is a creek. Tom would like to enclose a rectangular area, using the creek as one side and fencing

Mathematics
1 answer:
Anna71 [15]2 years ago
8 0

9514 1404 393

Answer:

  1250 square feet

Step-by-step explanation:

If x is the length of the side perpendicular to the creek, then the third side is (100 -2x) = 2(50 -x). The area is the product of length and width:

  A = x(2)(50-x)

We observe that this is a quadratic function with zeros at x=0 and x=50. The vertex (maximum) of a quadratic function is on the line of symmetry, halfway between the zeros. The value of x there is (0 +50)/2 = 25.

Then the maximum area is ...

  A = (25)(2)(50 -25) = 1250 . . . . square feet

_____

<em>Additional comment</em>

Note that half the length of the fence is used in one direction (parallel to the creek), and half is used in the other direction (perpendicular to the creek). This 50/50 split is the generic solution to all sorts of rectangular corral problems, with or without a creek, with or without internal partitions.

Half the fence is perpendicular to the other half. (If the costs are different in different directions, then the cost is what is split 50/50.)

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MrRa [10]

Answer:

Step-by-step explanation:

Rational Root Theorem: If the polynomial

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Example: F(x) = 4x² + 5x +2

If this polynomial has any rational roots, then they must be (factors of 2)/(factors of 4), so (±1, ±2)/(±1, ±2, ±4). So if this polynomial has any rational roots, they must be either: ±1, ±1/2, ±1/4, or ±2. Notice that this polynomial doesn't have to have any rational roots, but if it does, then the roots must fit the Rational Root Theorem.

Descartes' Rules of Signs:

a). In a polynomial, how many time the sign changes is how many positive roots the polynomial will have.

Example: 5x³ + 6x² - 2x - 1

In this expression, the sign only changed once, between 6x² and 2x, so it will only have one positive root.

Example 2: 6x³ - 4x² + x - 6

In this expression, the sign changed 3 times (remember there is a invisible "+" sign before the 6x³), so it will have 3 positive roots.

b). In a polynomial, if you plug in "-x" for all "x", then how many times the new polynomial changes sign is how many negative roots the old polynomial have.

Example: 5x³ + 6x² - 2x - 1.

If we plug in "-x" for all "x", then we get 5(-x)³ + 6(-x)² - 2(-x) -1, which simplifies to -5x³ + 6x² + 2x -1. In this new expression, the sign changed twice, so we have two negative roots for the expression. Notice how we got one positive root the first time and two negative roots the second time, and 1 + 2 = 3. The Fundamental Theorem of Algebra states that for a nth degree polynomial, it will have n complex roots. The polynomial we worked with was a 3rd degree polynomial, and we got 1 + 2 = 3 roots in the end.

4 0
3 years ago
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Answer:

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Step-by-step explanation:

Let the entry cost be y

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So, 5x+y=15.50 --- A

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So, 12x+y=26 -- B

Plot the lines

5x+y=15.50 --- Black color

12x+y=26  --- Red color

Intersection point provides the solution

(x,y)=(1.5,8)

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3 years ago
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8 0
3 years ago
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xeze [42]

Answer:

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Step-by-step explanation:

To find the inverse, interchange the variables and solve for  

y .

I hope this helps.

8 0
3 years ago
Read 2 more answers
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