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Tema [17]
3 years ago
6

What is the simplest form of root 3.025

Mathematics
1 answer:
Andreyy893 years ago
3 0
Answer: √3025

Explanation:

1) By convention if you do not mention the index of the root it is square root.

2) By definition the square root of a number x is the numberwhose square is the original number, i.e.

√3025 = 55 because 55^2 = 3025.

3) 3025 is a perfect square because it is the square of a whole numbe.

4) It is easy to find the square root of a perfect square, but if the number is not easily reknownm as a perfect square you will have to probe with several numbers until finding the square root.

For example, you might easily realize that 50^2 is 2500, and that 60^2 is 3600, so you start testing numbers greater thatn 50 and less than 60 until you get 55^2 = 3025.

5) How can you simplify a radical? If you know the properties of radicals you can simplify a radical easily.

You start by decomposing 3025 into its prime factors.

That will result into:

3025 =5^2{11}^2

Then, by radical properties:

\sqrt{5^2{11}^2} = \sqrt{5^2}  \sqrt{{11}^2} =(5)(11)=(55)

So, the simplest form of √3025 is 55.
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Answer:

a) P(c) = xc² + yc + z, and P(.15) = $124, P(.05) = 0, P(.17) = 0. Thus:

(#1) .0225x + .15y + z = 124

(#2) .0025x + .05y + z = 0

(#3) .0289x + .17y + z = 0

Subtracting #2 from #3: (#4) .0264x + .12y = 0

Subtracting #2 from #3: (#5) .02x + .1y = 124

Subtracting 1.2×#5 from #4: .0024x = -148.8 → x= -62000

Using this value of x in #5: -1240 + .1y = 124 → y = 13640

Using x and y in #1: -1395 + 2046 + z = 124 → z = -527

P(c) = -62000c² + 13640c - 527

b) To find the maximum of P(c), find a such that P'(a) = 0

-124000c + 13640 = 0

c = .11

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