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Sauron [17]
4 years ago
10

Which expression can be written as k square root 3 where k is an integer

Mathematics
1 answer:
Damm [24]4 years ago
8 0

Answer:

A simple expression is \sqrt{48} = 4\sqrt{3}

Step-by-step explanation:

Surds are irrational numbers expressed with respect to a square root. There are some basic rules required when dealing with surd.

Integers are numbers that do not have a decimal or fractional part i.e whole numbers. So, a simple expression that can be written as k square root 3 where k is an integer is \sqrt{48}.

So that,

                            \sqrt{48} = \sqrt{16 * 3}

                                   = 4\sqrt{3}

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a manufacturer has determined that if his company sells x items per day then their profit is given by P=-x^2+ 700 x-10000 euros.
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Answer:

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Step-by-step explanation:

To find the minimum amount of items, x, that need to be sold for the manufacturer to make a profit, we can use the quadratic formula

x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}; x=  \frac{-b-\sqrt{b^{2}-4ac } }{2a}

x= \frac{-700+\sqrt{700^{2}-4(a)(-10000) } }{2(1)}; x= \frac{-700-\sqrt{700^{2}-4(a)(-10000) } }{2(1)}

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In context of the problem, we can only rely on the positive value, as the negative value would lead to a loss of profit.

(-714.005)^2+700(-714.005)-10000=-0.360

Furthermore, we must round to the nearest whole number, as you cannot make part of an item.

Lastly, if you were to plug in 14 into the equation for Profit, you would still have a negative number (i.e. a negative profit), thus requiring the manufacturer to make no less than 15 items to make a profit:

(14)^2+700(14)-10000=-4\\\\(15)^2+700(15)-10000=725

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Step-by-step explanation:

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