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stepladder [879]
3 years ago
9

Determine if the equation defines y as a function of x: 2xy=1

Mathematics
1 answer:
Leona [35]3 years ago
3 0
Solve for y...

2xy=1

y=1/(2x)

So this is a function as each x value (with the exception of x=0) produces just one value for y.  However, technically there is a vertical asymptote about the vertical line x=0.  So there is a discontinuity as x=0.

I say this technically, because most would say that this function is true even with the discontinuity (as they do with say y=tana), but technically the discontinuity makes this not a function because another requirement of a function is for their to be an actual output value for each input value.  In this case division by zero when x=0 is undefined and cannot be included as part of a function.  So if you are picky about being absolute, 2xy=1 is really two functions.  One with a domain of (-oo,0) and another with a domain of (0,+oo).
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Answer:

The maximum cost is 41 dollars per necklace.

Step-by-step explanation:

The average cost in dollars/necklace is given by :

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Where

x is the number of necklaces that are created

To maximize the cost, find the value of x by putting dC/dx = 0

\dfrac{d}{dx}(0.5x^2-7x+65.5)=0\\\\x-7=0\\\\x=7

Now put the value of x = 7 in equation (1).

C(x)=0.5(7)^2-7(7)+65.5\\\\=41\ \text{dollars per necklace}

Hence, the maximum cost is 41 dollars per necklace.

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Step-by-step explanation:

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Answer:

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