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MariettaO [177]
3 years ago
11

Find two positive numbers whose product is 25 and whose sum is a minimum. (if both values are the same number, enter it into bot

h blanks.)
Mathematics
1 answer:
pshichka [43]3 years ago
4 0
Let xy = 25, x and y > 0.

y = \frac{25}{x}
\text{Denote S as: } x + y
S(x) = x + \frac{25}{x}

\text{Minimum: }S'(x) = 0, S''(x) > 0
S'(x) = 1 - \frac{25}{x^{2}}
1 - \frac{25}{x^{2}} = 0
x^{2} = 25
x = 5 (x > 0)

S''(x) = \frac{50}{x^{3}} > 0, (x > 0)

Thus, at x = 5, there lies a minimum summation, and this forms a square with side length of 5.
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Answer:

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* Vertex form is ...

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The answer is B.) one




Hope this helps :)
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Step-by-step explanation:

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