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masya89 [10]
3 years ago
11

The sum of two positive numbers is 12. what two numbers will maximize the product g

Mathematics
1 answer:
son4ous [18]3 years ago
4 0

Given two numbers x and y such that:

x + y = 12   ...    (1)


<span>two numbers will maximize the product g</span>

from  equation (1) 

y = 12 - x  

Using this value of y, we represent xy as

xy = f(x)= x(12 - x)

 f(x) = 12x - x^2

Differentiating the above function:

f'(x) = 12 - 2x

Maximum value of f(x) occurs at point for which f'(x) = 0.

Equating f'(x) to 0 we get:

12 - 2x = 0

 2x =  12

> x = 12/2 = 6

Substituting this value of x in equation (2):

y = 12 - 6 = 6

Therefore, value of xy is maximum when:

x = 6 and y = 6

The maximum value of xy = 6*6 = 36

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Suppose there are two lakes located on a stream. Clean water flows into the first lake, then the water from the first lake flows
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a.  For the first lake;

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c = m·t/200 - m·t²/80000

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Step-by-step explanation:

The flow rate of water in and out of the lakes = 500 liters/hour

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The volume of water in the second lake = 200 thousand liters

The mass of toxic substances that entered into the first lake =  500 kg

The concentration of toxic substance in the first lake = m₁/(100000)

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c = m/100000 × 500 × t - (m/100000 × 500 × t)/200000 × 500 × t

Using an online tool, we have;

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