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Roman55 [17]
3 years ago
7

Among all pairs of numbers with a sum of 105 , find the pair whose product is maximum. Write your answers as fractions reduced t

o lowest terms.
Mathematics
1 answer:
Bond [772]3 years ago
8 0

Answer: Hence Pair( x, y) = [ 105/2, 105/2]

Step-by-step explanation:

Given that;

Among all pairs of numbers with a sum of 105;

the pair whose product is maximum = ?

so let pairs of numbers with a sum of 105 be x and y respectively

x + y = 105

let y = 105 - x

now

product = xy =  x( 105 - x ) = 105x - x²

now

p(x) = 105x - x²

for maximum value of p

dp/dx =0

⇒ dp/dx = 105 - 2x = 0

2x = 105

x = 105/2

y + x = 105

y = 105 - x

y = 105 - 105/2 = 105/2

Hence Pair( x, y) = [ 105/2, 105/2]

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Answer:

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Step-by-step explanation:

The question requires that the equation should be in the slope-intercept form y = m \, x + c. The m and c in this equation are constants. In particular:

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The question states that the slope of this line is (-3). Therefore, m = -3. Thus, the equation for this line should be in the form y = (-3)\, x + c.

The value of constant c could be found using the other piece of information: the point (3,\, 1) is in this line. In other words, the solution \text{$x = 3$ and $y = 1$} should satisfy the equation y = (-3)\, x + c.

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