i need help with these probelms?

1.) A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the equation P = -25x2 + 350x. What number of clerks will maximize the profit?

2.) Jason plans to fence a rectangular area with 140 meters of fencing. He has written the formula A = w(70 - w) to express the area in terms of the width w. What is the maximum possible area enclosed with his fencing?

3.) The sum of the squares of two consecutive integers is 25. Find the integers. Type either of the integers (but only one) as your answer.

4.) Find the larger of two positive real numbers that differ by 3 and have a product of 9.

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  • 8 years ago
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    1. P = -25x^2 + 350x

    x = -b/2a

    a = -25, b= 350

    x = -(350)/(2)(-25)

    x = -350/-50

    x = 7

    thus, the number of clerks that will maximize the profit is 7

    2. A = w(70 - w)

    A = 70w - w^2

    A = -w^2 + 70w

    A = -(w^2 - 70 w)

    A = -(w^2 - 70w + 1225) + 1225

    A = -(w - 35)^2 + 1225

    thus, the maximum possible area enclosed with his fencing is 1225 m^2

    3. let x = be the first integer

    x+1 = be the 2nd integer

    x^2 + (x+1)^2 = 25

    x^2 + x^2 + 2x + 1 = 25

    2x^2 + 2x +1 - 25 = 0

    2x^2 + 2x - 24= 0

    2(x^2 + x - 12) = 0

    x^2 + x - 12 = 0

    (x + 4)(x - 3) = 0

    x+4 = 0, . . x -3 = 0

    x = -4, . . x = 3

    the integers are: -4 and -3

    or 3 and 4

    hence, the integers are 3 and 4 . . .

    4. let x = be the first number

    x - 3= be the second number

    so,

    x(x-3) = 9

    x^2 - 3x = 9

    x^2 - 3x - 9 = 0

    (x - 4.85)(x + 1.85) =0

    hence, the larger number is 4.85. ..

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