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Math Help - i have four math problems i have been struggling with for a while now

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    Question i have four math problems i have been struggling with for a while now

    Questions 1,2: using rational theorem + descartes's rule of sign to determine possible rational & real zeroes. find all zeroes & express the polynomial as a product of linear factors. sketch the graph of the function, indicating all intercepts. estimate turning points.
    1. f(x) = 3x^3 + 2x^2 - 19x + 6
    2. f(x) = X^4 - 3x^3 + 6x^2 - 12x + 8

    Question 3: a company manufactures scooters and estimates profit depending on advertising expenses using the function: f(x) = -.25x^2 + 20x + 100
    what expense in advertising will yield the maximum profit? what would the profit be?

    Question 4: i could not past the graph on this problem i hope that does not cause any problems.
    the graph above indicates the recent anticipated rise in global precipitation as greenhouse gases increase over time. selecting the coordinates (200,2) and (2050,4), write a linear function that would enable us to predict the % increase by 2150.

    again it is greatly appreciated to all you are willing to help me with these four questions.
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  2. #2
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    Quote Originally Posted by jiozzio View Post
    Questions 1,2: using rational theorem + descartes's rule of sign to determine possible rational & real zeroes. find all zeroes & express the polynomial as a product of linear factors. sketch the graph of the function, indicating all intercepts. estimate turning points.
    1. f(x) = 3x^3 + 2x^2 - 19x + 6
    Descarte's rule of signs say that this either 0 or 2 positive roots and one negative root. The "rational root theorem" tells you that the only possible rational roots are \pm 1 and \pm 2. Have you tried those?

    2. f(x) = X^4 - 3x^3 + 6x^2 - 12x + 8
    Descarte's rule of signs tells you that this has no negative roots. The "rational root theorem" tells you that any roots must be 1, 2, 4, or 8. Try them.

    Question 3: a company manufactures scooters and estimates profit depending on advertising expenses using the function: f(x) = -.25x^2 + 20x + 100
    what expense in advertising will yield the maximum profit? what would the profit be?
    f(x)= -.25(x^2- 80x)+ 100. 80/2= 40 and 40^2= 1600 so, completing the square, f(x)= -.25(x^2- 80x+ 1600- 1600)+ 100= -.25(x^2- 80x+ 1600)+ 400+ 100= -.25(x- 40)^2+ 500.

    Since a square is never negative but multiplying by -.25 means -.25(x- 40)^2 is never positive, that is always "500 minus something". It will never be larger than 500 but will be equal to 500 when x= 40.

    Question 4: i could not past the graph on this problem i hope that does not cause any problems.
    the graph above indicates the recent anticipated rise in global precipitation as greenhouse gases increase over time. selecting the coordinates (200,2) and (2050,4), write a linear function that would enable us to predict the % increase by 2150.
    Those look like years. I am going to assume that "200" was supposed to be "2000". A linear function is of the form y= ax+ b. Since it passes through (2000, 2), x= 2000, y= 2 satisfies that equation. Since it passes through (2050, 4), x= 2050, y= 4 satisfies that equation.

    That means we have 2= 2000a+ b and 4= 2050a+ b. Solve those equations for a and b (subtracting one equation from the other immediately eliminates b). Once you have found a and b, evaluate ax+ b for x= 2150.

    again it is greatly appreciated to all you are willing to help me with these four questions.
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