Problem solving with quadratic functions.

AI Thread Summary
The discussion focuses on a problem involving the relationship between the selling price per bushel (p) and the number of acres planted (q) by an Illinois farmer. It establishes that if p is $10, then 2000 acres will be planted, while at $6.25, only 800 acres will be planted. The user initially misapplies the linear relationship, calculating the slope incorrectly and confusing the variables. After clarification, it is emphasized that p should be treated as the independent variable (x) and q as the dependent variable (y), leading to a correct understanding of the problem. The conversation highlights the importance of correctly identifying independent and dependent variables in quadratic function problems.
davie08
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Homework Statement


okay I know understand that I should get a reasonable understanding about the questions I post before I post them sorry about before.

An Illinois farmer will plant from 800 to 2000 acres of soybeans. The number of acres q that he will plant depends on the selling price per bushel p that is being paid in April. Suppose that if p=$10, then all 2000 acres will be planted, but if p=$6.25, then only 800 acres will be planted.

a)Assuming p and q are linearly related, find q as a function of p, giving a suitable domain.


Homework Equations





The Attempt at a Solution



for some reason this question seems to work out to be the opposite of what I've been doing with my other word problems, here's what I tried.

(2000,10) and (800,6.25)


m=6.25-10/800-2000 = .003125

q-q1 = m(p-p1)

q-2000 = .003125(p-10)

q-2000 = .003125p - .03125

q= .003125p + 1999.96875 800<q<2000


so this is the wrong answer and to get the right answer I have to make p my x and q my y. Then for the domain you find what it is for price.

But I just saw a tutor and she has it on a formula sheet that x=q and p=y.
 
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davie08 said:
The number of acres q that he will plant depends on the selling price per bushel p

the clue here is "depends". Since q depends on p, p is the independent variable, which is always x.
 
okay thanks that makes sense.
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

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