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(a) is right... checking (b) now
b looks right, although it's hard to read the bottom. But you set it up right.. break even is when Profit = 0, so you set P(x) = 0 and use quadratic formula to solve for x
The bottom says 16 bags of gravel that must be sold to break even.
you found 15.stuff, right? But you can't sell a partial bag, so round up to 16 bags
Yes, it was 15.15 or 464.95
prob 2a looks right. I don't think you quite have it for 2b, although you have the roots correct
why does it have a vert asymptote? (not saying you're wrong, just asking) also, those solutions are places the curve crosses the x axis. You didn't say something contradictory, but just wanted you to be clear that knowing those solutions means you know places it crosses the x axis
I didn't really understand this question so since vertical asymptotes are x's, I just listed those. What would be the correct answer?
I don't think there are asymptotes at all. Check out this graph of the function: http://www.wolframalpha.com/input/?i=f%28x%29%3Dx^3%2B2x^2-35x
see how it crosses the x axis in 3 places? Those 3 places are the roots you found by factoring... sometimes they are called "zeros" because it's places the function value is zero
A cubed level function may have 3 distinct roots like this one does. f(x) = x^3 has just 1 distinct root, x=0 A squared function might have 2 roots (parabola starting below x axis, facing up, crosses in 2 points) or maybe just 1 (parabola at the origin)
So for 2(b), would I just write, "The three places where the graph crosses the x-axis are the roots found by factoring. Sometimes, they are called "zeros" because the function value is zero."?
you don't have to put in the zeros stuff... that's just bonus knowledge for you :) I would answer by saying "these solutions show that the graph of the function f(x) crosses the x-axis at x=-7, x=0, and x=5"
Okay :) And for 1(b), the answers were 15.15 or 464.85. So wouldn't the answer be "15 bags of gravel" rather than 16?
Why? I guess it's an interpretation thing... mathematically, breakeven is precisely the point at which P(x) = 0, but in the real world, I would think a business person would want to know the minimum number of bags that have to be sold to avoid losing money. If that number turns out to be an x where P(x) is exactly 0, that's fine. But here, if you stop after selling 15 bags, you will lose money because P(15) < 0. P(16) > 0, but at least you didn't lose money.
But wouldn't 15.15 round to 15 rather than 16?
it would round, yes... but I think you either need to answer with the unrounded number of 15.15 and point out that it is a fractional number of bags, or that you need to round up to the next larger number of bags. If I asked to buy ONLY 15 bags, you would lose money. You NEED to sell 15.15 bags to break even, and unless you can sell that extra 0.15 bag to exactly break even, you are really going to want to sell the whole extra bag, for 16 total, to avoid losing money.
Oh, okay, I understand now.
IF this wasn't a word problem with profit, but just a math problem, then P(x) = 0 when x = 15.15 and you're done
Can you check two more problems for me?
But they are trying to make you think about how the math relates to real worlds situations, so I think you need to play along :)
I can check... gotta run in a few minutes but I will try it till then. Maybe close this question and post them in a new question?
(less scrolling :) )