God I am SO confused on even where to start and I just gave a big what on this. Teachers are no help, and I don't have any other tools to use to help me solve this stupid take home exam.:bang: Anyway, if any of you guys can give me at least a little bit of assistance that would be extremely helpful to my situation! I'm not asking you guys to do these problems for me, I just need help of any kind since we've never done these problems in class and my professors are Nazis who like to torture us with these. So I'm just gonna show you guys the problems and see if you guys can at least point me in the right direction. 1. A picture framer has a piece of wood that measures one inch wide by 50 inches long. She would like to make a picture frame as shown below, and uses all 50 inches of wood she has. Notice that x and y in our sketch below are the outside dimensions of the frame. So essentially the picture looks like a rectangle with the measurements 1 inch around all sides and it says that the length of the rectangle is Y and the width is X. Alright with that knowledge... A. Write an equation that expresses the required relationship between variables x, y, and the total length of the wood. B. Solve your equation from part (A) for y in terms of x. C. Write an expression (i.e. a function) that gives the interior area of the frame as a function of its exterior height x. D. Find the values of x that make the interior area of the picture frame equal to zero. Explain why this is the case in the context of the picture frame problem. Draw the frames that correspond to these two extreme conditions. E. Use your function to find the inside dimensions that will make this area a maximum. State also the maximum internal area of the picture frame. The second part of it goes like this: Now the picture framer would like to rework this problem for a piece of wood of arbitrary length L. [In PART I, L was 50 inches. Now L becomes a new variable so that we can generalize what we did in PART I for a piece of wood of any arbitrary length, L] A. Write an equation that expresses the required relationship between variables x, y, and the total length of the wood L. In PART I, you had a linear equation of the form ax+by = 50 where a and b were numbers. Now you will have a slightly more complicated equation involving x, y and L, i.e. your equation will have three variables, x, y, and L in it. B. Solve your equation from part (A) for y in terms of x and L. C. Use your answer to part (B) to write an expression (i.e. a function) that gives the interior area of the frame as a function of its exterior height x, and the wood length L. [The variable y will not appear in this equation] D. Use your function to find the inside dimensions that will make this area a maximum. Now each of your inside dimensions will depend on L, i.e. they will be functions of L. Thanks again guys
Re: Math help? I think I learned this, but I can't remember how to do all of it. What grade are you in?
Re: Math help? Your textbook might have examples like the questions on the exam; those might help you figure it out. I can try to help you beyond that (as you can tell by my avatar, math is my thing), but I'd need more information from the picture you described than what you gave. If you could upload it as an attachment in a post, even if it's just a crude MS Paint recreation, I can do my best to lead you in the right direction.
Re: Math help? That's the thing, Owen, we don't use textbooks. The entire class is online and even if I did have a textbook, none of it would be in it. That, I'm sure of. x_x Anywho, the image in part 1 looks like this:
Re: Math help? Being that this is a take-home exam, we can't solve these for you, but we can give you guidance. Now, you know that y is the length of the horizontal pieces, so part of the fifty feet of wood is going to go toward making those two pieces. Whatever is left of the fifty feet after you cut off those two pieces will be split evenly, and those new pieces will become your vertical pieces of the frame. Now, notice that the vertical parts of the frame aren't x tall. X describes the vertical height of the entire frame, but the width of the horizontal pieces gives the height a boost of two inches. So the length of the vertical pieces is x-2. So two pieces are y long, two are x-2 long, and together, those four pieces need to add up to fifty feet. With that information, see if you can do 1a. With an answer to 1a, the way to solving the other parts should become more clear, since those other parts depend on either your answer to 1a or an answer to a question that came before them.
