Volume problem... (2 Viewers)
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Nooblet94
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Firstly, that is a shockingly worded question. Doesn't even define what x, y or h are and then specifies that your answer has to be functions of x and y in terms of h.hey guys, I stuck in this volume question. I don't even understand what is it talking aboutplease help me with part a.
any help would be appreciated.
thanks in advanceView attachment 25314
Basically, there's a linear relationship between h (the height) and x or y (length and width respectively), so you can write x and y in terms of h, i.e. x(h)=ah+b, y(h)=ch+d. Now you can substitute in the values you've been given. When the height is 0, i.e. at the base, the dimensions are 8 by 5 and when the height is 10 the dimensions are 4 by 3. Substitute those values into the equations for x and y and you'll get the answer.
I still don't get it...I'm sorry, but can you say it in more detail please? can't determine where is x/y :s
D94
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1. You are given a prism. You need to find the equations that form the shape of the prism. These two equations are linear, as one would expect. A linear equation is represented as y = mx + b.
2. We can also represent these two linear equations with parameters length (L), width (w), height (h).
3. So, we have L = hm + b, and, w = hm + c. (b and c are constants).
4. If we let the height (h) = 0, then the length = 8 (ie. the base length). Substituting this into the equation, we get L = hm + 8.
5. Then, if we let the height = 10, the length = 4. Again, substituting this into the equation, we now get the gradient, which is -2/5, as expected. We now have the linear equation, L = -2/5. h + 8.
6. We apply this same method for the width. Note that I've let x(h) = L and y(h) = W. It just makes it easier to understand.
7. So, for the next part, we need to find the volume of the prism with respect to the height (h). We then multiply the Length by the Width by the Height.
8. The Length is -2h/5 + 8, the Width is -h/5 + 5, and the Height is dh (like dx in functions of x) as we are taking rectangular slices, with limits from 0 to 10.
9. Remember to integrate with respect to h, then it's just like a normal integral.
10. The end.
2. We can also represent these two linear equations with parameters length (L), width (w), height (h).
3. So, we have L = hm + b, and, w = hm + c. (b and c are constants).
4. If we let the height (h) = 0, then the length = 8 (ie. the base length). Substituting this into the equation, we get L = hm + 8.
5. Then, if we let the height = 10, the length = 4. Again, substituting this into the equation, we now get the gradient, which is -2/5, as expected. We now have the linear equation, L = -2/5. h + 8.
6. We apply this same method for the width. Note that I've let x(h) = L and y(h) = W. It just makes it easier to understand.
7. So, for the next part, we need to find the volume of the prism with respect to the height (h). We then multiply the Length by the Width by the Height.
8. The Length is -2h/5 + 8, the Width is -h/5 + 5, and the Height is dh (like dx in functions of x) as we are taking rectangular slices, with limits from 0 to 10.
9. Remember to integrate with respect to h, then it's just like a normal integral.
10. The end.