The second statement is the ___ of the first
1 answer:
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The volume formula for a square or a rectangle, even, is V=l*w*h
Here, we are given our volume as 675, now we just have to find everything else, right?! Well, if you have a square, all 4 sides are the same exact length, so the length and the width of our formula are going to be the same so we only have to worry about finding a value for one and then use it twice. If you have a square of side length x and you cut 2 squares out of each side measuring 3 inches each, you are cutting away 6 inches. So the side now reflects a length of x - 6. Which is used for the length and the width in our formula. The height of the box will be 3 inches, or in other words, what you cut away from each corner to make a box in the first place! So our formula will look like this: 675 = (x - 6)(x - 6)3. Easiest thing to do is to divide away the 3 to get 225 = (x - 6)(x - 6). Now expand that by FOILing:
Set it equal to 0 to solve for x, the length and width of each side by moving the 225 over to the other side:
Now you just have to factor this. When you do, you get x values of 21 and -9. But we all know that you cannot have a side length be a negative number so the x value is 21. That's the side length of the original paper before you cut 6 inches away.
Here, we are given our volume as 675, now we just have to find everything else, right?! Well, if you have a square, all 4 sides are the same exact length, so the length and the width of our formula are going to be the same so we only have to worry about finding a value for one and then use it twice. If you have a square of side length x and you cut 2 squares out of each side measuring 3 inches each, you are cutting away 6 inches. So the side now reflects a length of x - 6. Which is used for the length and the width in our formula. The height of the box will be 3 inches, or in other words, what you cut away from each corner to make a box in the first place! So our formula will look like this: 675 = (x - 6)(x - 6)3. Easiest thing to do is to divide away the 3 to get 225 = (x - 6)(x - 6). Now expand that by FOILing:
Set it equal to 0 to solve for x, the length and width of each side by moving the 225 over to the other side:
Now you just have to factor this. When you do, you get x values of 21 and -9. But we all know that you cannot have a side length be a negative number so the x value is 21. That's the side length of the original paper before you cut 6 inches away.
We look for constants <em>a</em> and <em>b</em> such that
Rewrite all terms with a common denominator and set the numerators equal:
Then
<em>a</em> + 2<em>b</em> = 7
-2<em>a</em> - <em>b</em> = -8
Solve for <em>a</em> and <em>b</em>. Using elimination: multiply the first equation by 2 and add it to the second equation:
2 (<em>a</em> + 2<em>b</em>) + (-2<em>a</em> - <em>b</em>) = 2(7) + (-8)
2<em>a</em> + 4<em>b</em> - 2<em>a</em> - <em>b</em> = 14 - 8
3<em>b</em> = 6
<em>b</em> = 2
Then
<em>a</em> + 2(2) = 7 ==> <em>a</em> = 3
and so