An open box is formed by cutting squares with side lengths of 3 inches from each corner of a square piece of paper. what is a si
1 answer:
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.
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The period of a sinusoid 
is 
, so any range such that 
will give two complete periods.
Answer:
1 solution
Step-by-step explanation:
Jeremy can simplify the equation enough to determine if the x-coefficient on one side of the equation is the same or different from the x-coefficient on the other side. Here, that simplification is ...
-3x -3 +3x = -3x +3 +3
We see that the x-coefficient on the left is 0; on the right, it is -3. These values are different, so there is one solution.
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In the attached, the left-side expression is called y1; the right-side expression is called y2. The two expressions are equal where the lines they represent intersect. That point of intersection is x=3. (For that value of x, both sides of the equation have a value of -3.)
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<em>Additional comment</em>
If the equation's x-coefficients were the same, we'd have to look at the constants. If they're the same, there are an infinite number of solutions. If they are different, there are no solutions.
