If Molleigh had 40 apples and she had to have 2 times the she would have?
1 answer:
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The volume of a box like this is found by multiplying the length times the width times the height. We are told that the length is 8 more inches than the width, so the width is w and the length is w + 8. If we cut away 3 square inches from each corner, the height when we fold up those corners is going to be 3. The volume is given as 27, so our formula looks like this: 
. When we do that multiplication, we have 
. We need to solve for w so we can then solve for h. Move the 27 over and set the quadratic equal to 0. 
. We can then factor out a 3 to make the job easier: 
. Now we can factor to solve for w. The 2 numbers that add up to 8 and multiply to -9 are 9 and -1. So (w+9) = 0, (w-1) = 0, or 3 = 0. Of course 3 doesn't equal 0, so that's out. w + 9 = 0 so w = -9. w - 1 = 0 so w = 1. There are 2 things in math that can never EVER be negative and those are time and distance/length. So -9 is out. That means that w = 1. But don't forget that there was 6 inches cut off each side, so the width is 1 + 3 + 3 which is 7. The length is w + 8 which means that the length is 7 + 8 or 15. Those are the dimensions of the rectangle before it was cut.
Answer:
Explanation:
1) Charges are:
Flat fee: 500
First 100 tickets: 20(100) = 2000
Tickets over 100: 17 ( x - 100), where x is the number of tickets.
2) Total charges: 500 + 2000 + 17(x - 100) = 2500 + 17(x - 100)
3) Average cost per ticket = total charges / number of tickets
⇒ [2500 + 17(x - 100) ] / x
4) limit as the number of tickets, x, becomes very high ⇒ x → ∞
⇒
5) Here is the demostration of the value of that limit:
2500 / x + 17x / x - 1700/x = 0 + 17 + 0 = 17
Explanation:
1) Charges are:
Flat fee: 500
First 100 tickets: 20(100) = 2000
Tickets over 100: 17 ( x - 100), where x is the number of tickets.
2) Total charges: 500 + 2000 + 17(x - 100) = 2500 + 17(x - 100)
3) Average cost per ticket = total charges / number of tickets
⇒ [2500 + 17(x - 100) ] / x
4) limit as the number of tickets, x, becomes very high ⇒ x → ∞
⇒
5) Here is the demostration of the value of that limit:
2500 / x + 17x / x - 1700/x = 0 + 17 + 0 = 17