Ms. Bennett has a pile of board games sitting on the floor of her apartment that are taking up way too much space. Determine the
volume of the pile of board in order to let Ms. Bennett know how much space she will be saving if she donates the games to RPLS.
1 answer:
You might be interested in
Answer:
C,
Step-by-step explanation:
To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:
Given the complex number , we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.
One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression
Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression , and <em>now </em>we have something to work with.
Looking back at Euler's formula , we can map our expression inside the parentheses to the one on the right side of the formula, giving us
and
, or equivalently:
At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so , and we can finally replace our expression in parentheses with its exponential equivalent:
Which is c on the multiple choice section.
Answer: a loss of 4 cents
<u>Step-by-step explanation:</u>
The probability of rolling a sum of 2, 3, 4, 5, or 6 is which earns $2.00
The probability of rolling a sum of 28, 9, 10, 11, or 12 is which loses $2.00
The probability of rolling a sum of 7 is which loses $0.25