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NNADVOKAT [17]
3 years ago
11

Caitlin has a movie rental card worth $175.After she rents the first movie ,the card's value is $172.25. Aftershe rents the seco

nd movie ,its value is $169.50.After she rents the third movie, the card is worth $166.75.
Assuming the pattern continues,write an equation to define A(n), the amount of money on the rental card after n rentals
Mathematics
1 answer:
dedylja [7]3 years ago
4 0
The answer to this question is 175 - n x 2.75
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Answer:

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Step-by-step explanation:

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2 years ago
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LekaFEV [45]

Answer:

C, 4e^{i(7\pi/4)}

Step-by-step explanation:

To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:

e^{ix}=\cos{x}+i\sin{x}

Given the complex number 2\sqrt{2}-2i\sqrt{2}, 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 2(\sqrt{2}-i\sqrt{2})

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 4\left(\frac{\sqrt{2}}{2} -i\frac{\sqrt{2}}{2}\right) , and <em>now </em>we have something to work with.

Looking back at Euler's formula e^{ix}=\cos{x}+i\sin{x}, we can map our expression inside the parentheses to the one on the right side of the formula, giving us \cos{x}=\frac{\sqrt2}{2} and \sin{x}=-\frac{\sqrt2}{2}, or equivalently:

\cos^{-1}{\frac{\sqrt2}{2} }=\sin^{-1}-\frac{\sqrt2}{2} =x

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4\left(\frac{\sqrt2}{2}-i\frac{\sqrt2}{2}\right)=4e^{i(7\pi/4)}

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4 0
3 years ago
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