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3 years ago

How much would $125 invested at 8% interest compounded continuously be worth after 16 years

Mathematics

2 answers:

sweet [91]3 years ago

6 0

Answer:

Step-by-step explanation:

Stels [109]3 years ago

6 0

Answer:

$449.58

Hope this helps!!

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Precal help if you could could you answer both. Me finishing this helps me graduate.

oee [108]

Exercise 1:

The easiest way to compute powers of complex numbers is to write them in the form

$z = \rho e^{i\theta} = \rho(\cos(\theta)+i\sin(\theta))$

In this form, you have

$z^n = \rho^n e^{in\theta} = \rho^n(\cos(n\theta)+i\sin(n\theta))$

The magnitude of the number is given by

$z=a+bi \implies \rho = \sqrt{a^2+b^2}$

So, we have

$z=-1+\sqrt{3}i \implies \rho = \sqrt{1+3}=2$

As for the angle, we have

$z=a+bi \implies \theta = \text{atan2}\dfrac{b}{a}$

So, we have

$z=-1+\sqrt{3}i \implies \theta = \text{atan2}\left(\dfrac{-\sqrt{3}}{-1}\right) = -\dfrac{2\pi}{3}$

Finally,

$z=-1-\sqrt{3}i = 2\left(\cos\left( -\dfrac{2\pi}{3}\right) + i\sin\left( -\dfrac{2\pi}{3}\right)\right) \implies z^6 = 2^6\left(\cos\left( -4\pi\right) + i\sin\left(-4\pi\right)\right) = 64$

Exercise 2:

You simply have to compute the trigonometric function:

$\cos\left(-\dfrac{\pi}{4}\right) = \dfrac{\sqrt{2}}{2},\quad \sin\left(-\dfrac{\pi}{4}\right) = -\dfrac{\sqrt{2}}{2}$

So, we have

$z = \sqrt{2}\left(\dfrac{\sqrt{2}}{2} - i\dfrac{\sqrt{2}}{2}\right) = 1-i$

7 0

3 years ago

Help me guys???????????????

My name is Ann [436]

Answer:

118

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

I don't know how many thousandths go in 5,000 ones

Verizon [17]

5,000,000 is the answer.
5,000÷0.001=5,000,000

7 0

3 years ago

Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month

Natalija [7]

Answer:

Step-by-step explanation:

I need help with same question please

5 0

3 years ago

Determine the period of the function g(x) = (cos ;)

Romashka [77]

Answer:

6 $\pi$

Step-by-step explanation:

The period of a sinusoidal function in the form a * cos (b (x + h)) + m is $\frac{2\pi }{|b|}$ . Therefore, we can see that "b" in g(x) is 1/3 and 1/3 substituted into $\frac{2\pi }{|b|}$ is 2 $\pi$ /1/3 which is 6 $\pi$ .

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3 years ago