I need help pleasse

The interior angle of the regular pentagon below measures 108, and the pentagon has rotational symmetry. Which of the following

zysi [14]

Answer:

108

Step-by-step explanation:

4 0

3 years ago

From Euler’s relation eiθ = cosθ + isinθ,

adelina 88 [10]

Answer:

(a) The graphic representation is in the attached figure.

(b) $\cos(\theta) = \frac{e^{i\theta} + e^{-i\theta}}{2}$ .

(c) $\sin(\theta) = \frac{e^{i\theta} - e^{-i\theta}}{2i}$ .

Step-by-step explanation:

(a) Given a complex number $e^{i\theta}$ we know, from Euler's formula that $e^{i\theta} = \cos(\theta)+i\sin(\theta)$ . So, it is not difficult to notice that

$|e^{i\theta}|^2 = \cos^2(\theta)+\sin^2(\theta) =1$

so it is on the unit circumference. Also, notice that the Cartesian representation of the complex number is $(\cos(\theta), \sin(\theta))$ .

Now,

$e^{-i\theta} = \cos(\theta)+i\sin(-\theta) = \cos(\theta)-i\sin(\theta)$ .

Notice that $e^{-i\theta}$ has the same modulus that $e^{i\theta}$ , so it is on the unit circumference. Beside, its Cartesian representation is $(\cos(\theta), -\sin(\theta))$ .

So, the points $(\cos(\theta), \sin(\theta))$ and $(\cos(\theta), -\sin(\theta))$ are symmetric with respect to the X-axis. All this can be checked in the attached figure.

(b) Notice that

$e^{i\theta} + e^{-i\theta} = \cos(\theta)+i\sin(\theta) + \cos(\theta)-i\sin(\theta) = 2\cos(\theta)$

Then,

$\cos(\theta) = \frac{e^{i\theta} + e^{-i\theta}}{2}$ .

(c) Notice that

$e^{i\theta} - e^{-i\theta} = \cos(\theta)+i\sin(\theta) - \cos(\theta)+i\sin(\theta) = 2i\sin(\theta)$

Then,

$\sin(\theta) = \frac{e^{i\theta} - e^{-i\theta}}{2i}$ .

7 0

3 years ago

PLEASE. Help with question 12

Arlecino [84]

Answer:

The graph of the parent function f(x) = |x| is dashed and the graph of the transformed function g(x) = |x| + k is solid. Use the slider to change the value of k. How does changing the value of k affect the graph? Positive values of k shift the graph . Negative values of k shift the graph .

7 0

3 years ago

A rectangle has perimeter, P, length, land width, w. Which of the following represents lin

almond37 [142]

Answer:

$l=\frac{P}{2}-w$ .