Review the proof of de Moivre’s theorem. Proof of de Moivre's Theorem
[cos(θ) + i sin(θ)]k + 1
A = [cos(θ) + i sin(θ)]k ∙ [cos(θ) + i sin(θ)]1
B = [cos(kθ) + i sin(kθ)] ∙ [cos(θ) + i sin(θ)]
C = cos(kθ)cos(θ) − sin(kθ)sin(θ) + i [sin(kθ)cos(θ) + cos(kθ)sin(θ)]
D = ?
E = cos[(k + 1)θ] + i sin[(k + 1)θ]

Which expression will complete the proof?

If the wwight of a package is multiplied by 7/10 the result is 65.8 find the weight of the package

Question 3 (essay worth 10 points) (03.06 mc) part a: max rented a motorbike at $465 for 5 days. if he rents the same motorbike for a week, he has to pay a total rent of $625. write an equation in the standard form to represent the total rent (y) that max has to pay for renting the motorbike for x days. (4 points) part b: write the equation obtained in part a using function notation. (2 points) part c: describe the steps to graph the equation obtained above on the coordinate axes. mention the labels on the axes and the intervals. (4 points)

Based on the situation in part a, the width of a rectangular garden is x feet, and its length is 5 feet more than twice its width. the right side of the equation, g(x) = 2x2 − 13x + 6, can be factored to g(x) = (2x − 1)(x − 6). this function could represent an inner region of the garden from the first equation, such as a vegetable garden with a border around it. the length of this inner garden would be 2x − 1 feet, and the width would be x − 6, which would leave a 3-foot border around the garden. part d what is the value of g(8) for the function g(x) in part c? what does this value mean in the context of the situation you described in part c?