I took a picture of my math questions, here take a look.

Mathematics

1 answer:

PtichkaEL [24]2 years ago

7 0

Which one do you want to be awnserd

You might be interested in

Complex numbers & DeMoivre's theory If z=-1-√3 i and z^6=a+bi, a=_____ and b=_____

Mice21 [21]

Convert $z$ to exponential/polar/trigonometric form:

$r=|z|=\sqrt{(-1)^2+(-\sqrt 3)^2}=2$

$\tan\theta=\dfrac{-\sqrt3}{-1}\implies\theta=\dfrac{4\pi}3$

$\implies z=-1-\sqrt3\,i=2e^{4\pi/3\,i}=2\left(\cos\dfrac{4\pi}3+i\sin\dfrac{4\pi}3\right)$

By DeMoivre's theorem,

$z^6=\left(2e^{4\pi/3\,i}\right)^6=2^6e^{24\pi/3\,i}=64e^{8\pi\,i}$

$z^6=64\left(\cos8\pi+i\sin8\pi)=64$

so that $a=64$ and $b=0$ .

8 0

3 years ago

Alistair has a rectangular picture measuring 8 inches by 7 inches. He makes a frame for the picture, shown by the shaded area in

nydimaria [60]

You are given a rectangular picture measuring 8 inches by 7 inches. Also, Alistair wants this to be framed and that the total area is 34 square inches. The width of the frame is x inches. To solve the dimension of the frame with value of x we have:

We have to assume that x here will be equal to all sides of the frame and so, using the area of the rectangle, we can model the equation like this:
A = LW (where A is the area, L is the length and W is the width)
36 = (8 - x)(7 - x)
36 = 56 - 8x - 7x + x²
x² - 15x +20 = 0 → model of our equation and in quadratic form

x² - 15x + 20 = 0
using a calculator, x = 1.48 inches

3.Use the equation you created in part A to find the width of the picture frame

7 0

2 years ago

I need help with my math practice problems

vovangra [49]

I’m getting 61/24 I’m sorry if it’s wrong.