Weekly wages at a certain factory

Mathematics

1 answer:

shtirl [24]3 years ago

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Am I correct <br> 2017 -1846= 171<br> 2017-1781= 236<br> 1847-1781=65 yrs difference

Anit [1.1K]

Yes for the first one, yes for the second one, and yes for the third one although your subtraction equation had the wrong year (its not 1847 its 1846) but the answer was right, 65.

5 0

3 years ago

Show six <br> ways to add 2,3,4

Gnom [1K]

2 + 3 + 4
2 + 4 + 3
4 + 3 + 2
4 + 2 + 3
3 + 4 + 2
3 + 2 + 4

4 0

3 years ago

Read 2 more answers

Write -3+4i in the form r(cosx+isinx)

Zanzabum

$-3+4i$ is a complex number that satisfies

$\begin{cases}r\cos x=-3\\[1ex]r\sin x=4\\[1ex]r=\sqrt{(-3)^2+4^2}\end{cases}$

The last equation immediately tells you that $r=5$ .

So you have

$\begin{cases}\cos x=-\dfrac35\\[1ex]\sin x=\dfrac45\end{cases}$

Dividing the second equation by the first, you end up with

$\dfrac{\sin x}{\cos x}=\tan x=\dfrac{\dfrac45}{-\dfrac35}=-\dfrac43$

Because the argument's cosine is negative and its sine is positive, you know that $\dfrac\pi2$ . This is important to know because it's only the case that $y=\tan x\implies \arctan y=x$ whenever $-\dfrac\pi2$ . The inverse doesn't exist otherwise.

However, you can restrict the domain of the tangent function so that an inverse can be defined. By shifting the argument of tangent by $\pi$ , we have

$\tan(x-\pi)=y\implies x=\pi+\arctan y$

All this to say

$\tan x=-\dfrac43\implies x=\pi+\arctan\left(-\dfrac43\right)\approx2.2143\text{ rad}\approx126.9^\circ$

So, $-3+4i=5(\cos126.9^\circ+i\sin126.9^\circ)$ .