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2 years ago

Tim has twice as many marbles as Luke together they have 39 marbles how many marbles does time have

Mathematics

2 answers:

mash [69]2 years ago

4 0

Luke has 13 and Tim has 26, Tim has twice has many marbles as Luke which would be 13 times 2, 26+13=39

lina2011 [118]2 years ago

4 0

None

Or 26
39/3=13+13 because tim has twice so its 26

Or none because you said 'how many marbles does TIME have' and its not time its tim. I dont know if thats typo or thats the real question. Lol

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3 years ago

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2 years ago

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3 years ago

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1 year ago

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

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3 years ago