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2 years ago

True or False: If lim x → a f(x) does not exist, then f is undefined at the point x = a.

Mathematics

1 answer:

kkurt [141]2 years ago

8 0

Answer:

this is absolutely false.

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What type of sampling is shown here: Conduct a survey of everyone in your neighborhood to predict city elections.

WITCHER [35]

I'm pretty sure the answer would be C

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3 years ago

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Simplify the complex numbers using de Moivre's Theorem and match them with their solutions.

alexandr1967 [171]

For the numbers in $a+bi$ form, convert to polar form:

$1+i=\sqrt2\dfrac{1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)$

By DeMoivre's theorem,

$(1+i)^5=(\sqrt2)^5\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=4\sqrt2\dfrac{-1-i}{\sqrt2}=-4-4i$

$-1+i=\sqrt2\dfrac{-1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4}\right)$

$\implies(-1+i)^6=(\sqrt2)^6\left(\cos\dfrac{18\pi}4+i\sin\dfrac{18\pi}4\right)=8i$

$\sqrt3+i=2\dfrac{\sqrt3+i}2=2\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)$

$\implies2(\sqrt3+i)^{10}=2^{11}\left(\cos\dfrac{10\pi}6+i\sin\dfrac{10\pi}6\right)=2^{11}\dfrac{1-i\sqrt3}2=2^{10}(1-i\sqrt3)$

For the numbers already in polar form, DeMoivre's theorem can be applied directly:

$2\left(\cos20^\circ+i\sin20^\circ\right)^3=2\left(\cos60^\circ+i\sin60^\circ\right)=2\dfrac{1+i\sqrt3}2=1+i\sqrt3$

$2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)^4=2(\cos\pi+i\sin\pi)=-2$

At second glance, I think the 2s in the last two numbers should also be getting raised to the 3rd and 4th powers:

$\left(2(\cos20^\circ+i\sin20^\circ)\right)^3=8\left(\cos60^\circ+i\sin60^\circ\right)=4+4\sqrt3$

$\left(2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)\right)^4=16(\cos\pi+i\sin\pi)=-16$

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2 years ago

A customer can drive around a track 60 times for $12. At this rate, how many times can the customer drive around the track for $

Aleonysh [2.5K]

Answer:36 times for 8 dollars

Step-by-step explanation:

k so first you divide 54 and 12 =4.5 per dollar so you then multiply 4.5 and 8 to get the answer that =36 times for 8 dollars

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2 years ago

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Mischief Campbell math class lasts 45 minutes. Math class starts at 9:05. what time does math class end?

zhuklara [117]

Answer:

The correct answer is 9:50.

Step-by-step explanation:

9:05+0:45=9:50

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2 years ago

HURRY HELP i need helppp

suter [353]

Answer:

that answe is b

Step-by-step explanation:

b because i took this test

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