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3 years ago

2 3/5 divide 6 estimate the answer

Mathematics

1 answer:

STatiana [176]3 years ago

5 0

2 3/5 divide 6

pretend that 6 has a denominator which is 6

2 3/5 divide 6/1

make 2 3/5 into a improper fraction

multiply the whole number and denominator together

2*5=10

add 10 with the numerator

10+3=13

13/5 divide 6/1

always flip over the second fraction

13/5*1/6

13*1=13- multiply the numerators together

5*6=30 - multiply the denominators together

13/30- as a decimal=0.43333 ( the 3s continue forever )

answer:

0.433333

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From Euler’s relation eiθ = cosθ + isinθ,

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Answer:

(a) The graphic representation is in the attached figure.

(b) $\cos(\theta) = \frac{e^{i\theta} + e^{-i\theta}}{2}$ .

(c) $\sin(\theta) = \frac{e^{i\theta} - e^{-i\theta}}{2i}$ .

Step-by-step explanation:

(a) Given a complex number $e^{i\theta}$ we know, from Euler's formula that $e^{i\theta} = \cos(\theta)+i\sin(\theta)$ . So, it is not difficult to notice that

$|e^{i\theta}|^2 = \cos^2(\theta)+\sin^2(\theta) =1$

so it is on the unit circumference. Also, notice that the Cartesian representation of the complex number is $(\cos(\theta), \sin(\theta))$ .

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$e^{-i\theta} = \cos(\theta)+i\sin(-\theta) = \cos(\theta)-i\sin(\theta)$ .

Notice that $e^{-i\theta}$ has the same modulus that $e^{i\theta}$ , so it is on the unit circumference. Beside, its Cartesian representation is $(\cos(\theta), -\sin(\theta))$ .

So, the points $(\cos(\theta), \sin(\theta))$ and $(\cos(\theta), -\sin(\theta))$ are symmetric with respect to the X-axis. All this can be checked in the attached figure.

(b) Notice that

$e^{i\theta} + e^{-i\theta} = \cos(\theta)+i\sin(\theta) + \cos(\theta)-i\sin(\theta) = 2\cos(\theta)$

Then,

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3 years ago

New York is the 27th largest state in the United States.what percent of the 50 states in the us are larger than New York

Greeley [361]

there are 50 states, NY is the 27th largest so before NY there are other 26 states that are larger than NY.

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$\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 50&100\\ 26&x \end{array}\implies \cfrac{50}{26}=\cfrac{100}{x}\implies \cfrac{25}{13}=\cfrac{100}{x}\implies 25x=1300 \\\\\\ x=\cfrac{1300}{25}\implies x=52$

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4 years ago

Factor the expression 16a^2 - 81

Ray Of Light [21]

Answer:

(4a - 9)(4a + 9)

Step-by-step explanation:

Every value in the equation has a square root

The square root of 16 is 4

The square root of a^2 is a

The square root of 81 is 9.

To factor you split the equation by the square roots. For 81, since the original value is negative, one of the roots must be negative so when you multiply it back out to the original, it stays the same.

You can check your answer this way too.

(4a -9)(4a + 9)

= 16a^2 + 36a - 36a - 81

= 16a^2 - 81

I hope this helps!

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