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3 years ago

WORTH BRAINLIST!!! What is the value of the expression 2 + 3^2 ⋅ (3 − 1)? 20 22 23 32

Mathematics

1 answer:

Wittaler [7]3 years ago

3 0

Answer:

You have to use PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction), and solve in that order. Your question is:

2 + 32 ⋅ (3 − 1)

First, solve the Parentheses part of the question. 3-1 is 2. Your question is now:

2+32*2

Now, solve the multiplication part of the question. 32*2 is 64. Your question is now:

2+64

This is now an easy problem to solve.

The answer is 66.

Hope this helps! :)

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Evaluate -(2^-6)(2^3)

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Answer:

-0.125

Step-by-step explanation:

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5x + 13 + (2y-7)i = -2 + i please please help

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2 years ago

Use DeMoivre's Theorem to find the following. Write your answer in<br> standard form.

valina [46]

Answer:

Option C.

Step-by-step explanation:

The given expression is

$\left(\sqrt{2}cis \dfrac{9\pi}{20}\right)^5$

It can be rewritten as

$\left(\sqrt{2}\cos \dfrac{9\pi}{20}+i\sin\dfrac{9\pi}{20}\right)^5$

According to De moivre's Theorem:

$[r(\cos\theta+i\sin \theta)]^n=r^n(\cos n\theta +i\sin n\theta)$

Using De moivre's Theorem, we get

$(\sqrt{2})^5\left(\cos \dfrac{9\pi\times 5}{20}+i\sin\dfrac{9\pi\times 5}{20}\right)$

$=4\sqrt{2}\left(\cos \dfrac{9\pi}{4}+i\sin\dfrac{9\pi}{4}\right)$

$=4\sqrt{2}\left(\cos (2\pi +\dfrac{\pi}{4})+i\sin (2\pi+\dfrac{\pi}{4})\right)$

$=4\sqrt{2}\left(\cos \dfrac{\pi}{4}+i\sin \dfrac{\pi}{4}\right)$

$=4\sqrt{2}\left(\dfrac{1}{\sqrt{2}}+i\dfrac{1}{\sqrt{2}}\right)$

$=4+4i$

Therefore, the correct option is C.

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3 years ago

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At the beginning of a population study, the population of a large city was 1.65 million people. Three years later, the populatio

Maksim231197 [3]

Answer:

C. 1.8027

Step-by-step explanation:

The exponential population growth model is given by:

$P(t) = P_{0}e^{rt}$

In which P(t) is the population after t years, $P_{0}$ is the initial population and r is the growth rate.

At the beginning of a population study, the population of a large city was 1.65 million people. Three years later, the population was 1.74 million people.

This means that $P_{0} = 1.65, P(3) = 1.74$

Applying this to the equation, we find r. So

$P(t) = P_{0}e^{rt}$

$1.74 = 1.65e^{3r}$

$e^{3r} = \frac{1.74}{1.65}$

$e^{3r} = 1.0545$

Applying ln to both sides

$\ln{e^{3r}} = \ln{1.0545}$

$3r = \ln{1.0545}$

$r = \frac{\ln{1.0545}}{3}$

$r = 0.0177$

$P(t) = 1.65e^{0.0177t}$

What would be the population of the city 5 years after the start of the population study?

This is P(5).

$P(t) = 1.65e^{0.0177t}$

$P(5) = 1.65e^{0.0177*5}$

$P(5) = 1.8027$

So the correct answer is:

C. 1.8027

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3 years ago