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3 years ago

Work out an estimate for square root of 4.92 +2.18 x 7.31

Mathematics

1 answer:

user100 [1]3 years ago

5 0

Answer:

4.5.

Step-by-step explanation:

4.92 +2.18 x 7.31

= approximately 5 + 2 * 7.5

= 20

Now 4.5 * 4.5 = 20.25 so:

The estimate for the square root is 4.5.

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Solve this: x + 89 = 91 what is "x"?

egoroff_w [7]

Hey there!

2 + 89 = 91,

so x = 2

Hope this helps!
Have a great day (:

8 0

4 years ago

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Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fourth roots of -9i.

vitfil [10]

Answer:

Step-by-step explanation:

Given z = x+iy

The polar form of a complex number $z = r(cos\theta + isin\theta)$

The nth root of the complex number is expressed according to de moivre's theorem as;

$z^{\frac{1}{n} } = [r(cos\theta + isin\theta)]^{\frac{1}{n} } \\z^{\frac{1}{n} } = \sqrt[n]{r} (cos(\frac{\theta+2nk}{n} ) + isin(\frac{\theta+2nk}{n}))$

r is the modulus of the complex number and $\theta$ is the argument

r = √x²+y²

$\theta = tan^{-1} \frac{y}{x}$

Given z = -9i

r = √0+(-9)²

r = √81

r = 9

$\theta = tan^{-1}\frac{-9}{0} \\\theta = tan^{-1}-\infty\\\theta = -90^{0}$

The argument will be equivalent to 180-90 = 90°

The forth root of -9i will be expressed as shown according to de moivre's theorem;

$z_k^{\frac{1}{4} } = \sqrt[4]{9} (cos(\frac{90+2(4)k}{4} ) + isin(\frac{90+2(4)k}{4}))\\z_k^{\frac{1}{4} } = \sqrt[4]{9} (cos(\frac{90+8k}{4} ) + isin(\frac{90+8k}{4}))\\$

The complex roots are at when k = 0, 1, 2 and 3

When k = 0;

$z_0 = \sqrt[4]{9} (cos(\frac{90}{4} ) + isin(\frac{90}{4}))\\z_0 = \sqrt[4]{9} (cos(23) + isin(23))\\\\when\ k =1\\z_1 = \sqrt[4]{9} (cos(\frac{90+8}{4} ) + isin(\frac{90+8}{4}))\\z_1 = \sqrt[4]{9} (cos(25 ) + isin(25))\\\\when\ k =2\\z_2 = \sqrt[4]{9} (cos(\frac{90+16}{4} ) + isin(\frac{90+16}{4}))\\z_2 = \sqrt[4]{9} (cos(27 ) + isin(27))\\\\when\ k =3\\z_3 = \sqrt[4]{9} (cos(\frac{90+24}{4} ) + isin(\frac{90+24}{4}))\\z_3 = \sqrt[4]{9} (cos(29 ) + isin(29))\\$

Note that all the degrees are rounded to the nearest whole number.

6 0

3 years ago

11. An experiment is set up to study the weights of 45 frogs after they are given a hormone treatment. The population mean is 22

sveta [45]

Answer: The standard error of the sample mean = 0.44

Step-by-step explanation:

Standard error of the sample mean = $\dfrac{\sigma}{\sqrt{n}}$ , where $\sigma$ = population standard deviation , n= sample size.

Given : n= 45 , $\sigma= 2.96$ grams

The e standard error of the sample mean $=\dfrac{2.96}{\sqrt{45}}$

$=\dfrac{2.96}{6.7082039325}\\\\\approx\ 0.44$

Hence, the standard error of the sample mean = 0.44

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3 years ago

What are the steps into solving this equation?

zhannawk [14.2K]

First, you must do the parentheses!!!
Next, when you are done solving the parentheses, you will do the outside numbers!!
Then, when doing the outside numbers, you'll combine(doing +, ×, ÷ or -)
And finally, you get your answer!!!

:):):):):)

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3 years ago

A rectangle has an area of 12 square feet and a length of 5 feet. What is its width?

Lera25 [3.4K]

Well, you know that the area of the rectangle is 12 square feet. And you know one of the numbers multiplied to get 12 is 5, so divide 12 by 5. You would get 2.4 as the other number needed.
In this case, 5 feet is the width and 2.4 feet is the length.

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3 years ago

Read 2 more answers