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3 years ago

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Mathematics

1 answer:

grin007 [14]3 years ago

4 0

Answer:

23.5

Step-by-step explanation:

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The roots of \[z^7 = -\frac{1}{\sqrt{2}} - \frac{i}{\sqrt{2}}\]are $\text{cis } \theta_1$, $\text{cis } \theta_2$, $\dots$, $\te

stepan [7]

Decoding the LaTeX that didn't render, we seek sum of the angles of the seventh roots of

$- \frac 1 {\sqrt 2} - \frac i {\sqrt{2}}$

That's on the unit circle, 45 degrees into the third quadrant, aka 225 degrees.

The seventh roots will all be separated by 360/7, around 51 degrees. The first seventh root has

$\theta_1 = 225^\circ / 7$

That's around 32 degrees.

The next angle is

$\theta_2 = \frac{1}{7}( 225^\circ + 360^\circ)$

The next one is

$\theta_3 = \frac{1}{7}( 225^\circ + 720^\circ)$

and in general

$\theta_n = \frac{1}{7}( 225^\circ + (n-1)360^\circ) = \frac 1 7(-135^\circ + 360^\circ n)$

$S = \displaystyle \sum_{n=1}^7 \theta_n = \frac{1}{7} \sum_{n=1}^7 -135^\circ + \frac{360}{7} \sum_{n=1}^7 n$

The first sum is just -135° since it's one seventh of the sum of seven -135s.

We have 1+2+3+4+5+6+7 = (1+7)+(2+6)+(3+5) + 4 = 28 so

$S = -135^\circ + 360^\circ (\frac{28} 7) = 4(360)-135 = 1305^\circ$

If I didn't screw it up, that means the answer is

Answer: 1305°

4 0

4 years ago

Joe plans on saving $100 a month for a down payment on a new car. The car is $25,000 and Joe

Sphinxa [80]

10% of 25,000 is 2500 so it would take him 25 months to have enough money for a down payment

7 0

3 years ago

Please helpppp

Zarrin [17]

Answer:

|(15,055) is the number of pages in a book with

15,055 words.

Step-by-step explanation:

becuz the no of pages is a function to the words ..

8 0

3 years ago

What is the value of x in the equation 4 . 10 X+52 3 +35x+1 5 ?<br><br>:)

pashok25 [27]

Answer:

$x=-3$

Step-by-step explanation:

Given:

$4\frac{3}{10}-(2\frac{2}{5}x+5\frac{1}{2})=\frac{1}{2}(-3\frac{3}{5}x+1\frac{1}{5})$

Distribute to remove parentheses:

$4\frac{3}{10}-2\frac{2}{5}x-5\frac{1}{2}=-\frac{18}{10}x+\frac{6}{10}$

For simplification and clarity, reduce all mixed numbers to simplified common fractions:

$\frac{43}{10}-\frac{12}{5}x-\frac{11}{2}=-\frac{9}{5}x+\frac{3}{5}$

Combine like terms:

$-\frac{12}{5}x-\frac{6}{5}=-\frac{9}{5}x+\frac{3}{5}$

Add 6/5 to both sides, then add 9/5x to both sides:

$-\frac{3}{5}x=\frac{9}{5}$

Divide both sides by -3/5 to isolate x (recall dividing by a number is equal to multiplying by its reciprocal):

$x=\frac{9}{5}\cdot -\frac{5}{3}, \\x=\frac{-9}{3},\\x=\boxed{-3}$

3 0

3 years ago

How many different pizza's can be ordered if the restaurant offers 15 different toppings and there is not limit to the number of

RSB [31]

225 different pizzas can be ordered

4 0

4 years ago