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3 years ago

Which sets of numbers are closed under subtraction?

1 answer:

3 0

The answer is:

B.
rational numbers

Because if you perform subtraction in a set of rational numbers, the result you get would still be a rational number.

This does not apply to the other sets.

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Which of the following is a solution of z^5 = 1 + √3 i?

nordsb [41]

Answer:

Option 2 is right

Step-by-step explanation:

Given that

$z^5=1+\sqrt{3} i$

We can write this in polar form with modulus and radius

$|z^5|= \sqrt{1+3} =2\\tan of Angle t =\sqrt{3} \\$

Hence angle = 60 degrees and

$|z^5|= 2(cos60+isin60)$

Since we have got 5 roots for z, we can write 60, 420, 780, etc. with periods of 360

Using Demoivre theorem we get 5th root would be

5th root of 2 multiplied by 1/5 th of 60, 420, 780,....

$z= \sqrt[5]{2} (cos12+isin12)\\z=\sqrt[5]{2} (cos84+isin84)\\\\z=\sqrt[5]{2} (cos156+isin156)\\\\z=\sqrt[5]{2} (cos228+isin228)\\\\z=\sqrt[5]{2} (cos300+isin300)\\$

Out of these only 2nd option suits our answer

Hence answer is Option 2.

8 0

3 years ago

What is the equation that represents the sequence in this problem ? Find the price after the 8th month

AVprozaik [17]

ANSWER

$\begin{gathered} a_n=ar^{n\text{ - 1}} \\ a_8\text{ = \$38.26} \end{gathered}$

EXPLANATION

The problem represents a geometric progression.

The general form of a geometric sequence is:

$a_n=ar^{n\text{ - 1}}$

where a = first term

r = common ratio

The first term from the table is the first price (for the first month). That is $80.00

To find the common ratio, we divide a term by its preceeding term.

Let us divide the price of the second month from the first.

We have:

$\begin{gathered} r\text{ = }\frac{72}{80} \\ r\text{ = 0.9} \end{gathered}$

The price after the 8th month is the value of a(n) when n = 8

So, we have that:

$\begin{gathered} a_8\text{ = 80 }\cdot0.9^{(8\text{ - 1)}} \\ a_8\text{ = 80 }\cdot0.9^7 \\ a_8\text{ = \$38.26} \end{gathered}$

5 0

9 months ago

What mistake did he likely make?

gogolik [260]

Answer:

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6 0

3 years ago

What is the unit rate of the number of miles driven per number of hours of driving?

MariettaO [177]

35
Explaination : 70 divided by 2 is 35

5 0

3 years ago

Read 2 more answers

Identify the odd function.

Yuri [45]

Answer:

Step-by-step explanation:

odd functions are those function in which

-f(x) = f(−x)

if the function is odd , the graph of function is symmetrical about origin.

_________________________________________________

In the given problem

option B is correct answer

B) f(x) = 8x

replacing x with -x to satisfy the above described condition

f(-x) = 8(-x) = -8x

as we know 8x is equal to f(x)

f(-x) = -8x = -f(x)

hence,

f(-x) = -f(x)

hence, option B is correct answer.

3 0

2 years ago