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2 years ago

Five times the complement of an angle is equal to twice the supplement.

Mathematics

1 answer:

Juliette [100K]2 years ago

8 0

The answer would be 10 because 5x2 = 10
Please make me the brainliest ty

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Examine the pattern in the powers of i you wrote in the table, and create a rule for finding the value of large powers of i. Jus

denpristay [2]

Let $N$ be any integer. Then

$i^N=\begin{cases}1&\text{if }N\equiv0\mod4\\i&\text{if }N\equiv1\mod4\\-1&\text{if }N\equiv2\mod4\\-i&\text{if }N\equiv3\mod4\end{cases}$

In other words:

(1) If $N$ is a multiple of 4, then $i^N=1$ .

(2) If dividing $N$ by 4 leaves a remainder of 1, then $i^N=i$ , since $i^N=i^{4n+1}$ for some integer $n$ , and from (1) we know that $i^{4n+1}=i^{4n}i=i$ (because, obviously, $4n$ is a multiple of 4).

(3) If instead you get a remainder of 2, then $i^N=-1$ . This follows from (1) as well. $i^N=i^{4n+2}=i^{4n}i^2=(1)(-1)=-1$ .

(4) Finally, if you get a remainder of 3, then $i^N=i^{4n+3}=i^{4n}i^2i=(1)(-1)(i)=-i$ .

5 0

2 years ago

a tight roll of paper, as delivered to the printer, is 60cm in diameter, and the paper is wound on to a wooden cylinder 8cm in d

Alekssandra [29.7K]

The area of the paper is the amount of space it occupies.

The length of papers around the edge is 1607680 cm

The given parameters are:

$\mathbf{d_1 = 60cm}$

$\mathbf{d_2 = 60cm + 8cm = 68cm}$

The area of the circle head is:

$\mathbf{Area = \pi \frac{d^2}{4}}$

So, we have:

$\mathbf{Area = \pi \frac{d_2^2 - d_1^2}{4}}$

Substitute known values

$\mathbf{Area = \pi \frac{68^2 - 60^2}{4}}$

$\mathbf{Area = \pi \frac{1024}{4}}$

$\mathbf{Area = 256\pi}$

The length of the paper is then calculated as:

$\mathbf{Length = \frac{Area}{0.0005}}$

This gives

$\mathbf{Length = \frac{256\pi}{0.0005}}$

$\mathbf{Length = \frac{256 \times 3.14}{0.0005}}$

$\mathbf{Length = 1607680}$

Hence, the length of papers around the edge is 1607680 cm

Read more about areas at:

brainly.com/question/2264643

4 0

2 years ago

Read 2 more answers

If a cone has a height of 5 cm and a volume of 128π cm³<br> find the diameter of the circular base.

Gemiola [76]

The volume of a cone with respect to its diameter is:

V=(hπd^2)/12 solving this for d we have:

d=√[(12V)/(hπ)], we are given that V=128π and h=5 so

d=√(1536π)/(5π)

d=√(1536/5)

d=√307.2 cm

d≈17.53 cm (to nearest hundredth)

6 0

3 years ago

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A store item is originally priced at $80. the item goes on sale at a 25% discount. two weeks later that sales price is marked do

s2008m [1.1K]

First, the item goes on sale for 25% discount which means that the price will now be only 75% of the original price.

Case 1: Price = ($80)(0.75) = $60

Then, the item is sold for additional discount of 10% which the new price is only 90% of the supposed price.

Case 2: Price = ($60)(0.90) = $54

Answer: $54

3 0

2 years ago

What is the volume of a ball if it’s diameter is 6 inches

inn [45]

Answer:

V = 36 π cubic inches

Step-by-step explanation:

Volume of Sphere= (4/3) x pi x r^3

V= (4/3) x 3^3 x pi

V= (4/3) x 27 x pi

V= 36 pi

V = 36 π cubic inches

Hope this helps :)

3 0

2 years ago

Read 2 more answers