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Fiesta28 [93]
3 years ago
13

Simplify i^41 (please help me)

Mathematics
2 answers:
ira [324]3 years ago
8 0

Answer:

i

Step-by-step explanation:

SOVA2 [1]3 years ago
8 0

Answer:  Choice A) i

====================================================

Explanation:

Let's look at the pattern of powers of i

  • i^0 = 1
  • i^1 = i
  • i^2 = (sqrt(-1))^2 -1
  • i^3 = i*i^2 = i*(-1) = -i
  • i^4 = (i^2)^2 = (-1)^2 = 1

We loop back to 1, and the process starts all over again. The cycle is 4 units long. Ie, the pattern repeats every 4 terms.

What this means is that we can use remainders to quickly figure out something like i^41 without having to use a calculator or tons of paper.

Dividing 41/4 leads to a quotient of 10 and a remainder of 1. We only care about the remainder. The remainder 1 means i^41 = i^1 = i

Note how 41 and 1 lead to the same remainder when we divide by 4.

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Points B, D, and F are midpoints of the sides of ΔACE. EC = 38 and DF = 16. Find AC. The diagram is not to scale.
Lunna [17]

Answer: The measure of AC is 32.

Explanation:

It is given that the Points B, D, and F are midpoints of the sides of ΔACE. EC = 38 and DF = 16.

The midpoint theorem states that the if a line segments connecting two midpoints then the line is parallel to the third side and it's length is half of the third side.

Since F and D are midpoints of AE and EC respectively.

So by midpoint theorem length of AC is twice of DF.

AC=2\times DF

AC=2\times 16

AC=32

Therefore, the length of AC is 32.

7 0
2 years ago
In your computation, approximate its value as 3.14.
andrey2020 [161]

Answer: d

Step-by-step explanation:

Find the area of the rectangle.

A=l*w\\A=(15in)(12in)\\A=180in^2

Find the area of the base of the semicircle.

A=\pi r^2

12 in would be the diameter, divide by 2 to get the radius.

\frac{12}{2}=6

Plug this into the formula.

A=(3.14)(6)^2\\A=113.04in^2

Since we do not have a full circle but a semi one instead, we must divide our result by 2.

\frac{113.04}{2}=56.52in^2

Add both areas.

180+56.52=236.52in^2

7 0
3 years ago
Y = x2 - 6x - 8
Usimov [2.4K]

Answer:

I think type answer is A

3 0
3 years ago
a survey asked 72 randomly chosen students if they were going to attend the school play. twelve said yes. if there are 210 ticke
Ugo [173]
We can solve this by setting up a proportion:

12 seeing the play/ 72 students = 210 seeing the play/ x students

We can cross multiply to solve for x:

(12)x=(72)(210)
12x=15,120
x=1,260 students who attend the school
4 0
3 years ago
Given:
jekas [21]

Answer:

we conclude that:

If 4x - 6≠4, then 2x–5≠5 is the contrapositive of a conditional statement if 2x -5=5, then 4x-6=14.

Step-by-step explanation:

We know that the contrapositive of a conditional statement of the form "If p then q" is termed as "If ~q then ~p".

In other words, it is symbolically represented as:

' ~q ~p is the contrapositive of p q '

For example, the contrapositive of "If it is a rainy day, then they suspend the match" is "If they do not suspend the match, then it won't be a rainy day."

Given

p: 2x -5=5

q: 4x-6=14

As the contrapositive of a conditional statement of the form "If p then q" is termed as "If ~q then ~p

Thus, we conclude that:

If 4x - 6≠4, then 2x–5≠5 is the contrapositive of a conditional statement if 2x -5=5, then 4x-6=14.

4 0
2 years ago
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