¿Cuál es el valor de i51

?

A.

−1

B.

−i

C.

1

D.

i

Answers

Answer 1

Answer: Option B.

Step-by-step explanation:

We want to find the value of i^51

We know that

i^1 = i

i^2 = -1

i^3 = -i

i^4 = 1

and it repeats with a period of 4, so i^5 = i^(1 + 4) = i^1= i, and so on.

so we can write it as:

x + n*4 = 51

where n is an integer number, and x is a number between 1 and 4.

clearly  n must be an odd number, so we can try:

if x = 1.

1 + n*4 = 51

n*4 = 50

n = 50/4 = 12.5

This is not the solution for x, because n must be an integer number.

Now suppose x = 3.

3 + 4*n = 51

4*n = 48

n = 48/4 = 12

Then x is equal to 3, this means that:

i^51 = i^3*i^4*12 = i^3 = -i

The correct option is B


Related Questions

#1 Find the area of the rhombus. Each indicated distance is half the length of its respective diagonal.
#2 Find the area of the rhombus.

Answers

Answer:

1 area = 864

2 area =384

Step-by-step explanation:

Answer:

1 area = 864

2 area =384

Step-by-step explanation:

Do you still have this worksheet I really need help

A group of friends will host a party and split the cost of food and supplies evenly. The cost that each person will pay is inversely proportional to the number of friends who decide to host. If five friends host the party, each person pays $12 for food and supplies. Write an equation that describes the relationship between cost (c) that each host pays and the number of hosts (h).

Answers

Answer:

C=60/h

Step-by-step explanation:

Cost is inversely Proportional to the number of friends who decides to host.

If five (5) friends host the party,

And each friend pays $12 for food and supplies

The equation that describes the relationship is

C=k ×1/h

Where,

C= cost that each host pays

K=constant

h=number of host

Therefore,

$12=k×1/5

$12=k/5

Make k the subject of the formula

$12=k*1/5

Multiply both sides by 5

12×5=k*1/5×5

60=k*5/5

60=k*1

60=k

Sub the value of k into

C=k ×1/h

C=60*1/h

C=60/h

Answer:

D)  c = 60∕h

Step-by-step explanation:

what is the y-intercept i’d the equation 2y+5x=-14

Answers

Answer:

The y-intercept is -7

Step-by-step explanation:

Divide both sides by 2, to isolate the y -variable. Then you get

y = -5/2x - 7

Answer:

-7

Step-by-step explanation:

2y+5x=-14

-5x both sides

2y=-5x-14

/2 both sides

y=-5x-7

This is a easy 25 pts

Answers

Answer:

46440

Step-by-step explanation:

8% of 43,000+43,000

Answer:

46440

Step-by-step explanation:

First find the amount that the salary increased

43,000 * 8%

43000*.08

3440

Add this to the original salary to find the new salary

43000+3440

46440

Find f(2) if f(x) = (x + 1)2.

5
6
9

Answers

Answer:

6

Step-by-step explanation:

(2+1)2=

(3)2=

6

Hope this helps!

The answer is 6 that’s what I got

Graph y = 3/4 + 2.??? Idk what this is

Answers

Answer:

This equation is for a linear graph.

y = mx + b, where m is the slope and b is the y-intercept. To graph this, plot a point at (0, 2), as that is your y-intercept.

As for the slope, always remember [tex]\frac{rise}{run\\}[/tex]. What this means is you first count up before counting horizontally for the slope. Your slope is 3/4, so from your y-intercept, count three numbers up, and four to the right (since the slope is positive). This second point should be at (4, 5)

Step-by-step explanation:

linear line. but not passing through the origin

Can anyone help with polynomials?

Answers

Yes. I can help. What do you need with help with concerning polynomials?

Emily is training for a 10K race. On day one, she runs for 20 minutes. On day two, she runs for 30 minutes. On day three, she runs for 40 minutes. If this pattern continues, how many minutes will she run on day 8?

Answers

Answer:

90 minutes

Step-by-step explanation:

Given that On day one, she runs for 20 minutes. On day two, she runs for 30 minutes. On day three, she runs for 40 minutes, this pattern may be presented as an arithmetic sequence shown below

20, 30, 40 ...

For an arithmetic sequence whose first term is a, and a common difference d, the nth term of the sequence may be given as

Tn = a + (n - 1)d

Hence the first term is 20, the common difference d is 10

On the 8th day, the 8th term

T8 = 20 + (8 - 1) 10

= 20 + 70

= 90 minutes

Final answer:

Emily will run for 90 minutes on day 8, calculated by applying the formula for the n-th term of an arithmetic sequence with a first term of 20 minutes and a common difference of 10 minutes.

Explanation:

Emily is training for a 10K race with a pattern of increasing her running time by 10 minutes each day. On day one, she runs for 20 minutes, on day two for 30 minutes, and on day three for 40 minutes. To calculate how many minutes she will run on day 8, we can observe this as an arithmetic sequence where the common difference is 10 minutes.

Using the formula for the nth term of an arithmetic sequence, which is an = a1 + (n-1)d, where:

a1 is the first termd is the common differencen is the term number

We know that a1 is 20 minutes, d is 10 minutes, and n is 8 because we are looking for the time on day 8.

Therefore, a8 = 20 + (8-1)
10 = 20 + 70 = 90 minutes.

So, on day 8, Emily will run for 90 minutes.

The length of an alligator in a zoo is 1458 feet. The Everglades National Park lists the longest alligator ever recorded in Florida at 17512 feet. Which is the difference in their lengths?

Answers

Final answer:

The difference in length is 16,054 feet.

Explanation:

The difference in length between the alligator in the zoo and the longest alligator ever recorded in Florida is 16,054 feet.



To find the difference, you subtract the length of the alligator in the zoo from the length of the longest alligator recorded. So, 17,512 feet - 1,458 feet = 16,054 feet.

Learn more about Alligator length difference here:

https://brainly.com/question/28634292

#SPJ12

30 pts for any one who answers this question just use the image
and also i will be giving you a brainly if you answer this question right

Answers

Answer: 50,50,70

Step-by-step explanation:

Part A : 50 Males preferred playing sports

Part B : 50 people(including male and female both)

Part C : 70 females

A rectangle has a height of k2 + 3 and a width of k2 + 7.

Express the area of the entire rectangle.

Your answer should be a polynomial in standard form.

k2

2

+

Answers

Answer:

The area of the rectangle in polynomial form is [tex]k^4 +10 k^2 + 21[/tex]

Step-by-step explanation:

Given

Shape: Rectangle

[tex]Height: k^2 + 3[/tex]

[tex]Width: k^2 + 7[/tex]

Required

Area of the rectangle

The area of a rectangle is calculated as thus;

[tex]Area = Length * Width[/tex]

By substituting [tex]k^2 + 3[/tex] for height and [tex]k^2 + 7[/tex] for width; This gives

[tex]Area = (k^2 + 3)(k^2 + 7)[/tex]

Expand the bracket

[tex]Area = k^2(k^2 + 7) + 3(k^2 + 7)[/tex]

Open each bracket

[tex]Area = k^2*k^2 + k^2*7 + 3*k^2 + 3*7[/tex]

[tex]Area = k^4 +7 k^2 + 3k^2 + 21[/tex]

[tex]Area = k^4 +10 k^2 + 21[/tex]

Hence, the area of the rectangle in polynomial form is [tex]k^4 +10 k^2 + 21[/tex]

How can you find the area of a two-dimensional composite figure, or the surface area of a three-dimensional composite figure?

Answers

Step-by-step explanation:

a. the area of a two-dimensional composite figure

In this situation, we need to draw any necessary segments to view the figure as basic shapes, then:

Step 1: add basic shape areas belonging to the composite shape Step 2: subtract basic shape areas NOT belonging to the composite shape

b. the surface area of a three-dimensional composite figure

As we know (3D) composite objects are made of two or more objects put together. To find the surface area of a 3D composite object, we need:

Step 1:  find the outside surface area of each object Step 2: add the surface areas together

Hope it will find you well

Final answer:

To find the area of composite figures, break them down into simpler shapes and sum up their areas. For three-dimensional figures, find individual surface areas and add them up.

Explanation:

Area can be determined by counting the number of squares inside a shape on 1 cm x 1 cm graph paper. For composite figures, break them down into simpler shapes, find their individual areas using appropriate formulas, then add them up. For three-dimensional composite figures, calculate surface area by finding the sum of individual surface areas of each component shape.

suppose you know the following facts about angle ABC and angle DEF ​

Answers

Answer:

i would say the third choice.

Step-by-step explanation:

both sides in question are all the hypotenuse(s) of the triangles , hence one gets the  same way , i.e , the Pythogrean method

Can someone please help me with this.​

Answers

Answer: The answer it C. 135

Step-by-step explanation:

It is a supplementary angle so therefore it’s supposed to equal 180 degrees.

So, 180-45= 135

Pleasee help
Slope from graph

Answers

Answer:

-1 is the slope

Step-by-step explanation:

to find the slope, you should find two different points on the line which is exactly on the grid. For example, (-2,0) and (-1,-1) is an ok choice. The formula for slope is y^2 - y^1 / x^2 - x^1 = slope

so it would look like -1-0 / -1-(-2)

then -1/1

which is -1

good luck

nssnsjsjzsbsbshajmznznznsnsjsnsnsns

find the hypotenuse for the following ​

Answers

Answer:

6.403 units

or [tex]\sqrt{41}[/tex]

Step-by-step explanation:

We want the hypotenuse.

The hypotenuse is from the point (-3, -1) to point  (2, 3)

D( (-3, -1), (2, 3)) = root ( (2 - (-3))^2 + (3 - -1)^2 ) =

D( (-3, -1), (2, 3)) = root ( 5^2 + 4^2)  =  root( 25 + 16)

D( (-3, -1), (2, 3)) = root ( 41)

D( (-3, -1), (2, 3)) = 6.403 units

Answer:

6.4 (rounded to nearest tenth)

Step-by-step explanation:

Distance from (-3,-1) to (2,-1) is 5 units

Distance from (2,-1) to (2,3) is 4 units

4^2+5^2=x^2     x=hypothenuse

16+25=x^2

41+x^2

(take square root of both sides)

x=6.4

How do you find the circumference of a circle

Answers

Answer:

You can find the circumference of a circle by using the measurement of its diameter, radius or area. The circumference of a circle is the distance around the circle's edge from one point, meeting back at that point.

Example: C = π ⋅ d = 2 π ⋅ r

The daily gazzette has 25 companies that pay for advertising each month the newspaper wants to increase its advertisers by 5 each month what equation can be used to determine m the number of months it will take to double it

Answers

Answer: 25+5m =50

Step-by-step explanation:

Hi, to answer this question we have to write an equation:

The actual number of companies that pay for advertising each month (25) plus the product of the companies added per month (5) and the number of months (m) must be equal to the actual number of advertisers multiplied by 2 ( since they want to double it ).

Mathematically speaking:

25 +5m = 25 (2)

25+5m =50

Feel free to ask for more if needed or if you did not understand something.  

Answer:

m=a/5

Step-by-step explanation:

From the statement, you have that the number of advertisers would be equal to the number of companies the daily gazzette has plus the 5 advertisers the newspaper wants to increase each month multiply for the number of months. From this, the expression would be:

2a=a+5m, where

a= number of advertisers

From this, we can isolate m:

5m=a

m=a/5

You can solve it to find the number of months it will take to double the advertisers:

m=25/5= 5

It will take 5 months as:

25+(5*5)= 25+25= 50

simplify the expression 2(2+4v)

Answers

Step-by-step explanation:

2(2+4v)

multiply 2 with the number in bracket

4+8v=0

8v= -4

v=-4/8

v= -1/2

Step-by-step explanation:

2(2 + 4v)

4 + 8v

If you have to find the value of v

4 + 8v = 0

8v = - 4

V = - 4/8 = - 1/2

Brad had $530.45 in his checking account. He wrote checks for $16.50 and $95.68. He also made a deposit of $19.13. What is the approximate final balance in his account?

Answers

Answer:

Around $437.4

Step-by-step explanation:

Answer:

437.40

Step-by-step explanation:

a check would be a decrease to his checking account balance so 530.45 minus 16.50 would equal 513.95. 513.95 minus 95.68 equals 418.27. a deposit would be a increase to his balance. 418.27 plus 19.13 would equal 437.40.


You can swim 200 meters in 15 minutes. Your friend can swim 240 meters at the same
pace at you. How long does your friend swim?​

Answers

Answer:

18 minutes

Step-by-step explanation:

trust me

answer: 18 minutes

explanation: 15/ 200=.075 so they both swim at .075 minutes for every meter so multiply .075 by 240 and you get 18

What is the sum? StartFraction 3 y Over y squared + 7 y + 10 EndFraction + StartFraction 2 Over y + 2 EndFraction

Answers

Answer:

[tex]\dfrac{5}{y+5}[/tex]

Step-by-step explanation:

Here, we have to find the sum of 2 fractions:

1st fraction: [tex]\dfrac{3y}{y^{2}+7y+10}[/tex]

2nd fraction: [tex]\dfrac{2}{y+2}[/tex]

Considering the denominator of 1st fraction:

[tex]y^{2}+7y+10[/tex]

Using factorization method:

[tex]7y[/tex] can be written as [tex](2y + 5y)[/tex].

[tex]\Rightarrow y^{2}+2y+5y+10[/tex]

Taking 5 common from [tex]5y+10[/tex] and y common from [tex]y^{2}+2y[/tex]: [tex]\Rightarrow y(y+2)+5(y+2)[/tex]

Now taking [tex](y+2)[/tex] common:

[tex]\Rightarrow (y+5)(y+2)[/tex]

[tex]\dfrac{3y}{y^{2}+7y+10}[/tex] can be written as [tex]\dfrac{3y}{(y+5)(y+2)}[/tex]

Now, calculating the sum:

[tex]\dfrac{2y}{(y+5)(y+2)} + \dfrac{2}{y+2}[/tex]

Taking LCM and solving:

[tex]\Rightarrow \dfrac{3y+2(y+5)}{(y+5)(y+2)}\\\Rightarrow \dfrac{5y+10}{(y+5)(y+2)}\\\Rightarrow \dfrac{5(y+2)}{(y+5)(y+2)}\\\Rightarrow \dfrac{5}{(y+5)}[/tex]

Hence, answer is [tex]\dfrac{5}{y+5}[/tex].

Answer:

its c

Step-by-step explanation:

i have takin da test

- (7p + 6) - 2 (-1 - 2p)

Answers

The answer will be -3p -4

Mr. Valdez puts $10,000 in a retirement account and does not make any deposits or withdrawals. The table below shows the amount of money in the account after x years.

A 2-column table with 5 rows. The first column is labeled years with entries 0, 10, 20, 30, 40. The second column is labeled amount (dollar sign) with entries 10,000; 16,000; 27,000; 43,000; 70,000.
What values, rounded to the nearest hundredth, complete the exponential regression equation that models the data?



f(x) =
(
)x

Answers

Answer:

f(x)= 9,974.73  (1.05)x

Step-by-step explanation:

edge 2022

increased competition for power among European states and led to imperialism.
Ethnocentrism
Communism
Industrialization
Social Darwinism

Answers

The answer is c:industrialization

Answer:

INDUSTRIALiZATION

Step-by-step explanation:

got it right

Find the product using the number line. 3(-6) = A number line going from negative 7 to positive 3. An arrow goes from negative 6 to negative 4, from negative 4 to negative 2, and from negative 2 to 0. What error(s) are shown here? Check all that apply. The arrows should be a length of 2. The arrows should be a length of 6. The arrows should be pointing in the positive direction. The arrows should start at zero. The arrows should point in the negative direction.

Answers

Answer:

B - The arrows should be length of 6.

D - The arrows should start at zero.

E - The arrows should point in the negative direction

Step-by-step

since it is asking us to find the product you will have to  start at negative 6 and then you are going to jump 3 spaces 3(-6)

Answer:

B - The arrows should be length of 6.

D - The arrows should start at zero.

E - The arrows should point in the negative direction

Step-by-step explanation:

Ms. Davis schedules after-school group
activities for 18 girls and 24 boys. She wants
to make equal groups with the same number
of girls and the same number of boys in
each group. Ms. Davis says that the greatest
number of equal groups she can make is 3.

Answers

Answer:

Ms. Davis is wrong

Step-by-step explanation:

she can make equal groups of 6

The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached the
spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s?
m
10
10
S.
m
3
0 m
ma
30

Answers

The equation that relates the mass of the object m and the length of the spring s is s = 0.3m, based on the given information that a 30-gram object stretches the spring 9 centimeters.

The direct variation between the mass of an object and the length of a spring can be described by the equation:

s = k × m, where s is the spring length, m is the mass of the object, and k is the constant of proportionality.

For a 30-gram object stretching the spring to 9 centimeters, the constant k can be found using:

k = s/m, which is k = 9 cm / 30 g, so k = 0.3 cm/g.

Therefore, the equation that relates the mass of the object m and the length of the spring s is s = 0.3m.

Can somebody help me find the Domain, Range, Horizontal Asymptote, Y-Intercept, and End Behavior of the function f(x) = -2e^x + 4 ?

Answers

Answer:

Domain = R

Range = (-∞, 4)

Hor. asymp = y=4

Y intercept: f(0) = (0,2)

end behaviour:

x → -∞: f(x) → 4

x→ ∞: f(x) → -∞

Step-by-step explanation:

For the domain, it is R because e^x works for all values of x

For the range, y will never be above 4.

The hor. asymptote is found via [tex]\lim_{x \to -\infty} f(x)[/tex] there the e term will be zero, so what is left is y=4.

Y intercept, fill in f(0)

end behaviour: for small x, y goes to the asymptote, for large x, y goes to minus infinity.

Final answer:

Explained the Domain, Range, Horizontal Asymptote, Y-Intercept, and End Behavior of f(x) = -2e^x + 4

Explanation:

Domain and Range:

Domain: All Real Numbers

Range: f(x) ≤ 4

Horizontal Asymptote:

Horizontal Asymptote: y = 4

Y-Intercept:

Y-Intercept: (0, 2)

End Behavior:

End Behavior: As x → ∞, f(x) → 4; As x → -∞, f(x) → -∞

Peter & Alex share a lottery win of £4450 in the ratio 4 : 1. Peter then shares his part between himself, his wife & their son in the ratio 1 : 6 : 3. How much more does his wife get over their son?

Answers

Answer:

His wife gets $1068 more than his son.

Step-by-step explanation:

Peter and Alex:

Peter gets [tex]\frac{4}{4+5} = \frac{4}{5}[/tex] of the total amount.

[tex]\frac{4*4450}{5} = 3560[/tex]

Peter gets $3560. He divides with his wife and son.

Peter gets [tex]\frac{1}{1+6+3} = \frac{1}{10}[/tex] of the amount, the wife gets [tex]\frac{6}{1+6+3} = \frac{6}{10}[/tex] and the son gets [tex]\frac{3}{1+6+3} = \frac{3}{10}[/tex]

Wife:

[tex]\frac{6*3560}{10} = 2136[/tex]

His wife gets $2136

Son:

[tex]\frac{3*3560}{10} = 1068[/tex]

How much more does his wife get over their son?

2136 - 1068 = 1068

His wife gets $1068 more than his son.

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