All Answers 358479 Answers

i^12345

(i^4)^3086 * i

(i^4)==(i^2)^2 ==(-1)^2==1

1^3086 * i==1 * i ==i

uh. Are there supposed to be numbers in the question?

divide by the power by four which will give 3086 1/4. Meaning the when i^1 = i meaning 

When i¹²³⁴⁵ it will equal i

(136, 145, 154, 163, 226, 235, 244, 253, 262, 316, 325, 334, 343, 352, 361, 415, 424, 433, 442, 451, 514, 523, 532, 541, 613, 622, 631)>>Total = 27 ways

You have

  2x          -6

------  =  --------.

x + 2      x + 4

cross multiplying (or multiplying both sides by the denominators at the same time) yields:

2x (x+4) = -6 (x+2)

Dividing by 2 makes it simpler

x (x+4) = -3 (x+2)

expanding gets us

\(x^2+4x=-3x-6\)

Now we shift stuff over to the same side (add/subtract to set it equal to 0)

\(x^2+7x+6=0\)

Now we just factor. 6 can be divided up into 1 & 6 or 2 & 3. We want the factors to sum to +7 so we choose +1 and +6.

(x + 6) (x + 1) = 0

For a product to equal 0, one or both of its factors should be 0. So either:

x + 6 = 0, or

x + 1 = 0

meaning that there are 2 possible x values which are -1 and -6.

To solve this question, it would probably be a good start to first get rid of the fractions. Why don't you multiply both sides by (x+2) and (x+4)

You would get an equation along the lines of

(2x)(x+4)=(-6)(x+2)

Why don't you try expanding that, and then finding x

(please some fancy math professional check this. this is my first time answering somebody's question)

I was able to find the answer...it's   88

Ans. 177.03km

The total surface area of a box is 100. The length of the box is twice its width, as well as 3 less than its height. How many units are in the height of the box?   

L = 2W        ——>    W = L / 2   

L = H – 3     ——>    H  = L + 3   

                                        Total Area  =  2 • L • W  +  2 • L • H  +  2 • W • H    

Substitute equivalent  

terms for W and H  

                                         A  =  (2)(L)(L/2)  +  (2)(L)(L + 3)  +  (2)(L/2)(L + 3)    

                                         A  =  2L² / 2        +  2L² + 6L        +  2L² / 2 + 6L / 2  

                                         A  =  L²               +  2L² + 6L         +  L² + 3L    

                                         100  =  4L²  +  9L     

Rearrange as     

a quadratic     

                                         4L²  +   9L  –  100  =  0    

Factor                              (4L + 25)(L – 4)  =  0   

                                          4L = –25   Disregard.  A box can't have a negative length.   

                                            L = 4    

W = L / 2     ———>            W = 2   

H = L + 3     ———>            H = 7    

check answers    

                                         Total Area  =  2 • L • W  +  2 • L • H  +  2 • W • H    

                                                   100  =  (2)(4)(2)  +  (2)(4)(7)  +  (2)(2)(7)    

                                                   100  =  16   +  56  +  28    

                                                   100  =  100     

_.

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?   

To find b, consider                                                  ab⁴  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³)  

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

_.

Good catch, second guest.    

regarding      36/x + 8/(x^2) = 0  

                      Multiplying both sides of the equation by x2, we get:  

                      36 + 8x = 0   

Maybe if I write it like this,   

it will be easier to see   

                                                 36          8  

                                               ––––  +  ––––  =  0       

                                                  x            x²     

Multiplying both sides

by x², we get    

                                                        36x  +  8  =  0   

                                                                36x  =  –8   

                                                                                8 

                                                                    x  =  – –––  =  – 2/9      

                                                                                36         

_.

That answer is wrong.

You made a typo in your final answer: x = - 8/36 = - 2 / 9

The given equation is:

(9 + 27)/x + 8/(x^2) = 0

We can simplify the equation as follows:

36/x + 8/(x^2) = 0

Multiplying both sides of the equation by x2, we get:

36 + 8x = 0

Solving for x, we get:

x = -4/9

Therefore, the only solution to the equation is x=−4/9.

1 + 999 =1000
2 + 998 =1000
3 + 997 =1000
.
.
500 + 500 =1000 [That is 500 pairs]

There are 180 integers between 1 and 999 inclusive, with at least one "0" in them:
Therefore: 180 / 2 =90 - pairs that should not be included

So: 500 pairs - 90 pairs =410 - ordered pairs.

The volume of a cone is 31​πr2h, where r is the radius of the base and h is the height of the cone. Since the cone has a volume of 432π cubic centimeters and a radius of 12 centimeters, its height is h=12π432π​=36 centimeters.

The cone is formed by joining the two bases of the sector, which have radius 12 and AB=BC=12. Therefore, the central angle of the sector that is not used is 12360∘​=30∘.

The unshaded sector has central angle 30∘, so the shaded sector has central angle 360∘−30∘=330∘.

The answer is 330​ degrees.

Find all values of x such that 3x^2 14x 8 = 0. If you find more than one value, then list your solutions, separated by commas.   

My monitor isn't displaying the signs between terms.   

I'm assuming that they should have been plus signs.  

Like this

                                                   3x² + 14x + 8 = 0    

Factor the equation   

                                                   (3x + 2)(x + 4) = 0   

Set each factor = zero    

                                                   3x + 2 = 0   which means   x = –3/2   

                                                     x + 4 = 0   which means   x = –4    

Separated by commas   

                                                     x =    (–3/2, –4)    

If the polarity of 14x was       

supposed to be negative,     

and polarity of 8 positive,    

then change the minuses   

in the answer to pluses.                 

_.

Thanks, that's right!

Will and Grace are canoeing on a lake.  Will rows at 50 meters per minute and Grace rows at 20 meters per minute. Will starts rowing at 2 p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at 2 p.m. If they always row directly towards each other, and the lake is 3800 meters across from the west side of the lake to the east side, at what time will the two meet?   

Will's rate is 50 m/min.  

Grace's rate is 20 m/min.  

They're rowing toward each other,  

so their rate of closure is 70 m/min.  

The lake is 3800 meters across.  

The time it will take them to meet is given by  

                                                                                    Distance  

                                                                            T  =  –––––––  

                                                                                       Rate  

                                                                                    3800 m  

                                                                            T  =  –––––––  

                                                                                    70 m/min  

The time it takes them to meet                             T  =  54.29 min  

Note that (0.29 min • 60 sec/min)  =  17 seconds

The time on the clock is                                             2:54:17 pm 

_.

We can factor the quadratic equation 3x^2 + 14x + 8 as follows:

(3x + 2)(x - 4) = 0

This means that either 3x + 2 = 0 or x - 4 = 0. Solving for x in each case, we get x = -4/3 or x = 4. Therefore, the solutions to the equation 3x^2 + 14x + 8 = 0 are x = -4/3, 4.

If neither a nor b has a zero digit, then the largest digit that either a or b can have is 9. Therefore, a must be between 1 and 999, inclusive, and b must be between 1 and 901, inclusive. Note that (2,998) and (998,2) should be counted as two distinct solutions.

We can count the number of solutions by considering the ones digit, the tens digit, and the hundreds digit of a and b separately. If the ones digit of a is 9, then the ones digit of b must be 1, so there is only 1 solution for this case. If the ones digit of a is 1 through 8, then the ones digit of b can be anything from 0 through 8, so there are 10 solutions for this case. Similarly, there are 10 solutions for each of the cases where the tens digit of a is 9, 1 through 8, and 0, and there are 10 solutions for each of the cases where the hundreds digit of a is 9, 1 through 8, and 0. Therefore, there are a total of 1+10⋅3⋅10=450​ solutions.

(a) Grogg's answer was probably arrived at by considering the two cases of exactly 4 A's and exactly 2 A's separately. For exactly 4 A's, there are (46​) ways to choose the 4 A's, and then 26 choices for each of the remaining two letters. For exactly 2 A's, there are (26​) ways to choose the 2 A's, and then 26 choices for each of the remaining four letters. So Grogg's answer is (46​)⋅262+(26​)⋅264.

(b) Grogg's answer is wrong because it does not account for license plates with 5 A's or 6 A's. There are (56​) ways to choose the 5 A's, and then 1 choice for the remaining letter, so there are (56​)=6 license plates with 5 A's. There is only 1 license plate with 6 A's. So Grogg's answer should be (46​)⋅262+(26​)⋅264+6+1. The correct answer is larger than Grogg's answer because Grogg's answer does not account for all the possible license plates.

(c) The correct answer to Ms. Q's problem is (46​)⋅262+(26​)⋅264+6+1=15⋅676+1560+7=26353. This is the number of license plates that contain exactly 4 A's, exactly 2 A's, 5 A's, or 6 A's.

Here is a more detailed explanation of how to solve the problem:

Case 1: Exactly 4 A's. There are (46​) ways to choose the 4 A's, and then 26 choices for each of the remaining two letters. So there are (46​)⋅262=15⋅676=10140 license plates with exactly 4 A's.

Case 2: Exactly 2 A's. There are (26​) ways to choose the 2 A's, and then 26 choices for each of the remaining four letters. So there are (26​)⋅264=1560 license plates with exactly 2 A's.

Case 3: 5 A's. There are (56​) ways to choose the 5 A's, and then 1 choice for the remaining letter. So there is 1 license plate with 5 A's.

Case 4: 6 A's. There is only 1 license plate with 6 A's.

The total number of license plates is 10140+1560+1+1=26353​.

I used google translate    Я использовал переводчик гугл...


The camp has an equal number of boys and girls. The number of children under the age of 13 is 2 times higher than the number of children over 13 years of age. If the same number is written to the right and left of the number 4, the number of children in the camp is formed. What is this number?

В лагере отдыхает равное количество мальчиков и девочек. Количество детей в возрасте до 13 лет в 2 раза превышает количество детей старше 13 лет. Если справа и слева от цифры 4 написать одно и то же число, образуется количество детей в лагере. Какой это номер?

I only understood the first part...   Я понял только первую часть...

here's a hint...    вот подсказка

u = children under thirteen years            u =  дети до тринадцати лет

o = children over thirteen                        o =  дети старше тринадцати лет

u = 2o           


I hope this helps...

надеюсь, это поможет

Each face of a cube is painted randomly one of the colors red, orange, yellow, green, blue, purple, brown, black, or white. What is the probability that the cube has at least one pair of faces that share an edge and are the same color? Express your answer as a decimal to the nearest thousandth.    

The first face that we're comparing can be any of them,   

so all that needs to concern us is the second face.    

There are 4 faces that share an edge with the first face.  

All of them except the face directly opposite.  

There are 9 colors available, so the second face has a 1/9   

chance of being the same color as the first face.   

But there are 4 adjacent faces, so you have 4 shots at   

getting the same color.  This makes the probability 4/9.   

Expressed as a decimal fraction, 4/9 = 0.444.  

_.