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# magic square 16 boxes each box has to give a number up to16 but when added any 4 boxes equal 34

hi friends, in magic square there 16 boxes each box has to give each number upto 16 but when we add any 4 boxes we should get 34 in this question it is a magic square if we add each row we get 34 if it is in diagonal also pls replay fast friends

## Research, Knowledge and Information :

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The number 15 is called the magic number of the 3x3 square. ... The magic number is (1+2+...+15+16):4 = 34. ... You find the complementary square, if you replace each ...

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## Suggested Questions And Answer :

### magic square 16 boxes each box has to give a number up to16 but when added any 4 boxes equal 34

The magic square consists of 4X4 boxes. We don't yet know whether all the numbers from 1 to 16 are there. Each row adds up to 34, so since there are 4 rows the sum of the numbers must be 4*34=136. When we add the numbers from 1 to 16 we get 136, so we now know that the square consists of all the numbers between 1 and 16. We can arrange the numbers 1 to 16 into four groups of four such that within the group there are 2 pairs of numbers {x y 17-x 17-y}. These add up to 34. We need to find 8 numbers represented by A, B, ..., H, so that all the rows, columns and two diagonals add up to 34. A+B+17-A+17-B=34, C+D+17-C+17-D=34, ... (rows) A+C+17-A+17-C=34, ... (columns) Now there's a problem, because the complement of A, for example, appears in the first row and the first column, which would imply duplication and mean that we would not be able to use up all the numbers between 1 and 16. To avoid this problem we need to consider other ways of making up the sum 34 in the columns. Let's use an example. The complement of 1 is 16 anewd its accompanying pair in the row is 2+15; but if we have the sum 1+14 we need another pair that adds up to 19 so that the sum 34 is preserved. We would perhaps need 3+16. We can't use 16 and 15 because they're being used in a row, and we can't use 14, because it's being used in a column, so we would have to use 6+13 as the next available pair. So the row pairs would be 1+16 and 2+15; the column pairs 1+14 and 6+13; and the diagonal pairs 1+12 and 10+11. Note that we've used up 10 of the 16 numbers so far. This type of logic applies to every box, apart from the middle two boxes of each side of the square (these are part of a row and column only), because they appear in a row, a column and diagonal. There are only 10 equations but 16 numbers. In the following sets, in which each of the 16 boxes is represented by a letter of the alphabet between A and P, the sum of the members of each set is 34: {A B C D} {A E I M} {A F K P} {B F J N} {C G K O} {D H L P} {D G J M} {E F G H} {I J K L} {M N O P} The sums of the numbers in the following sets in rows satisfy the magic square requirement of equalling 34. This is a list of all possibilities. However, there are also 24 ways of arranging the numbers in order. We've also seen that we need 10 out of the 16 numbers to satisfy the 34 requirement for numbers that are part of a row, column and diagonal; but the remaining numbers (the central pair of numbers on each side of the square) only use 7 out of 16. The next problem is to find out how to combine the arrangements. The vertical line divides pairs of numbers that could replace the second pair of the set. So 1 16 paired with 2 15 can also be paired with 3 14, 4 13, etc. The number of alternative pairs decreases as we move down the list. 17 X 17: 1 16 2 15 | 3 14 | 4 13 | 5 12 | 6 11 | 7 10 | 8 9 2 15 3 14 | 1 16 | 4 13 | 5 12 | 6 11 | 7 10 | 8 9 3 14 4 13 | 1 16 | 2 15 | 5 12 | 6 11 | 7 10 | 8 9 4 13 5 12 | 1 16 | 2 15 | 3 14 | 6 11 | 7 10 | 8 9 5 12 6 11 | 1 16 | 2 15 | 3 14 | 4 13 | 7 10 | 8 9 6 11 7 10 | 1 16 | 2 15 | 3 14 | 4 13 | 5 12 | 8 9 7 10 8 9 | 1 16 | 2 15 | 3 14 | 4 13 | 5 12 | 6 11 16 X 18: 1 15 2 16 | 4 14 | 5 13 | 6 12 | 7 11 | 8 10 2 14 3 15 | 5 13 | 6 12 | 7 11 | 8 10 3 13 4 14 | 2 16 | 6 12 | 7 11 | 8 10 4 12 5 13 | 2 16 | 3 15 | 7 11 | 8 10 5 11 6 12 | 2 16 | 3 15 | 4 14 | 8 10 6 10 7 11 | 2 16 | 3 15 | 4 14 | 5 13 7 9 8 10 | 2 16 | 3 15 | 4 14 | 5 13 | 6 12 15 X 19: 1 14 3 16 | 4 15 | 6 13 | 7 12 | 8 11 2 13 4 15 | 3 16 | 5 14 | 7 12 | 8 11 3 12 5 14 | 4 15 | 6 13 | 8 11 4 11 6 13 | 3 16 | 5 14 | 7 12 5 10 7 12 | 3 16 | 4 15 | 6 13 | 8 11 6 9 8 11 | 3 16 | 4 15 | 5 14 | 7 12  7 8 9 10 | 3 16 | 4 15 | 5 14 | 6 13 14 X 20: 1 13 4 16 | 5 15 | 6 14 | 8 12 | 9 11 2 12 5 15 | 4 16 | 6 14 | 7 13 | 9 11 3 11 6 14 | 4 16 | 5 15 | 7 13 | 8 12 4 10 7 13 | 5 15 | 6 14 | 8 12 | 9 11 5 9 8 12 | 4 16 | 6 14 | 7 13 | 9 11 6 8 9 11 | 4 16 | 5 15 | 7 13 13 X 21: 1 12 5 16 | 6 15 | 7 14 | 8 13 | 10 11 2 11 6 15 | 5 16 | 7 14 | 8 13 | 9 12 3 10 7 14 | 5 16 | 6 15 | 8 13 | 9 12 4 9 8 13 | 5 16 | 6 15 | 7 14 | 10 11 5 8 9 12 | 6 15 | 7 14 | 10 11 6 7 10 11 | 5 16 | 8 13 | 9 12 12 X 22: 1 11 6 16 | 7 15 | 8 14 | 9 13 | 10 12 2 10 7 15 | 6 16 | 8 14 | 9 13 | 10 12 3 9 8 14 | 6 16  4 8 9 13 | 6 16 | 7 15  5 7 10 12 | 6 16 11 X 23: 1 10 7 16 | 8 15 | 9 14 2 9 8 15 | 7 16  3 8 9 14 | 7 16  10 X 24: 1 9 8 16 To give an example of how the list could be used, let's take row 3 in 17 X 17 {3 14 4 13}. If 3 is the number in the row column and diagonal, then we need to inspect the list to find another row in a different group containing 3 that doesn't duplicate any other numbers. So we move on to 15 X 19 and we find {3 12 8 11} and another row in 13 X 21 with {3 10 5 16}. So we've used the numbers 3, 4, 5, 8, 10, 11, 12, 13, 14, 16. That leaves 1, 2, 6, 7, 9, 15. In fact, one answer is: 07 12 01 14 (see 15x19) 02 13 08 11 16 03 10 05 09 06 15 04

### 0.8x0.9x0.8 is how many square inches

0.8x0.9x0.8 is how many square inches I need to know how many square inches the above would equal You will not get SQUARE INCHES by multiplying three numbers. You get CUBIC INCHES. Multiplying the first two numbers gives you a rectangular area, measured in square inches. Then, multiplying by the third number gives you a cubic volume, with height added to the rectangular area. 0.8 x 0.9 = 0.72 square inches, a flat area 0.72 x 0.8 = 0.575 cubic inches, a block, with volume

### what 3 numbers when added together will give you the same total as when they are multiplied?

let number =x , so add them together gives you 3x then multiple them equal to x^3 so solve the two equation then you have x= 0,square root of 3,_ square root of 3 :)

### What two numbers added up to get 12 but when multipled equal 54

Let a and b represent the numbers, then a+b=12 ands ab=54. Substitute b=12-a in the product: a(12-a)=54. 12a-a^2=54, so a^2-12a+54=0. Before applying the quadratic formula, we note that the result is going to b complex because the roots have to be positive because the constant 54 is positive and the minimum sum of the roots is greater than 12 (minimum would be about 14.7). For example, 1+54, 2+27, 3+18, 6+9, are all greater than 12. The formula gives (12+sqrt(144-216))/2=(12+sqrt(-72))/2=(12+6sqrt(-2))/2=6+3isqrt(2). In these solutions i is the imaginary number equal to the square root of -1. So the two numbers are 6+3isqrt(2) and 6-3isqrt(2). The sum of these is 12 and the product is 36+18=54.

### how to evaluate expression

The quadratic x^2+10x+23=0 has roots -5+sqrt(2). We can write the quadratic x(x+10)=-23, so x=-23/(x+10). We can bring in sqrt(2) iteratively: put x=-5 into the expression on the right: x=-23/5=-4.6. Then we put x=-4.6 into the expression so we have x=-23/5.4=-4.259259... Put x=-4.259259 into the expression we get x=-4.0064516, and then we get x=-3.83746, and so on until after numerous iterations (repeating the process) we get to -3.585786438. This is very close to one of the roots of the equation, in other words -5+sqrt(2). The initial value of -5 guides the process to this root rather than the other root. Therefore, we can evaluate sqrt(2) by adding 5 to this number: 5-3.585786438=1.414213562. This iterative process can be performed by a calculator by repeatedly putting the value of x back into the same expression to get the next value of x. Some calculators allow you to build up an expression and keep applying it iteratively as you get each approximation. Using this method you can see the values converging until you reach the accuracy limits of the calculator and you get an unchanging result. You can apply this method using x=1/(x-2). Start with x=1, then you get x=-0.5, then -0.4, then -0.4167 up to -0.4142135624. Then you add 1 to get sqrt(2). This gives you a more accurate answer because we have an extra digit 4 at the end. The iterative process can give you slightly better accuracy than simply working out sqrt(2) directly on your calculator.

### what two numbers added together make 49 but when multiplied equal a negative 100

what two numbers added together make 49 but when multiplied equal a negative 100 x + y = 49            xy = -100 y = 49 - x            x(49 - x) = -100 x(49 - x) = -100 49x - x^2 = -100 -1 * (49x - x^2) = -100 * -1 -49x + x^2 = 100 x^2 - 49x = 100                  1/2 of 49 is 24.5 Complete the square x^2 - 49x + 24.5^2 = 100 + 24.5^2 (x - 24.5)^2 = 100 + 600.25 = 700.25 Take the square root of both sides x - 24.5 = ±26.462237    This has been rounded, so multiplication that                                         use these values will be slightly off x = 26.462237 + 24.5 = 50.962237 x = -26.462237 + 24.5 = -1.962237 50.962237 + (-1.962237) = 49 50.962237 - 1.962237 = 49 50.962237 * (- 1.962237) = -99.999987 The two numbers are 50.962237 and -1.962237

### show that the function f(x)= sqrt (x^2 +1) satisfies the 2 hypotheses of the Mean Value Theorem

f(x) = sqrt(x^2 + 1) ; [(0, sqrt(8)] Okay, so for the Mean Value Theorem, two things have to be true: f(x) has to be continuous on the interval [0, sqrt(8)] and f(x) has to be differentiable on the interval (0, sqrt(8)). First find where sqrt(x^2 + 1) is continous on. We know that for square roots, the number has to be greater than or equal to zero (definitely no negative numbers). So set the inside greater than or equal to zero and solve for x. You'll get an imaginary number because when you move 1 to the other side, it'll be negative. So, this means that the number inside the square root will always be positive, which makes sense because the x is squared and you're adding 1 to it, not subtracting. There would be no way to get a negative number under the square root in this situation. Therefore, since f(x) is continuos everywhere, (-infinity, infinity), then f(x) is continuous on [0, sqrt(8)]. Now you have to check if it is differentiable on that interval. To check this, you basically do the same but with the derivative of the function. f'(x) = (1/2)(x^2+1)^(-1/2)x2x which equals to f'(x) = x/sqrt(x^2+1). So for the derivative of f, you have a square root on the bottom, but notice that the denominator is exactly the same as the original function. Since we can't have the denominator equal to zero, we set the denominator equal to zero and solve to find the value of x that will make it equal to zero. However, just like in the first one, it will never reach zero because of the x^2 and +1. Now you know that f'(x) is continous everywhere so f(x) is differentiable everywhere. Therefore, since f(x) is differentiable everywhere (-infinity, infinity), then it is differentiable on (0, sqrt(8)). So the function satisfies the two hypotheses of the Mean Value Theorem. You definitely wouldn't have to write this long for a test or homework; its probably one or two lines of explanation at most. But I hope this is understandable enough to apply to other similar questions!

### what two numbers multiplied together equal -8 and added together equal 6?

If the numbers are a and b, we have ab=-8 and a+b=6. We can replace b with 6-a in the first equation: a(6-a)=-8 so 6a-a^2=-8. Rearranging: a^2-6a-8=0 and completing the square: a^2-6a+9-17=0. Therefore (a-3)^2=17. Taking the square root of each side we have a-3=+sqrt(17) and a=3+sqrt(17) and b=6-(3+sqrt(17))=3-sqrt(17), which is the other alternative for a, so whichever way round the two numbers are 3+sqrt(17)=7.1231 and -1.1231 (approx). Add them together and we get 6; multiply them and we get -8.

### what 2 numbers when multiplied equal 30 but added equal -10?

xy = 30 x + y = -10 x = -y - 10 (-y-10)(y) = 30 -y^2 - 10y = 30 y^2 + 10y + 30 = 0 quadratic formula y = (-10 +- sqrt(100 - 4(1)(30)))/2(1) y = (-10 +- sqrt(100 - 120))/2 y = (-10 +- sqrt(-20))/2 Can't take the square root of a negative number. No solution. Answer:  There are no numbers that, when multiplied, equal 30, but when added equal -10. . Note:  There sort of are two numbers that work, but it's a thing called 'complex math' that you won't encounter in Algebra 1.  For an Algebra 1 class/student, the answer is 'no solution.'