What does the number I get from solving the dot product represent?
Lots of possibilities, depending on the context. The first two echo other answers previously given.The length of the projection of one vector onto another. If the two lists of numbers represent the coordinates of two separate vectors, the dot-product gives you a sense of the degree to which the two vectors point in the same direction.A weighted sum of values. If one list of numbers represents weights, and the other represents the items to sum up, the dot-product between the two lists of numbers gives the weighted sum.The cross-correlation of two lists of numbers at a single point. You can compute the cross-correlation at different offsets by "sliding" one list past the other. Cross-correlation has many applications in signal processing, including identifying best matches.The convolution of one list with another. Convolution and correlation are closely related. In convolution, though, you reverse the order of one of the lists. Convolution shows up quite often in digital filters.The evaluation of a polynomial at a single point. If one list of numbers represents the coefficients of the polynomial and the second list represents values for each of the variable expressions, the result is the value of the expression.The evaluation of a single point in a matrix multiply. If you're multiplying two matrices, each point in the result matrix is the dot product between a column in one matrix and a row in the other. Note: Since matrices are often used to represent systems of equations, this is directly related to the previous bullet.Lots of different interpretations of the result of dot product, depending on what you're using it for.I used dot product quantize analog joystick positions to a 16-direction control scheme, by taking the dot product of the joystick X/Y deflection against 16 direction vectors, and returning the direction vector that had the largest dot product. You could interpret this against the projection or cross-correlation interpretations of dot-product.
What's the sum of the reciprocal of X and Y?
We know that reciprocal of X and Y are 1/X and 1/Y respectively.Now the sum of reciprocal of X and Y = 1/X + 1/Y= (Y + X) / XY= ( X + Y )/ XY.IT IS THE ANSWER.Hopefully it will help you.Thank you.You also can read more about sum of raciprocals on :-http://snshort.com/BbTm9MK
One eighth of a positive number is twice its reciprocal. What is the number?
The number is 4:x/8=2/x, x^2=16, x=4(The answer cannot be -4, as a positive number was stipulated)
Are there two irrational numbers whose sum and products are rationals?
Yes—in fact there are infinitely many!Consider any irrationals [math]x,y[/math] of the form[math]\quad x=p+\sqrt{q}[/math],[math]\quad y=p-\sqrt{q}[/math],where [math]p[/math] and [math]q[/math] are rational.Then[math]\quad x+y=2p[/math]and[math]\quad xy=p^2-q[/math],both of which are rational.
What does -11 equal to in rational numbers?
-11 is a rational numberIt can be represented as the ratio of two numbersIn this case, -11/1, or you could use -22/2 or -33/3 etc etc etc.Irrational numbers are numbers for which there IS no ratio of two numbers which can represent that number.The square root of two for example, look however hard you like, you’ll never find a number which, divided by another number, when squared, is equal to two. Ever.Similarly, the ratio of the radius of a circle to the diameter of a circle cannot, although the Bible implies differently, be represented by the rational number 3, nor by 22/7, nor will you ever find the final digit of the decimal which begins 3.14159…not only will you not find the end, but you won’t find a pattern, as an end or a pattern would mean you could find a ratio that represents it, and that would be RATION-al, which pi is not.
What are the conditions (or relationship) on two numbers for which the sum of reciprocals of these two numbers to be equal to the reciprocal of the sum of the numbers?
The condition put by you translates to(1/a)+(1/b) = 1/(a+b) ==> a.b = (a+b)^2 >/= 0 and hence a and b are of same sign and according to the question a.b is nonzero. Hence (a-b)^2=(a+b)^2 - 4a.b = a.b -4a.b =(-3a.b) < 0, as a.b >0. This leads to a contradiction, as (a-b)^2 >/= 0, so that such real numbers a, b do not exist.
An inspector of schools wishes to distribute 84 balls and 180 bats equally among a number of boys. Find the greatest number receiving the gift in this way?
No relation Between Inspector & School
If the sum of two real numbers is 1, what is the least value of the sum of the reciprocals?
Let the two numbers be x and (1-x)Now to find;Min[1/x+1/(1-x)]= Min(1/(x(1-x))By using the conventional method of finding maxima and minima we differentiate 1 /(x(1-x)) and equate it’s slope with ‘0′ thus obtaining the value of ‘x’ as x=1/2.So putting the value of x in 1/(x(1-x)) we get the minimum value as 4.The Graph of the function 1/(x(1-x)) [ graph indicated in black ]From the graph we can see that the ordinate has its least value at 4(marked by red) i.e the function 1/(x(1-x)) has its minimum value as 4.But the point to be noted is this conventional method of finding maxima and minima finds the point for which the slope of the function is zero [within the interval (−∞,∞) ] and gives us the Local Maxima or Minima.Not Global Maxima or Minima..Here 4 is also a local minima.And if you want global minima it tends to negative infinity.
What are sets of Egyptian fractions that sum to 1 and that form arithmetic sequences? (Egyptian fractions are those where 1/a+1/b+1/c...=1 ...) one such set that works is {1/2,1/3,1/6}
Note that arithmetic sequences of reciprocal integers summing to 1 correspond to arithmetic sequences of integers where each term divides the nonzero sum of the sequence [the latter arising from the former by multiplying through by any common multiple of the denominators, and the former arising from the latter by dividing through by the sum; to make this correspondence one-to-one, consider two arithmetic sequences equivalent if one is simply a rescaling of the other].Freely rescaling, we may assume our arithmetic sequences of integers are such that the greatest common denominator of the terms is 1. For an arithmetic sequence, it follows that the terms are all coprime to each other (let's call such an arithmetic sequence "primitive"), and thus that the least common multiple of the terms is their product.So we are looking for primitive arithmetic sequences of integers whose product divides their nonzero sum. (Note that the integers within the sequence must be nonzero as well)However, given any set of nonzero integers, its product is greater in magnitude than its sum, except for sets of the form {x}, or {3, 2, 1}, or {x, 1}. (Proof: it suffices to restrict attention to sets of positive integers, since negating some of the terms will leave the magnitude of the product unchanged, while at most reducing the magnitude of the sum. At this point, see When is the product of a set of numbers greater than the sum of them?)Thus (up to reversal and/or negation), the only non-constant primitive arithmetic sequences of the sort we are interested in are "3, 2, 1" (the only arithmetic sequence corresponding to {3, 2, 1}), or "3, 1, -1" (the only non-constant arithmetic sequence with a nonzero sum corresponding to {x, 1}). In Egyptian fraction terms, these become {1/2, 1/3, 1/6} and {1/1, 1/3, 1/-3}.As for constant sequences, these are all equivalent to a sequence of all 1s. In Egyptian fraction terms, this becomes n many copies of 1/n. If we are not to have duplicates, then n must be 1, yielding the singleton set {1/1}.Thus, those are the only solutions!