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What dies 4 and t b b in a p stand for?
4 and twenty blackbirds baked in a pie.
What is a partial sums?
Partial sums are used in calculus: for integration. Suppose you wish to integrate an algebraic fraction of the form f(x)/g(x) where f and g are polynomial functions of x with integer coefficients. If the coefficients are rational but not integer then they can be converted to integer simply by using the LCM. Also, suppose that the order of f(x) is less than that of g(x). Otherwise divide f(x) by g(x) to reach a position where the order of f is less. Then if g(x) can be factorised as g(x) = p(x)*q(x) where p and q are polynomials in x and are of lower order than g. Then f(x)/g(x) can be written as u(x)/p(x) + v(x)/q(x) where u and v are of lower order than p and q, respectively. This is particularly important when g(x) is a quadratic and g(x) = p(x)*q(x) where p and q are binomials. Then f(x)/g(x) = A/p(x) + B/q(x) where A and B are constants. and then, if I represents the integral, I(f/g) = I(A/p) + I(B/q) = A*I(1/p) + B*I(1/q) = A*ln|p| + B*ln|q| + C where C is the constant of integration. = k*ln{|p|^A/|q|^B} where k = e^C u(x)/p(x) + v(x)/q(x) are partial fractions for f(x)/g(x). Because partial fractions are polynomials of lower order than the original fractions, there is a greater chance that there is a simple analytical integral.
How do you subtract fractions butterfly method?
For the denominator, multiply the denominators together. For the numerator, subtract the second numerator multiplied by the first denominator from the first numerator multiplied by the second denominator: a/b - p/q = (a x q - b x p)/b x q eg: 6/7 - 3/4 = (6 x 4 - 7 x 3)/7 x 4 = (24 - 21)/28 = 3/28
What does the b stand for in the formula y equals mx plus b?
That is the value called the y intercept - value of y when x = 0 for example if y = 3x + 4 b = 4 and y = 4 when x = 0
Prove that if a and b are rational numbers then a multiplied by b is a rational number?
If a is rational then there exist integers p and q such that a = p/q where q>0. Similarly, b = r/s for some integers r and s (s>0) Then a*b = p/q * r/s = (p*r)/(q*s) Now, since p, q r and s are integers, p*r and q*s are integers. Also, q and s > 0 means that q*s > 0 Thus a*b can be expressed as x/y where p and r are integers implies that x = p*r is an integer q and s are positive integers implies that y = q*s is a positive integer. That is, a*b is rational.
