answer:To determine which of the given equations is a quadratic equation in terms of x, we analyze each option: A: 2x-1=4 can be rewritten as 2x = 5, which simplifies to x = frac{5}{2}. This equation is linear because it can be expressed in the form ax + b = 0 where a and b are constants. Therefore, it is not a quadratic equation. B: xy + x = 3 involves two variables, x and y. Although it could be rearranged to a form that resembles a quadratic equation in terms of x (if y is considered a constant), it inherently involves two variables. Thus, it does not meet the criteria for a quadratic equation in one variable. C: x - frac{1}{x} = 5 can be rewritten as x^2 - 1 = 5x, which after rearranging gives x^2 - 5x - 1 = 0. Despite appearing to be quadratic, the original form involves a term with x in the denominator, making it a rational equation rather than a standard quadratic equation in its simplest form. D: x^2 - 2x + 1 = 0 is in the standard form of a quadratic equation, ax^2 + bx + c = 0, where a = 1, b = -2, and c = 1. This equation is quadratic in one variable, x, and meets the requirements of the problem. Therefore, the correct answer is boxed{D}.

answer:Solution: (1) Since 18^b=5, we have log_{18}5=b. log_{36}45= frac{log_{18}45}{log_{18}36} = frac{log_{18}5+log_{18}9}{1+log_{18}2}, Since log_{18}2=1-log_{18}9=1-a, we have log_{36}45= frac{a+b}{2-a}. So, boxed{log_{36}45= frac{a+b}{2-a}}. (2) f(x)=sin^2x+cos x=-cos^2x+cos x+1=-left(cos x- frac{1}{2}right)^2+ frac{5}{4}. Since -1leq cos x leq 1, the maximum value of f(x) is achieved when cos x= frac{1}{2}, which gives f(x)= frac{5}{4}. Thus, boxed{text{The maximum value of } f(x) text{ is } frac{5}{4}}.

answer:Since a=cos61°cdotcos127°+cos29°cdotcos37°=-cos61°cdotsin37°+sin61°cdotcos37°=sin(61°-37°)=sin24°, b= frac {2tan13 ° }{1+tan^{2}13 ^circ }=sin26°, c= sqrt { frac {1-cos50 ° }{2}}=sin25°, Therefore, by the monotonic increase of y=sin x in (0°, 90°) and using the knowledge of the unit circle, we can deduce: sin24°＜sin25°＜sin26°＜tan26°, Therefore, a＜c＜b. Hence, the correct option is: boxed{D}. This solution involves using trigonometric identities, the formula for the sine of the difference of two angles, the formula for the tangent of double angles, and simplification, then utilizing the monotonicity of the sine function and the unit circle to find the solution. This question mainly examines the comprehensive application of trigonometric identities, the formula for the sine of the difference of two angles, the formula for the tangent of double angles, and the monotonicity of the sine function, focusing on transformational thinking, and is considered a basic question.

answer:Using the formula for the determinant of a 2x2 matrix, we calculate: [ begin{vmatrix} -6 & 5 7 & -3 end{vmatrix} = (-6)(-3) - (5)(7) = 18 - 35 = -17. ] Thus, the determinant of the matrix is (boxed{-17}).