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Find the value of m given two equations with two variables
February 2, 2025
The solution to the system of equations 5m + n = 26 and m - n = 4 is m = 5 and n = 1. Calculating m^n results in 5^1 = 5.
Solving for x in a linear equation
February 2, 2025
To solve for x in the equation 2x + 5 = 13, subtract 5 from both sides, then divide both sides by 2 to get x = 4.
Calculate the expression -5^2 + (-5)^2 / 5^2
February 2, 2025
The expression evaluates to 0 after calculating the numerator and denominator separately and then dividing them.
Find the value of x given that the angles are equal.
February 2, 2025
The sum of three angles around a point, 2x, x, and x, equals 360 degrees, leading to the solution x = 90 degrees.
Find the value of x in a triangle with given angles.
February 1, 2025
To find the unknown interior angle x, the exterior angle theorem was used, setting up and solving an equation to find x = 40 degrees.
Simplify and express products in standard form
January 31, 2025
The provided text contains a series of math problems, including algebraic expressions, exponents, fractions, and polynomial operations. The solutions demonstrate various techniques for simplifying and manipulating these expressions, such as factoring, expanding, and applying the rules of exponents and fractions.
Find the maximum and minimum value of f(x, y) = x^2 + 3xy^2 - 3x^2 - 3y^2 + 4
January 21, 2025
The function f(x,y) = -2x^2 + 3xy^2 - 3y^2 + 4 has a local maximum value of 4 at (0,0).
Finding Fourier Coefficients for a Periodic Square Pulse
January 13, 2025
The solution determines the Fourier coefficients for a periodic square pulse with a width of 3 and period of 12, finding the values of α, β, and λ in the given formula for ak.
Derivation of the tangent function from a right triangle
January 9, 2025
The derivative of tan(θ) with respect to θ is sec^2(θ), derived using right-angled triangles and the definition of the derivative.
Determine if functions are continuous at given points
December 26, 2024
The provided examples demonstrate the continuity of functions at specific points. Polynomials are continuous everywhere, functions with undefined points are not continuous at those points, and absolute value functions are continuous everywhere, including at points where the expression inside the absolute value is zero.