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By solving the system of equations x + y = 3 and x - y = 9, we find x = 6 and y = -3. Then, substituting these values into (x/y)^2, we get 4.

The total volume of infinitely many cubes with side lengths decreasing according to the sequence 1, 1/√2, 1/√3, ... is finite, while the total surface area is infinite.

The expression 2^(n+4) - 2(2^n) / 2(2^(n+3)) simplifies to 7/8.

The derivative of xy + sin(x) = e^y with respect to x is found using implicit differentiation, applying the product rule and chain rule, and solving for dy/dx.

The derivative of x² + y² = 25 with respect to x is -x/y.

The derivative of sin(2x² + 3x) is found using the chain rule, differentiating the outer sine function and the inner quadratic function separately, and then multiplying the results: cos(2x² + 3x) * (4x + 3).

The derivative of the function f(x) = 3x^2 - 4x + 7 is f'(x) = 6x - 4.

The problem involves finding the value of x in an expression where the greatest common factor (GCF) of two terms is given. The GCF is used to determine the value of x, but the problem cannot be solved without additional information about the variable y.

To find the area of the shaded region, subtract the area of a circle (formed by two semicircles) from the area of the enclosing rectangle.

The equation "\[\sqrt{(M-4)(M+4)} = 3\]" was solved by squaring both sides, expanding, simplifying, and taking the square root to find the solutions M = 5 and M = -5.