answer:In his novel The Great Gatsby, Fitzgerald criticizes the American Dream through various literary techniques. For instance, the green light symbolizes Gatsby's aspirational yet unattainable pursuit of Daisy and the idealized life she represents. The Valley of the Ashes, on the other hand, symbolizes the corruption and moral decay resulting from the relentless pursuit of wealth. Through these symbols, Fitzgerald suggests that the American Dream has become a hollow and illusionary pursuit, devoid of the original ideals of equality, opportunity, and self-improvement. He implies that the pursuit of wealth and status has corrupted the dream, ultimately leading to its death.

answer:The arclength L of the function f(x) = tan(4x) on the interval [3, 7] can be found using the integral formula for arclength: L = int_3^7 sqrt{1 + left(frac{df}{dx}right)^2} , dx First, we need to find the derivative of f(x): frac{df}{dx} = frac{d}{dx}[tan(4x)] = 4sec^2(4x) Now, we square this derivative: left(frac{df}{dx}right)^2 = (4sec^2(4x))^2 = 16sec^4(4x) Substituting this into the arclength formula gives: L = int_3^7 sqrt{1 + 16sec^4(4x)} , dx This integral represents the arclength of the function f(x) = tan(4x) from x = 3 to x = 7. To find the exact value, one would need to evaluate this integral, possibly through numerical methods, as an exact analytical solution may be complex.

answer:We are given x = -25/41. To find -x, we simply multiply both sides of the equation by -1: -x = -1 * (-25/41) -x = 25/41 Therefore, the value of -x when x = -25/41 is 25/41.

answer:Given Data: Volume of H₂ = 25.0 L The reaction between Mg and HNO₃ is: 2HNO₃ + Mg → H₂ + Mg(NO₃)₂ At STP, 1 mol of gas occupies 22.4 L. Calculation: 1. Calculate moles of H₂: ``` Moles of H₂ = Volume of H₂ / Volume of 1 mol gas at STP Moles of H₂ = 25.0 L / 22.4 L/mol Moles of H₂ = 1.116 mol ``` 2. Calculate moles of Mg (from the balanced equation, 1 mol Mg produces 1 mol H₂): ``` Moles of Mg = Moles of H₂ Moles of Mg = 1.116 mol ``` 3. Calculate mass of Mg: ``` Mass of Mg = Moles of Mg x Molar mass of Mg Mass of Mg = 1.116 mol x 24.305 g/mol Mass of Mg = 27.1 g ``` Therefore, 27.1 g of magnesium would react with excess nitric acid to produce 25.0 L of H₂ at STP.