answer:The reaction between ammonia and sulfur dioxide is an acid-base reaction, where ammonia acts as a base and sulfur dioxide acts as an acid. The balanced chemical equation for this reaction is: {eq}4NH_3 + 3SO_2 to 2N_2 + 3S + 6H_2O {/eq}

answer:To find the real solutions for the given equation, we can start by squaring both sides to eliminate the square roots: begin{align*} (sqrt{4x - 13} + sqrt{7x - 1})^2 &= 8^2 4x - 13 + 2sqrt{(4x - 13)(7x - 1)} + 7x - 1 &= 64 11x - 14 + 2sqrt{(4x - 13)(7x - 1)} &= 64 2sqrt{(4x - 13)(7x - 1)} &= 75 - 11x 4(4x - 13)(7x - 1) &= (75 - 11x)^2 112x^2 - 324x + 52 &= 825 - 2530x + 121x^2 121x^2 - 112x^2 + 2530x - 324x - 825 + 52 &= 0 9x^2 + 2206x - 773 &= 0 end{align*} Now, we solve the quadratic equation for x: begin{align*} x &= frac{-2206 pm sqrt{2206^2 - 4 cdot 9 cdot (-773)}}{2 cdot 9} &= frac{-2206 pm sqrt{4865956 + 27252}}{18} &= frac{-2206 pm sqrt{4893208}}{18} &= frac{-2206 pm 4sqrt{1223302}}{18} end{align*} However, since we are looking for real solutions, we note that both square roots of a real number must also be real. Thus, we can simplify further: begin{align*} x &= frac{-2206 pm 4sqrt{1223302}}{18} &= frac{-2206 pm 4sqrt{4 cdot 3058255}}{18} &= frac{-2206 pm 4 cdot 2 sqrt{3058255}}{18} &= frac{-2206 pm 8sqrt{3058255}}{18} end{align*} The solutions are irrational numbers, so we express them in terms of the square root of the prime factorization of 3058255. However, for simplicity in an educational context, we can leave the solution in this form: x = frac{-2206 pm 8sqrt{3058255}}{18} Please note that the original answer seems to have derived from a numerical solver, and while it may be mathematically equivalent, it is not in a form that is typically expected in an educational context.

answer:The general equation for a synthesis reaction (A + B ---> AB) shows the combination of two molecules (A and B) into a larger molecule (AB). Conversely, the general equation for a decomposition reaction (AB ---> A + B) shows the breakdown of a larger molecule (AB) into two smaller molecules (A and B). This demonstrates that synthesis and decomposition reactions are inverse processes, with one building up molecules while the other breaks them down.

answer:Sequence: 10, 30, 90, 270, ... a_1 = 10, a_2 = 30, a_3 = 90, a_4 = 270, ... a_2/a_1 = 30/10 = 3, a_3/a_2 = 90/30 = 3, a_4/a_3 = 270/90 = 3, ... The ratio of each term to the previous term is constant, indicating a geometric sequence. The common ratio is 3.