Predict the pH of a solution of potassium fluoride.
When potassium fluoride is dissolved in water, the ions will interact with water according to the equilibrium constants of the following equations: K+ + H2O --> KOH + H+ and F- + H2O --> HF + OH-. Because potassium hydroxide is a strong base, there will be no formation of H+. Because hydrofluoric acid is a weak acid, there will be some formation of hydroxide ion. Thus, the pH of the solution will be slightly basic.
Describe cellular respiration.
Cellular respiration is the process by which chemical energy stored in glucose is converted to energy stored in the form of ATP. The first step in cellular respiration is glycolysis, in which a glucose molecule is broken down to form two pyruvate molecules. During this process, glucose is oxdized by cofactor NAD+. The pyruvate molecules are then again by NAD+ to form acetyl-CoA. Acetyl-CoA then enters the Krebs cycle in the mitochondria, where it is further oxidized by NAD+. Reduced NADH from these three steps is then transported to the inner mitochondrial membrane, where the electrons are donated to the electron transport chain. Through this process of chemiosmosis, a proton gradient is established, powering the formation of ATP.
Given the function f(x,y) = 2x^2y - 3xy^2, find equation of the tangent plane at the point (2, 1, 2)
a) gradf = fxi + fyj gradf = (4xy - 3y^2)i + (2x^2 - 6xy)j gradf(2,1) = 5i-4j df = gradf dot dr Therefore, equation of the tangent plane is z-2 = 5(x-2) - 4(y-1)