Prove that the following are equivalent ¬(r + q(¬r→¬ p) )and¬ r( p +¬ q) by logical equivalence

Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 4p cubedplusx squaredequals38 comma 400. determine the rate at which sales are changing at a time when xequals80, pequals20, and the price is falling at the rate of $.20 per week.

Solve 2^x=32 and rewrite this equation in a logarithmic form

Which shows the correct substitution of the values a,b and c from the equation 1=-2x+3x^2+1