This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — here are the solutions to the questions. Evaluate the expression: 3x^3 + 4x^2 - x + 2, if x = -2. Step 1: Substitute x = -2 into the expression. 3(-2)^3 + 4(-2)^2 - (-2) + 2 Step 2: Calculate the powers of -2. (-2)^3 = -8 (-2)^2 = 4 Step 3: Substitute these values back into the expression. 3(-8) + 4(4) - (-2) + 2 Step 4: Perform the multiplications. -24 + 16 + 2 + 2 Step 5: Perform the additions and subtractions. -8 + 2 + 2 -6 + 2 -4 The value of the expression is -4. In the right-angled triangle below, angle QPR is x. From the diagram, find the following: The triangle has sides: Hypotenuse (PR) = 15 Adjacent to x (PQ) = 9 Opposite to x (RQ) = 12 (i) (x) Step 1: Use the definition of cosine: (x) = AdjacentHypotenuse. (x) = (PQ)/(PR) Step 2: Substitute the side lengths. (x) = (9)/(15) Step 3: Simplify the fraction. (x) = (3)/(5) (x) = (3)/(5) (ii) (x) Step 1: Use the definition of tangent: (x) = OppositeAdjacent. (x) = (RQ)/(PQ) Step 2: Substitute the side lengths. (x) = (12)/(9) Step 3: Simplify the fraction. (x) = (4)/(3) (x) = (4)/(3) Got more? Send 'em!