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
Here are the solutions to the questions: i) Express -150^ into radians. Step 1: Use the conversion factor radians180^ to convert degrees to radians. -150^ × ()/(180^) Step 2: Simplify the fraction. -(150)/(180) = -(15)/(18) = -(5)/(6) The angle in radians is -(5)/(6) radians. ii) Find , when l=2cm and r=3.5cm. Step 1: Use the formula for arc length, l = r, where is in radians. Rearrange the formula to solve for : = (l)/(r) Step 2: Substitute the given values for l and r. = 2 cm3.5 cm Step 3: Calculate the value of . = (2)/(3.5) = (2)/(7)2 = (4)/(7) The angle is (4)/(7) radians. iii) Verify that: (^2 )/( ) + = . Step 1: Start with the left-hand side (LHS) of the equation. LHS = (^2 )/( ) + Step 2: Find a common denominator for the terms, which is . LHS = (^2 )/( ) + ( · )/( ) LHS = (^2 )/( ) + (^2 )/( ) Step 3: Combine the terms over the common denominator. LHS = (^2 + ^2 )/( ) Step 4: Apply the Pythagorean identity ^2 + ^2 = 1. LHS = (1)/( ) Step 5: Recognize that (1)/( ) is equal to . LHS = This matches the right-hand side (RHS) of the equation. Therefore, the identity is verified. (^2 )/( ) + = That's 2 down. 3 left today — send the next one.