(a) Solve for the letter indicated in brackets in each of the following formulac \( \begin{array}{ll}\text { (1) } A=\frac{1}{2} b h & \text { (b) } \\ \text { 3) } V=\frac{4}{3} m r^{3} & \text { (r) } \\ \text { 5) } v^{2}+a=2 m u & \text { (v) }\end{array} \)

We are given three formulas in which one variable (indicated by the letter in brackets) must be isolated. We’ll work through each one step by step. ────────────────────────────── (1) Formula: A = (1/2)·b·h  [solve for b] Step 1. Write the equation:   A = (1/2)·b·h Step 2. Multiply both sides by 2 to eliminate the 1/2:   2A = b·h Step 3. Divide both sides by h to solve for b:   b = (2A) / h ────────────────────────────── (3) Formula: V = (4/3)·m·r³  [solve for r] Step 1. Write the equation:   V = (4/3)·m·r³ Step 2. Multiply both sides by 3/4 to isolate m·r³:   (3V)/4 = m·r³ Step 3. Divide both sides by m:   r³ = (3V) / (4m) Step 4. Take the cube root of both sides:   r = ³√[(3V) / (4m)] ────────────────────────────── (5) Formula: v² + a = 2·m·u  [solve for v] Step 1. Write the equation:   v² + a = 2·m·u Step 2. Subtract a from both sides:   v² = 2·m·u − a Step 3. Take the square root of both sides. Remember that taking the square root gives both positive and negative solutions:   v = ±√(2·m·u − a) ────────────────────────────── Final Answers: • For (1): b = (2A) / h • For (3): r = ³√[(3V) / (4m)] • For (5): v = ±√(2·m·u − a)