Consider a ladder sliding down a wall as in the figure. The variable a is the length of the ladder. The variable h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottom. Suppose that the length of the ladder is 4.6 meters and the top is sliding down the wall at a rate of 0.6m/s Calculate (dx)/(dt) when h=3.3 (Use decimal notation. Give your answer to three decimal places.) (dx)/(dt)vert _(vert xvert 5)approx square _(x,8)

To solve this problem, we will use the **Pythagorean theorem** and related rates. Here's the step-by-step solution:---### Step 1: Relating , , and The ladder forms a right triangle with the wall and the ground. The Pythagorean theorem gives us the relationship: where:- is the height of the ladder's top from the ground,- is the distance of the ladder's bottom from the wall,- is the length of the ladder (constant).Since the ladder's length is constant ( ), we have: ---### Step 2: Differentiate with respect to time Differentiate both sides of the equation with respect to : Simplify: Solve for : ---### Step 3: Substitute known valuesWe are given:- ,- ,- m/s (negative because the height is decreasing).First, calculate when using the Pythagorean theorem: Now substitute , , and into the formula for : ---### Final Answer: