Final answer:
To find the inverse of the formula, rewrite it as t = ±√((d - 25)/15). To find the distance that corresponds to a time of 30 seconds, substitute t = 30 into the inverse formula.
Step-by-step explanation:
To find the inverse of the formula, we need to solve for t in terms of d. Let's start by rewriting the formula: d = 25 + 15t². Subtracting 25 from both sides gives us 15t² = d - 25. Dividing both sides by 15 gives us t² = (d - 25)/15. Finally, taking the square root of both sides gives us the inverse formula: t = ±√((d - 25)/15).
To find the distance that corresponds to a time of 30 seconds, we can substitute t = 30 into the inverse formula: d = 25 + 15(30)². Simplifying this equation gives us d = 70025 feet.
Then, solve for d by subtracting 25 from both sides and dividing by 15: d = (t - 25) / 15. Now take the square root of both sides to solve for d: d = √((t - 25) / 15). Hence, the inverse function is d(t) = √((t - 25) / 15). To find the distance corresponding to a time of 30 seconds, substitute t = 30 into the inverse equation and calculate.