Question

a car leaves a parking ramp and travels 5 miles due east. The car makes a 90 degree turn and travels 12 due north . The car has enough gas in the tank to travel 12.7 miles. Can the car make it back to the parking ramp using a direct ramp?

Answer 1

Using the Pythagorean theorem, the direct route back to the parking ramp is 13 miles, which exceeds the car's remaining fuel range of 12.7 miles. Therefore, the car cannot make it back using a direct route.

Step-by-step explanation:

To determine if the car can make it back to the parking ramp using a direct route, we need to figure out the direct distance from the final position after the turn back to the starting point. This involves calculating the hypotenuse of a right-angled triangle with sides of 5 miles (east) and 12 miles (north).

Using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):

`c^2 = a^2 + b^2`

Therefore, the hypotenuse is:

`c = \sqrt (5^2 + 12^2) = \sqrt (25 + 144) = \sqrt 169 = 13 miles`

The car has enough gas to travel 12.7 miles, which is less than the 13 miles required to return directly to the parking ramp. Hence, the car cannot make it back to the parking ramp using a direct route.

Answer 2

answer is yes it can good luck