Raquel has created a program for a robot. The robot travel 10 meters and stops. The program is design for wheels that are 2.5 cm in diameter. When Raquel replaces the wheels she can only find wheels having a diameter of 2.75 cm. How should she adjust the program so the robot travels the same distance?

To adjust the program so that the robot travels the same distance with the new wheels, Raquel needs to take into account the change in wheel diameter.

Let's start by calculating the circumference of the old wheels with a diameter of 2.5 cm. The circumference of a circle is given by the formula:

C = π * d

where C is the circumference and d is the diameter. Plugging in the values, we get:

C = π * 2.5 cm

Next, we need to calculate the number of rotations the wheels need to make to cover a distance of 10 meters. Since the circumference of the wheel represents the distance covered in one rotation, the number of rotations can be calculated as:

Number of rotations = Distance / Circumference

Plugging in the values, we get:

Number of rotations = 10 m / (π * 2.5 cm)

Now, to find the distance covered by the robot with the new wheels, we need to calculate the new circumference using the diameter of 2.75 cm:

C' = π * 2.75 cm

Finally, we can calculate the new distance covered by the robot using the formula:

Distance' = Number of rotations * C'

Plugging in all the values we have, we get:

Distance' = (10 m / (π * 2.5 cm)) * (π * 2.75 cm)

Simplifying further, we can cancel out the π and cm units, resulting in:

Distance' = (10 m / 2.5) * 2.75

Now, let's calculate the final value:

Distance' = 11 m

Therefore, Raquel needs to adjust the program so that the robot travels a distance of 11 meters with the new wheels having a diameter of 2.75 cm instead of 10 meters with the old wheels having a diameter of 2.5 cm.

(2.5 / 2.75) * wheel rotations