Maria is going for a walk. She begins by walking north for 1 km. She then turns and walks east for 22 km, then turns and walk south for 3 km. She walks at a constant 4 km/hr. Express the distance from Maria to her starting point as a multipart function of t, the time she has been walking.

During 0 <t < 0.25 h, y = 4t and x = 0

R = Distance from starting point = y

During 0.25 < t < 5.75 h, y = 4 and x = 4(t-0.25)
R = sqrt(x^2 + y^2)

You do the last leg. That should give you the idea

To express the distance from Maria to her starting point as a multipart function of time, we need to determine the total distance she has walked in each direction.

First, let's break down the distance Maria has walked in each direction:

- Distance walked north is constant at 1 km.
- Distance walked east is given by the product of her speed (4 km/hr) and the time she has been walking eastward (t). So, the distance walked east is 4t km.
- Distance walked south is given by the product of her speed (4 km/hr) and the time she has been walking southward (t). So, the distance walked south is 4t km.

Now, to determine the distance from Maria to her starting point, we need to consider the net displacement in the north-south and east-west directions.

In the north-south direction, distance north is 1 km, and distance south is 4t km. Since Maria initially walks north and then south, the net displacement is given by the difference between these distances: 1 km - 4t km = 1 - 4t km.

In the east-west direction, Maria walks east for 22 km. Since there is no westward movement, the net displacement is 22 km.

Using the Pythagorean theorem, we can calculate the distance from Maria to her starting point as:

Distance = √[(net displacement north-south)² + (net displacement east-west)²]
= √[(1 - 4t)² + 22²]
= √[1 - 8t + 16t² + 484]
= √[16t² - 8t + 485]

Therefore, the distance from Maria to her starting point is a multipart function of t:

Distance(t) = √[16t² - 8t + 485]