Question

1. the ski slopes in the scotch pine ski resort are marked by color as an indicator of the incline. the colors used are green, blue, red and black. green is used for slopes with less than 20% incline, blue for 20 - 25%, red for 25 - 40% and black for above 40% incline. classify the following slopes as blue, green, red or black:

a. p1 with a horizontal change of 450 m and a vertical change of 280 m that passes through o (0,0).

b. p2 with a horizontal change of 150 m and a vertical change of 50 m that passes through o (0,0).

c. p3 with a starting point at the top b (310,48) and an end at o (0,0).

d. p4 with a starting point at the top b (230,56) and an end at o (0,0).

Explanation:

Step1: Calculate incline percentage for P1

Incline % = $\frac{\text{Vertical Change}}{\text{Horizontal Change}} \times 100\% = \frac{280}{450} \times 100\% \approx 62.22\%$

Step2: Classify P1 per color rules

62.22% > 40%, so P1 is black.

Step3: Calculate incline percentage for P2

Incline % = $\frac{\text{Vertical Change}}{\text{Horizontal Change}} \times 100\% = \frac{50}{150} \times 100\% \approx 33.33\%$

Step4: Classify P2 per color rules

25% < 33.33% < 40%, so P2 is red.

Step5: Calculate incline percentage for P3

Horizontal change = 310 m, Vertical change = 48 m
Incline % = $\frac{48}{310} \times 100\% \approx 15.48\%$

Step6: Classify P3 per color rules

15.48% < 20%, so P3 is green.

Step7: Calculate incline percentage for P4

Horizontal change = 230 m, Vertical change = 56 m
Incline % = $\frac{56}{230} \times 100\% \approx 24.35\%$

Step8: Classify P4 per color rules

20% < 24.35% < 25%, so P4 is blue.

Answer:

a. P1: black
b. P2: red
c. P3: green
d. P4: blue