Answer :
Mrs. Opal's overtime pay for the week is $87.12.
To find the coordinates of point B that divides the segment AC in the ratio AB = 3:2, use the section formula.
Given:
- Ratio AB= 3:2
- Coordinates of A = (1, 0)
- Coordinates of C = (6, 6)
- Section Formula
For a point B dividing AC in the ratio m, the coordinates of B are given by:
B(x, y) = [(mx₂ + nx₁) / (m + n), (my₂ + ny₁) / (m + n)]
Step 2: Plug in the Values
Here:
- m = 3
- n = 2
- x₁ = 1 (coordinates of A)
- y₁ = 0 (coordinates of A)
- x₂ = 6 (coordinates of C)
- y₂ = 6 (coordinates of C)
- Substitute these values into the formula:
x = (3 × 6 + 2 × 1) / (3 + 2) = (18 + 2) / 5 = 20 / 5 = 4
y = (3 × 6 + 2 × 0) / (3 + 2) = 18 / 5 = 3.6
Final Answer:
The coordinates of point B are (4, 3.6).
To calculate Mrs. Opal's overtime pay, follow these steps:
Identify the Overtime Hours:
Opal works an 8-hour day, so any hours beyond 8 in a day are considered overtime.
- For each day:
Monday: 8 hours (no overtime)
Tuesday: 8 hours (no overtime)
Wednesday: 8 hours (no overtime)
Thursday: 11 hours (overtime = 11 - 8 = 3 hours)
Friday: 8 hours (no overtime)
Total overtime hours for the week = 3 hours
- Calculate the Overtime Pay Rate:
Regular pay rate = $19.36 per hour
Overtime pay rate is time-and-a-half, which is 1.5 times the regular rate: Overtime pay rate = 1.5 × 19.36 = $29.04 per hour
- Calculate the Overtime Pay:
Multiply the total overtime hours by the overtime pay rate: Overtime pay = 3 × 29.04 = $87.12.
