Answer:
- rate of the boat in still water = 6.5 miles / hour
- rate of the current = 2.5 miles / hour.
Explanation:
<u>1) Name the two variables:</u>
- b: rate of the boat in still water:
With that, the net rates of the boat down the river and upstrean are:
<u>2) Now set the equations for the distance as a function of the times and the rates:</u>
- downstream: 18 miles = (b + c) × 2 hours
- upstream: 18 miles = (b - c) × 4.5 hours
<u>3) Set the system of equations:</u>
- 18 = 2(b + c) ⇒ 9 = b + c . . . Equation (1)
- 18 = 4.5 (b - c) ⇒ 4 = b - c . . . Equation (2)
<u>4) Solve the system by </u><u>elimination</u><u>:</u>
- Add equations (1) and (2): 9 + 4 = 2b
- Divide both sides by 2: 13/2 = b
- Replace b with 6.5 in equation (2) and solve:
4 = 6.5 - c ⇒ c = 6.5 - 4 = 2.5
<u>5) Results:</u>
- b = rate of the boat in still water = 6.5 miles / hour
- c = rate of the current = 2.5 miles / hour.
For every point A = (x,y) in your figure, a 180 degree counterclockwise rotation about the origin will result in a point A' = (x', y') where:
x' = x * cos(180) - y * sin(180)
y' = x * sin(180) + y * cos(180)
Happy-fun time fact: This is equivalent to using a rotation matrix from Linear Algebra!
Because a rotation is an isometry, you only have to rotate each vertex of a polygon, and then connect the respective rotated vertices to get the rotated polygon.
You can rotate a closed curve as well, but you must figure out a way to rotate the infinite number of points in the curve. We are able to do this with straight lines above due to the property of isometries, which preserves distances between points.
Answer:
1800
Step-by-step explanation:
Labor quantity variance= Actual quantity ×standard price - standard quantity ×standard price
Standard quantity=2×2600=5200
Labor quantity variance
5050×12-5200×12=1800
<span>The Federal Insurance Contributions Act (FICA) requires employers to withhold a certain percentage of an employee's income as tax. The categories are:
6.2% as social security tax
1.45% as Medicare tax
0.9% as Medicare surtax for employees earning more than $200,000
In this case, the percentage of tax applied will be 6.2 + 1.45 = 7.65%
The FICA tax will be 110,330 * 0.0765
FICA tax = $8,440.24</span>
Answer:
x=7.5
y=1.5
Step-by-step explanation:
subtract x from both sides
combine like terms
subtract 1.8 from both sides
divide both sides by 0.3
x=7.5
y=1.5
