If cos x= 5/13 and sin x <0 find cos (x/2) and sin (2x)
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Using the information in the table given, the Gross pay, deductions and net pay for Orville staples are :
- $30,000
- $2340
- $1860
- $600
- $450
- $34.50
- $15.00
- $24700.50
Given the tax time table :
- Social security tax = 6.2% of $97,500
- Medicare = 1.45% of gross income
- State tax = 2% of gross pay
- Local tax = 1.5% of gross pay
- Gross pay = $30,000
1.) Gross pay, total amount earned prior to tax = $30,000
2.) <u>Using the weekly payroll for singles</u> :
Number of weeks in a year = 52
Weekly earning = 30000/52 = 600
The Federal income tax = $25 per week (3 allowances claimed)
Total FIT = $45 × 52 = $2340
3.) <u>Social security tax</u> :
SS tax = 6.2% × $30,000 = $1860
4.) <u>State tax</u> :
2% of gross pay
2% × $30,000 = $600
5.) <u>Local tax</u> :
1.5% × 30,000 = $450
6.) <u>Medical dues</u> = $34.50
7.) <u>Others</u> : = $15.00
8.) <u>Net pay = Gross pay - Total deduction</u>
Net pay = 30000 - $(2340+1860+600+450+34.50+15)
Net pay = 30,000 - 5299.50 = $24700.50
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4) .
5) The areas of the rectangles QRST and Q'R'S'T' are the same since the translation of the <em>geometric</em> loci conserved the <em>Euclidean</em> distance.
6) x = 1, w = 3, y = - 1/4, z = 1/3
<h3>How to analyze and apply rigid transformations</h3>
<em>Rigid</em> transformations are transformations applied on <em>geometric</em> loci such that <em>Euclidean</em> distance is conserved. In this question we have applications of translations, a kind of <em>rigid</em> transformation.
Exercise 4
In this part we must determine the areas of rectangles QRST and Q'R'S'T':
Rectangle QRST
A = RS · QT
A = 3 · 3
A = 9
Rectangle Q'R'S'T'
Q'(x, y) = (2, - 3) + (- 3, - 3)
Q'(x, y) = (- 1, - 6)
R'(x, y) = (2, 4) + (- 3, - 3)
R'(x, y) = (- 1, 1)
S'(x, y) = (5, 4) + (- 3, - 3)
S'(x, y) = (2, 1)
T'(x, y) = (5, - 3) + (- 3, - 3)
T'(x, y) = (2, - 6)
A = R'S' · Q'T'
A = 3 · 3
A = 9
The rectangles QRST and Q'R'S'T' have both an area of 9 square units.
Exercise 5
The areas of the rectangles QRST and Q'R'S'T' are the same since the translation of the <em>geometric</em> loci conserved the <em>Euclidean</em> distance.
Exercise 6
In this case, we must solve the following equations:
PQ = A'(x, y) - A(x, y)
(4, 1) = (2 · x + 1, 4) - (- 1, w)
(4, 1) = (2 · x + 2, 4 - w)
(4, 1) = (2 · x, - w) + (2, 4)
(2, - 3) = (2 · x, - w)
(x, w) = (1, 3)
PQ = B'(x, y) - B(x, y)
(4, 1) = (3, 3 · z) - (8 · y - 1, 1)
(4, 1) = (2 - 8 · y, 3 · z)
(4, 1) = (- 8 · y, 3 · z) + (2, 0)
(2, 1) = (- 8 · y, 3 · z)
(y, z) = (- 1/4, 1/3)
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