The following table shows part of a monthly income tax rates for a certain year. In a certain month an employee paid a net tax of Ksh. 2 200 after getting a tax relief of Ksh. 1 280. Calculate the emp

Fresh day Oliverkoome@gmail254.Com., let's solve. 2. The following table shows part of a monthly income tax rates for a certain year. | Monthly taxable income (Ksh.) | Tax rate (%) | | :---------------------------- | :----------- | | 0 to 11 180 | 10 | | 11 181 to 21 714 | 15 | | 21 715 to 32 248 | 20 | In a certain month an employee paid a net tax of Ksh. 2 200 after getting a tax relief of Ksh. 1 280. Calculate the employee's taxable income that month. Step 1: Calculate the gross tax paid before tax relief. Gross Tax = Net Tax + Tax Relief Gross Tax = 2200 Ksh + 1280 Ksh Gross Tax = 3480 Ksh Step 2: Calculate the tax from the first income bracket. The first bracket is from 0 to 11 180 Ksh at 10%. Tax from 1st bracket = 11180 × (10)/(100) = 1118 Ksh Step 3: Calculate the remaining tax to be paid after the first bracket. Remaining Tax = Gross Tax - Tax from 1st bracket Remaining Tax = 3480 Ksh - 1118 Ksh = 2362 Ksh Step 4: Calculate the tax from the second income bracket. The second bracket is from 11 181 to 21 714 Ksh at 15%. The income range for this bracket is 21714 - 11180 = 10534 Ksh. Tax from 2nd bracket = 10534 × (15)/(100) = 1580.10 Ksh Step 5: Calculate the remaining tax to be paid after the second bracket. Remaining Tax = 2362 Ksh - 1580.10 Ksh = 781.90 Ksh Since there is still remaining tax, the employee's income extends into the third bracket. Step 6: Calculate the income from the third bracket that generates the remaining tax. The third bracket has a tax rate of 20%. Let x be the income in the third bracket. x × (20)/(100) = 781.90 x = (781.90 × 100)/(20) x = (78190)/(20) x = 3909.50 Ksh Step 7: Calculate the total taxable income. Total Taxable Income = Income from 1st bracket + Income from 2nd bracket + Income from 3rd bracket Total Taxable Income = 11180 Ksh + 10534 Ksh + 3909.50 Ksh Total Taxable Income = 21714 Ksh + 3909.50 Ksh Total Taxable Income = 25623.50 Ksh The employee's taxable income that month is: 25623.50 Ksh 13. The equation of a circle is given by x^2 + y^2 - 3x + 4y = 0. Determine: a) the coordinates of the centre of the circle; Step 1: The general equation of a circle is x^2 + y^2 + 2gx + 2fy + c = 0, where the centre is (-g, -f). Step 2: Compare the given equation x^2 + y^2 - 3x + 4y = 0 with the general equation. 2g = -3 g = -(3)/(2) 2f = 4 f = 2 Step 3: Determine the coordinates of the centre. Centre = (-g, -f) = (-(-(3)/(2)), -2) = ((3)/(2), -2) The coordinates of the centre of the circle are: ((3)/(2), -2) b) the area of the circle in terms of . Step 1: Calculate the radius r of the circle using the formula r = sqrt(g^2 + f^2 - c). From part (a), g = -(3)/(2), f = 2, and from the equation, c = 0. r = sqrt((-(3)/(2))^2 + (2)^2 - 0) r = sqrt((9)/(4) + 4) r = sqrt((9)/(4) + (16)/(4)) r = sqrt((25)/(4)) r = (5)/(2) Step 2: Calculate the area of the circle using the formula A = r^2. A = ((5)/(2))^2 A = ((25)/(4)) A = (25)/(4) square units The area of the circle in terms of is: (25)/(4) square units Send me the next one 📸