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

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.

$$\text{Gross Tax} = \text{Net Tax} + \text{Tax Relief}$$ $$\text{Gross Tax} = 2200 \text{ Ksh} + 1280 \text{ Ksh}$$ $$\text{Gross Tax} = 3480 \text{ Ksh}$$

Step 2: Calculate the tax from the first income bracket.
The first bracket is from 0 to 11 180 Ksh at 10%.

$$\text{Tax from 1st bracket} = 11180 \times \frac{10}{100} = 1118 \text{ Ksh}$$

Step 3: Calculate the remaining tax to be paid after the first bracket.

$$\text{Remaining Tax} = \text{Gross Tax} - \text{Tax from 1st bracket}$$ $$\text{Remaining Tax} = 3480 \text{ Ksh} - 1118 \text{ Ksh} = 2362 \text{ Ksh}$$

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.

$$\text{Tax from 2nd bracket} = 10534 \times \frac{15}{100} = 1580.10 \text{ Ksh}$$

Step 5: Calculate the remaining tax to be paid after the second bracket.

$$\text{Remaining Tax} = 2362 \text{ Ksh} - 1580.10 \text{ Ksh} = 781.90 \text{ Ksh}$$

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.

$$x \times \frac{20}{100} = 781.90$$ $$x = \frac{781.90 \times 100}{20}$$ $$x = \frac{78190}{20}$$ $$x = 3909.50 \text{ Ksh}$$

Step 7: Calculate the total taxable income.

$$\text{Total Taxable Income} = \text{Income from 1st bracket} + \text{Income from 2nd bracket} + \text{Income from 3rd bracket}$$ $$\text{Total Taxable Income} = 11180 \text{ Ksh} + 10534 \text{ Ksh} + 3909.50 \text{ Ksh}$$ $$\text{Total Taxable Income} = 21714 \text{ Ksh} + 3909.50 \text{ Ksh}$$ $$\text{Total Taxable Income} = 25623.50 \text{ Ksh}$$

The employee's taxable income that month is:

$$\boxed{25623.50 \text{ Ksh}}$$

13. The equation of a circle is given by $x^2 + y^2 - 3x + 4y = 0$. Determine: