Formula: แบบฝึกหัด

In the formula \( y = 3x + \frac{z}{2} \), express \( z \) as the subject of the formula.

Make $$x$$ the subject of the formula $$y = \frac{3x+1}{x-2}$$.

A total value \( V \) for two items is given by \( V = a x + b y \), where \( a \) and \( b \) are the unit prices for items 1 and 2 respectively, and \( x \) and \( y \) are the quantities of items 1 and 2. Make \( x \) the subject of the formula.

Make $$b$$ the subject of the formula $$c = \frac{ab}{2}$$.

Given the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), express \( y_1 \) in terms of \( m \), \( x_1 \), \( x_2 \), and \( y_2 \).

The formula for the total cost, \( C \), of producing \( n \) items is given by \( C = 500 + 10n \). If the total cost is \( \$1200 \), find the number of items produced, \( n \).

The total cost $$C$$ of producing $$n$$ items is given by the formula $$C = 150 + 2.5n$$. If the total cost is $$ \$400 $$, find the number of items produced, $$n$$.

Make $$x$$ the subject of the formula $$y = \frac{x+a}{bx-c}$$.

The formula for converting a temperature measured in degrees Celsius (\(C\)) to degrees Fahrenheit (\(F\)) is given by:

a) If the temperature is \(25^\circ\text{C}\), find the temperature in degrees Fahrenheit (\(F\)).

b) Change the subject of the formula to \(C\).

c) Use the result from (b) to find the temperature in degrees Celsius (\(C\)) when the temperature is \(77^\circ\text{F}\).

In electrical engineering, a formula is used to estimate the total heat energy output \(H\) (in kilojoules, kJ) generated in a complex circuit segment over a specific time \(t\) (in seconds). This heat output depends on the current \(I\) (in Amperes, A) and the resistance \(R\) (in Ohms, \(\Omega\)), according to the formula:

$$ H = \frac{I^2 R t}{k + I R} $$

Where \(k\) is a fixed constant representing internal factors of the circuit.