A rectangle has a length of 14 centimetres and an area of 56 square centimetres. Find w, the width of the rectangle in centimetres.
The area of triangle is defined by the formula A = \dfrac{b \times h}{2}. Find the height, h, of a triangle with a base of 5 \text{ mm} and an area of 30 \text{ mm}^{2}.
P = 2 \left(a + b\right) describes the perimeter of a rectangle. Find b if a = 2 \text{ m} and P = 22 \text{ m}.
The volume of a prism is given by the formula V = a \times b \times h.
Find h, if a = 2 \text{ mm}, b = 6 \text{ mm} and V = 108\text{ mm}^{3} .
The relationship between F degrees Fahrenheit and C degrees Celsius is F = 1.8 C + 32.
Find the temperature in degrees Celsius, C, that is equivalent to 51.8 degrees Fahrenheit.
The equation of a straight line can be expressed in the form y = m x + c.
Determine the value of x, if y = 38, m = 6 and c = 8.
Determine the value of m, if y = 0, x = 8 and c = - 4.
The circumference, C, of a circle can be calculated by the formula C = 2 \pi r, where r is the radius of the circle. Use the formula to calculate the radius of a circle which has a circumference of 47.1 \text{ cm}. Round your answer to one decimal place.
The velocity, v, of an object can be calculated using the formula v = u + a t.
Determine the value of u if v = 60, a = 5 and t = 3.
Determine the value of a if v = 4.8, u = 5 and t = 10.
The surface area of a rectangular prism is given by formula S = 2 \left( a b + b h + a h\right).
Find the value of h if a = 4 \text{ mm}, b = 8 \text{ mm} and S = 304 \text{ mm}^{2}.
The body mass index (BMI) of an individual can be calculated using the formula B = \dfrac{m}{h^{2}}, where m is the mass of the individual in kilograms and h is their height in metres.
Determine the value of m when B = 20 and h = 1.5 \text{ m}.
Determine the value of m when B = 22.43 and h = 1.72 \text{ m}. Round your answer to two decimal places.
For S = \dfrac{n}{2}\left( 2 a + \left(n - 1\right) d\right), find a if n = 20, d = 4 and S = 840.
The temperature C, in degrees Celsius, can be calculated from the corresponding temperature F, in degrees Fahrenheit, by the formula C = \dfrac{5}{9} \left(F - 32\right).
If the temperature today in Sydney is 25.5\degree\text{C}, use the formula to calculate this temperature in degrees Fahrenheit.
Ohm's law, given by V = I R, is a formula that describes the relationship between the voltage, V, current, I, and resistance, R, of some circuit components, such as resistors.
Determine the value of I if V = 30 and R = 5.
Determine the value of R if V = 7 and I = 21.
Newton's second equation of motion is s = u t + \dfrac{1}{2} a t^{2}.
Find the value of a if s = 4000, u = 300 and t = 20.
The declining balance depreciation formula is given by S = V \left(1 - r\right)^{n}, where S is the salvage value, V is the initial cost, r is the depreciation rate per year, and n is the number of years.
A particular item has a salvage value of \$10\,599.85. Determine the initial cost if the depreciation rate has been 0.04 over 5 years. Round your answer to the nearest dollar.
The resistance of a parallel circuit is given by the formula \dfrac{1}{a} = \dfrac{1}{b} + \dfrac{1}{c}. Find the value of b (correct to two decimal places) if a = 12 and c = 27.
Albert Einstein's famous formula E = m c^{2} relates the mass, m \text{ kg} , of a body with its equivalent energy E, where c is the speed of light.
Given that the speed of light is approximately 3 \times 10^{8}\text{ m/s}, calculate the mass of an object that has an equivalent energy of 5 \times 10^{14} joules. Round your answer to four decimal places.
The reactance of a capacitor is given by the formula X = \dfrac{1}{2 \pi f C}. Find the value of f (correct to one decimal place) if X = 58.9 and C = 180 \times 10^{ - 9 }.
The gravitational force between two masses is given by F = \dfrac{G M m}{d^{2}}.
Find M (correct to 2 decimal places) if F = 12, G = 6.67 \times 10^{ - 11 },m = 1 and d = 4 \times 10^{ - 5 }.