The area of a triangle is given by  \(A=\dfrac{1}{2} b h\), where  \(b\) is the base length and \(h\) is the height. Given that the base length is  \(4 \mathrm{~cm}\) and the area is  \(15 \mathrm{~cm}^{2}\), find the height.

 According to one theory, the recommended nightly hours of sleep for a child is \(S=8+\dfrac{18-a}{2}\), Where \(a\) is the age of the child in years. What is the age of a child who requires 12 hours of sleep? 

The formula for converting  \(k\) kilometres to miles is \(M=\dfrac{5k}{8}\). Convert 15 miles to kilometres.

Given that \(s=ut+\dfrac{1}{2} at^{2}\), find \(s\) when \(u=-4, a=10, t=4\)

Given that \(d=180-\dfrac{360}{n}\) , find \(d\) when \(n=12\)

Given that  \(v=u+at\) , find \(v\) when \(u=12\), \(a=10\) and \(t=3\)

Given that \(V=IR\), find \(V\) when \(I=12\) and \(R=20\)

Given that the surface area of a cylinder is \(A=2 \pi r h+2 \pi r^{2}\) Find  \(h\), given that \(A=96 \pi \mathrm{~cm}^{2}\) and \(r=4 \mathrm{~cm}\).

The formula \(F = \dfrac{9}{5}C + 32\), converts degrees Celsius, \(C\), to degrees Fahrenheit, \(F\). Convert 38 degrees Fahrenheit to degrees Celsius.

The volume of water (V litres) in a tank is given by \(V = 2000 - 2.5t\) where \(t\) is the time in seconds after a tap is turned on. Find the time it takes for the volume to reach 1500 litres. Round to the nearest minute.

The profit, $P, made by a bakery shop is given by \(\$ P = 6y - 1000\) where \(y\) represents the number of cakes sold. Find the number of cakes sold if the profit is $3836.

The formula \(s = \dfrac{d}{t}\) gives the speed, \(s\), of a car travelling a distance, \(d\), in time, \(t\). Find the speed of a car that has travelled 7500 m in 0.5 hours into m/s. Round to 2 dp

The given formula is \(y = 8x + a{\rm{,}}\) use the formula to find \(a\) if \(y = 50\) and \(x = 4\).