The volume, VVV, of a spherical weather balloon is increasing at a constant rate of 120π cm3 s−1120\pi \text{ cm}^3\text{ s}^{-1}120π cm3 s−1. Find the rate of increase of the radius, rrr, of the balloon in cm s−1\text{cm s}^{-1}cm s−1 at the instant when the radius is 6 cm6 \text{ cm}6 cm. [The volume VVV of a sphere of radius rrr is given by the formula V=43πr3V = \frac{4}{3}\pi r^3V=34πr3]
The height of a pile of sand, h metresh \text{ metres}h metres, under a conveyor belt is monitored over time. The rate of increase in the height of the pile is modeled by the differential equation
dhdt=kh2 \frac{\text{d}h}{\text{d}t} = \frac{k}{h^2} dtdh=h2kwhere kkk is a positive constant and ttt hours is the time after the measurement began. Given that:
Solve the differential equation to find the value of TTT. Give your answer to one decimal place.
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.