(a) Find, in terms of , the x coordinate of the point A and the x coordinate of the point B.
The finite region S enclosed by the curve and the x-axis is shown shaded in Figure 3. The region S is rotated through 2π radians about the x-axis.
(b) Find, by integration, the exact value of the volume of the solid generated.
where λ and μ are scalar parameters.
(a) Given that l1 and l2 meet, find the position vector of their point of intersection.
(b) Find the acute angle between l1 and l2 giving your answer in degrees to 1 decimal place.
Given that the point A has position vector 4i + 16j – 3k and that the point P lies on lthat AP is perpendicular to 11
(c) find the exact coordinates of P.
The rate of change of the temperature of the water in the bottle is modelled by the differential equation,
dθ/dt = (3 - θ)/125
(a) By solving the differential equation, show that,
θ = Ae–0.008t + 3
where A is a constant.
Given that the temperature of the water in the bottle when it was put in the refrigerator was 16 °C,
(b) find the time taken for the temperature of the water in the bottle to fall to 10 °C, giving your answer to the nearest minute.
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.