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The height (h) of water flowing out of a tank decreases at a rate proportional to the square root of the height of water still in the tank. If h=9 at t=0 and h=4 at t=5, what is the water’s height at t=15? What is the physical interpretation of this?

Note: time, t, is measured in minutes, and height, h, is measured in metres. Let k>0, a constant. The differential equation to be solved is given by: dh/dt = - k(h)^0.5. Using 'separation of variables' gi...
SN
Answered by Sandie N. • Maths tutor
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curve C with parametric equations x = 4 tan(t), y=5*3^(1/2)*sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.

dy/dx = dy/dt *dt/dx (chain rule). x=4tan(t) hence dx/dt = 4 sec 2 (t) y = 5 3 1/2 sin(2t) hence y'= 10 3 1/2 cos(2t) therefore dy/dx = 10 3 1/2 cos(2t) / 4 sec 2 (t). Since P is on point with x=4 3 1/2 we c...
HP
Answered by Harry P. • Maths tutor
8608 Views

Find the first derivative of r=sin(theta+sqrt[theta+1]) with respect to theta.

To find the first derivative we must apply the chain rule. Our aim is to find dr/d(theta). We start by bringing the differential of what's inside the sine brackets outside and multiplying it by the different...
TD
Answered by Tutor61926 D. • Maths tutor
5328 Views

The distance from the Earth to the Sun is 93 million miles. Assume: it takes 365 days for the Earth to travel once around the Sun and the Earth travels in a circle with the Sun at the centre. Work out the average speed of the Earth in miles per hour.

This question is testing your understanding of speed, distance and time and sounds much more complicated than it actually is. For a question like this one, it is best to draw a picture to help you get a bett...
JH
Answered by Jack H. • Maths tutor
22259 Views

Perhaps an introduction to integration with a simple integral, e.g. the integral of x^2

I would first write out the integral with correct notation, explaining to my tutee exactly what I am drawing and why. I will then explain the 'n+1' rule for integrating simple powers. I will go through the i...
RC
Answered by Reece C. • Maths tutor
3755 Views