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"He is far gone:" do you think Hamlet is mad any point during the play?

When Hamlet says that he will "put an antic disposition on" (Act 1, Scene V, 189), he positions himself as being a sane man playing the part of an insane man in order to confuse and deceive his unc...
CJ
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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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How would 12 be represented in binary?

Decimal (the system you use everyday) is a base- 10 number system, meaning it only uses 10 digits: 0-9. - Binary is a base- 2 number system, meaning it only uses 2 digits: 0 and 1. - The decimal system's pla...
AD
Answered by Aiden D. • Computing 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
8624 Views

z = 4 /(1+ i) Find, in the form a + i b where a, b belong to R, (a) z, (b) z^2. Given that z is a complex root of the quadratic equation x^2 + px + q = 0, where p and q are real integers, (c) find the value of p and the value of q.

a) Need to multiply with conjugate to bring z to form a+ib. => z= z * (1-i)/(1-i) = (4-4i) / 2 = 2-2i b) z^2 = (2-2i)^2 = 4-8i+4 i^2 = 4-8i-4 = 8i since z is root of x^2+px+q=0 then z* (conjugate) is also...
HP
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