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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
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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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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
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“Outline two criticisms of functionalist based explanations of crime and deviance” [10 marks]

One criticism of the functionalist based explanations of crime and deviance is that functionalists rely on a pattern of crime shown in official crime statistics. However, a lot of crime is never actually rep...
OP
Answered by Olivia P. • Sociology tutor
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Describe the series of events from the arrival of an action potential at the pre-synaptic membrane of a cholinergic synapse to the generation of a new action potential at the post synaptic membrane?

An action potential arriving at the pre-synaptic membrane stimulates voltage-gated calcium channels to open and calcium ions diffuse into the neuron through these calcium channels. Influx of calcium causes s...
DZ
Answered by Daniella Z. • Biology tutor
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