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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 sec2(t)

y = 531/2sin(2t) hence y'= 1031/2 cos(2t)

therefore dy/dx = 103...

HP
Answered by Harry P. Maths tutor
8172 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* (c...

HP
6877 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 differ...

TD
Answered by Tutor61926 D. Maths tutor
4958 Views

“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 ...

OP
Answered by Olivia P. Sociology tutor
8465 Views

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?

  1. 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 channe...

DZ
Answered by Daniella Z. Biology tutor
11881 Views

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