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During the cardiac cycle , there is a delay between the excitation of the atria and excitation of the ventricles. Explain how this is achieved and why this delay is essential.

Excitation from SAN (sino-atrial node) spreads across atria , causing them to contract first. The excitation is conducted to the AV (atrio-ventricular) node, which introduces a 0.12s delay . This refractory ...
JE
Answered by Jane E. • Biology tutor
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Find, without using a calculator, integral of 1/sqrt(15+2x-x^2) dx, between 3 and 5, giving your answer as a multiple of pi

To get the denominator into something usable, you have to complete the square so you have it in one of the forms you can use a trig or hyperbolic substitution for. The minus sign in front of the x2 means we'...
LD
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Integrate 2x/(x^2+3) using the substitution u=x^2+3

u=x 2 + 3 du/dx=2x dx=du/2x 2x/(x 2 +3) dx becomes (2x/u) * (du/2x) the 2x terms cancel out giving 1/u du this integrates to ln(u)+c becoming ln(x 2 +3)+c
TS
Answered by Tom S. • Maths tutor
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If timber prices fall by 30%, what will be the expected % change in demand for timber in the economy if the Price Elasticity of Demand is -0.5, and explain the effect on revenue for a timber-selling firm.

Price Elasticity of Demand (PED) is a measure of the responsiveness of demand to a change in price. A PED of -0.5 suggests demand is price inelastic – as Price falls by 1%, Demand will increase by 0.5% (less...
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Answered by Harry C. • Economics tutor
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Core 1: Given that y = x^4 + x^2+3. Find dy/dx

First what we need to do is we need to think of what the question is asking us to find. In this case it is dy/dx but what is this. This is the rate of change of y with respect to x. For understanding purpose...
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Answered by David S. • Maths tutor
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