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Solve the simultaneous equations y+4x+1 = 0 and y^2+5x^2+2x = 0

x = -1/3 and y = 1/3 or x = -1/7 and y = -3/7

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What is a Pacinian corpuscle and how does it work?

The Pacinian corpuscle is a mechanoreceptor, which means it is a sensory receptor that responds to touch, pressure or vibration. Pacinian corpuscles are found deep in the skin, and respond to both pressur...

Answered by • Biology tutor

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Prove that 1 + tan^2 x = sec^2 x

We know that tan x = sin x/cos x and so tan²x = sin²x/cos²x. We also know that sin²x + cos²x = 1 because this is a Pythagorean identity. We can rewri...

Answered by Eleanor F. • Maths tutor

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Integrate 2x^2 + 4

When we integrate, we raise the power by one and divide the term by the new power. So let's break the question down term by term. When integrating 2x² we raise the power by 1 to get 2x³

Answered by Eleanor F. • Maths tutor

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In a science experiment a substance is decaying exponentially. Its mass, M grams, at time t minutes is given by M=300e^(-0.05t). Find the time taken for the mass to decrease to half of its original value.

Firstly, calculate the initial value of of M, by substituting t = 0 into the equation M=300e^-0.05tInitially, M₀= 300e⁰=300 x 1 = 300When the substance mass has decreased t...

Answered by Bony R. • Maths tutor

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