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Girls may achieve better due to having more positive role models in schools, 86% of teachers in primary schools are female, so from a young age, girls see that they can achieve highly, subsequently giving...

2x²y + 2x + 4y - cos(πy) = 45Applying implicit differentiation:4xy + 2x²(dy/dx) + 2 + 4(dy/dx) + πsin(πy)(dy/dx) = 0Moving all (dy/dx) terms to one side:2x² (dy/dx) + 4(dy...

We begin by rewriting it in a more workable form: 2x⁴ - 4x^-1/2 + 3. Indices are easier to integrate than fractions.Now, we integrate each term separately. The first term is 2x^4...

(x^2+4x+10)/(x+3)(x+4)(x+1) = A/(x+3) + B/(x+4) + C/(x+1) [A(x+4)(x+1) + B(x+3)(x+1) + C(x+3)(x+4)]/(x+3)(x+4)(x+1) = (x^2+4x+10)/(x+3)(x+4)(x+1) [A(x+4)(x+1) + B(x+3)(x+1) + C(x+3)(x+4)] = (x^2+4x+10) A(...

Oxygen diffuses from the air where it is present at a higher concentration and pressure, to the lungs where it is at a lower concentration and pressure - we say it moves 'down' these gradients; high to lo...