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Find the integral of [ 2x^4 - (4/sqrt(x) ) + 3 ], giving each term in its simplest form

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...

Answered by Prahlad M. • Maths tutor

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y = p x q^(x - 1), When x = 1, y = 10, and when x = 6, y = 0.3125. Find the value of 'y' when x = 3

When x = 1, y = 10Therefore, p x q^{(1 - 1)} = 10 p x q⁰ = 10 p x 1 = 10, p = 10When x = 6, y = 0.3125 p x q^{(6 - 1)}= 0.3125 10 x q⁵ = 0.3125 q⁵ = 0.0312...

Answered by Prahlad M. • Maths tutor

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Write 16 × 8^2x as a power of 2 in terms of x

16 = 4² = (2²)² = 2⁴8 = 2³ , therefore 8^2x= 2^3(2x) = 2^6x2⁴ x 2^6x = 2^{4 + 6x}

Answered by Prahlad M. • Maths tutor

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In the early 20th Century the plum pudding model of the atom was replaced by the nuclear model of the atom, explain why this happened.

The plum pudding model defined the atom as a particle in which the charge and the mass of the atom was spread evenly. An experiment was set up in which alpha particles where shot to a thin gold foil. The ...

Answered by Joel P. • Physics tutor

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Express the following in partial fractions: (x^2+4x+10)/(x+3)(x+4)(x+5)

(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(...

Answered by Alessandro S. • Maths tutor

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