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If 4x = 9y, and 2x + 5y = 95. What is the value of y^2 - x?

This is a simultaneous equation problem.If 4x = 9y then 2x = 4.5y.Then by substitution, 4.5y + 5y = 95.Then 9.5y = 95 (divide by 9.5) gives y = 10.By using back substitution 2x = 4.5*10 = 45 (divide by 2 ...

Answered by Riku G. • Maths tutor

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(Core 3 level) Integrate the function f(x) = 2 -cos(3x) between the bounds 0, pi/3.

f(x) = 2 - cos(3x)integrate function x term2 -> 2x (raise power of x then divide by new power for polynomial functions of x) -cos(3x) -> -(1/3)(sin(3x)) (using a substitution of 3x = u, then cos(u) ...

Answered by Riku G. • Maths tutor

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How do I work out if two lines are parallel?

The gradients of the two lines must be the same. The gradient is m in the equation: y=mx+c For example: L1: y = 3x – 2L2: 3y – 9x + 5 = 0 First rearrange L2 so it is in the same form as L1 to get:3y=9x-5T...

Answered by Alexandra B. • Maths tutor

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What is the value of sin(theta), cos(theta), tan(theta) where theta = 0, 30, 45, 60, 90

sin(0) = 0 ; sin(30) = 1/2; sin(45) = 1/sqrt(2); sin(60) = sqrt(3)/2; sin(90) = 1cos(0) = 1; cos(30) = sqrt(3)/2; cos(45) = 1/sqrt(2); cos(60) = 1/2; cos(90) = 0 tan(0) = 0; tan(30) = 1...

Answered by Luqman B. • Maths tutor

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(i) Prove sin(θ)/cos(θ) + cos(θ)/sin(θ) = 2cosec(2θ) , (ii) draw draph of y = 2cosec(2θ) for 0<θ< 360°, (iii) solve to 1 d.p. : sin(θ)/cos(θ) + cos(θ)/sin(θ) = 3.

For (i) Start by looking at left hand side of the equation. It is usually much easier to reduce large expression into smaller ones. So, LHS = sin²(θ) +cos²(θ)/ sin(θ)cos(θ). Since, s...

Answered by Rabin K. • Maths tutor

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