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A cuboid has length x cm. The width of the cuboid is 4 cm less than its length. The height of the cuboid is half of its length. The surface area of the cuboid is 90 cm^2 . Show that 2x^2 − 6x − 45 = 0

Take each side of the cuboid as an algebraic expression and multiply each by 2 to account for both sides of the shape. For example, (x)(x-4), which could be expanded to x 2 -4x, and then multiplied by 2 to r...
TM
Answered by Tom M. • Maths tutor
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How does one find the equation of a line passing through 2 points of a graph?

The general equation for a line on a graph is: y = mx + b ,where a is called the slope of the graph and b is the y-intercept(or the point where the line crosses the y axis). Let's assume the 2 points have th...
DD
Answered by Dimitar D. • Maths tutor
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f(x) = x^3 - 13x^2 + 55x - 75 , find the gradient of the tangent at x=3

f(x) = yy= x 3 - 13x 2 + 55x - 751) find f'(x) [=dy/dx] Differentiation is (1) multiplying the coefficient by the original power --> 2) reducing the original power by 1dy/dx = 3x 2 - 26x + 55 2) find f'(3...
KO
Answered by Kiitan O. • Maths tutor
4085 Views

Solve the simultaneous equations: 3x + 2y = 4 and 4x + 5y = 17

Step 1: multiply one or both equations so that the 2 equations have the same coefficient for either x or y (pick easier one) 5(3x + 2y) = 5(4) --> 15x + 10y = 20 AND 2(4x + 5y) = 2(17) --> 8x + 10y = 3...
RD
Answered by Rania D. • Maths tutor
5612 Views

Solve 2sin2θ = 1 + cos2θ for 0° ≤ θ ≤ 180°

sin2θ = 2sinθcosθ (double angle formula for sine)cos2θ = cos 2 θ - sin 2 θ (double angle formula for cosine) = 2cos 2 θ - 1 (utilising the trignometric identity sin 2 θ + cos 2 θ = 1) We substitute these int...
SN
Answered by Samuel N. • Maths tutor
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