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A cuboid with a volume of 912cm^3 has the dimensions 4 cm, (x + 2) cm and (x + 9) cm. Find an equation in terms of x and solve to find the dimension.

912 = 4(x+2)(x+9)228 = (x+2)(x+9)228 = x 2 + 11x + 180 = x 2 + 11x -210using the quadratic formula we obtain x = -10 or x = 21As dimensions must be positive; x must equal 21Hence; the dimensions are 4, (21+2...
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Answered by Carys R. • Maths tutor
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Differentiate, from first principles, y=x^2

According to first principles, the differential is found as the limit as h->0 of:[f(x+h)-f(x)] / hif we set our f to x^2, then we find that this expression becomes (x^2+2hx+h^2 - x^2)/hWhich simplifies to...
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Answered by Milo E. • Maths tutor
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How do i know where a stationary point is and what type of stationary point it is?

Stationary points are points on a curve where the gradient is zero. There are three types of stationary point maximum, minimum and point of inflexion. (will draw diagrams). They can be found by differentiati...
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Answered by Omar H. • Maths tutor
4100 Views

Given that w=x * e^-w use implicit differentiation to show that dw/dx=1/(e^w + x)

Given that w=x e -w use implicit differentiation to show that dw/dx = 1/(e w +x)Answer:Use product rule to simplify:dw/dx = x (de -w /dx) + e -w (dx/dx)Use chain rule to simplify even further:dw/dx = -x e -w...
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Answered by Panagiota G. • Maths tutor
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The perimeter of a right angled triangle is 72cm. The length of its sides are in the ratio 3:4:5. Work out the area of the triangle.

Total perimeter - 72cm. Perimeter - (3+4+5)x -> 72=12x therefore x=6. The area of the triangle is 0.5(3x 4x) (because 5x is the longest side) therefore the answer is 0.5(18 24) = 216cm^2
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Answered by Sam T. • Maths tutor
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