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Express 3x^2+18x-1 in the form a(x+b)^2 +c

3x^2+18x-1 Bracket out 3x^2+18x Factorise by bringing out the common factor of 3 = 3(x^2+6x) Divide the x coefficient by 2 = 3(x^2+3x) And then remove the square on the x^2 variable and add a square to the o...
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Answered by Chukwudi O. • Maths tutor
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Find the x-values of the turning points on the graph, y=(3-x)(x^2-2)

The minimum point occurs where dy/dx=0 We have 2 options: 1.) Expanding the brackets 2.) The product rule of differentiation The shortest is the product rule: dy/dx= (d/dx)(3-x).(x 2 -2) + (3-x).(d/dx)(x 2 -...
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Answered by Zita E. • Maths tutor
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The height (h) of water flowing out of a tank decreases at a rate proportional to the square root of the height of water still in the tank. If h=9 at t=0 and h=4 at t=5, what is the water’s height at t=15? What is the physical interpretation of this?

Note: time, t, is measured in minutes, and height, h, is measured in metres. Let k>0, a constant. The differential equation to be solved is given by: dh/dt = - k(h)^0.5. Using 'separation of variables' gi...
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Answered by Sandie N. • Maths tutor
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curve C with parametric equations x = 4 tan(t), y=5*3^(1/2)*sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.

dy/dx = dy/dt *dt/dx (chain rule). x=4tan(t) hence dx/dt = 4 sec 2 (t) y = 5 3 1/2 sin(2t) hence y'= 10 3 1/2 cos(2t) therefore dy/dx = 10 3 1/2 cos(2t) / 4 sec 2 (t). Since P is on point with x=4 3 1/2 we c...
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Answered by Harry P. • Maths tutor
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Find the first derivative of r=sin(theta+sqrt[theta+1]) with respect to theta.

To find the first derivative we must apply the chain rule. Our aim is to find dr/d(theta). We start by bringing the differential of what's inside the sine brackets outside and multiplying it by the different...
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Answered by Tutor61926 D. • Maths tutor
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