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A curve is defined by the parametric equations x = 2t and y = 4t^2 + t. Find the gradient of the curve when t = 4

the gradient of the curve = dy/dx and dy/dx = (dy/dt)(dt/dx) dy/dt = 8t + 1 dx/dt = 2 therefore dt/dx = 1/2 dy/dx as above = (8t + 1) * 1/2 = (8t + 1)/2 where t = 4, dy/dx = (8*4 + 1)/2 = (32 + 1)/2 = 33/2
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Answered by Angus B. • Maths tutor
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Nancy is driving and makes a wrong turn. The satnav indicates that her journey will take an extra 7 minutes. Nancy drives at an average speed of 60km/h to the nearest 5km/h. What's the greatest possible distance traveled in this detour in km to 2.d.p?

Start by selecting useful information in the text.time = 7 minutesspeed = 60km/h to the nearest 5km/hmaximum possible distance travelled = ? kmWe know a time and speed and want to know a distance. So we can ...
LG
Answered by Louis G. • Maths tutor
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Solve 7x+6>1+2x

For this such question, we need to find what values x can be. We need to get all the terms containing x one side of the equation and all the other terms on the other side then isolate x. To do this, we must ...
AM
Answered by Annie M. • Maths tutor
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a) i) find dy/dx of y = 3x^4 - 8x^3 - 3 ii) then find d^2y/dx^2 b) verify that x=2 at a stationary point on the curve c c) is this point a minima or a maxima

So the first step is to find the first differential of yTo do this we simply have to differentiate:so with C being our coefficient, n being the power that x is.we need to reduce the power of x by 1, whilst m...
CM
Answered by Charlie M. • Maths tutor
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Solve simultaneously. x^2+y^2 = 25 ; y - 3x = 13

y = 3x + 1310x^2 + 78x + 169 = 2510x^2 +78x +144 = 0(5x+24)(2x+6) = 0x = -24/5 or -3y = -7/5 or 16
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Answered by Ben H. • Maths tutor
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