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A curve is defined by the parametric equations x=t^2/2 +1 and y=4/t -1. Find the gradient of the curve at t=2 and an equation for the curve in terms of just x and y.

To find the gradient of the curve at t=2 we need to find an expression for dy/dx and then substitute in for t=2. We can make use of the chain rule to find this expression because dy/dx = (dy/dt)/(dx/dt) a...

SC
Answered by Steven C. • Maths tutor
8844 Views

Solve the inequality. x^2 + 2x -15 > 0

To solve the inequality, it must first be factorised. This could be done by the ‘complete the square’ method. However in this example it is more efficient to find a pair of numbers that multiply to give t...

EF
Answered by Elizabeth F. • Maths tutor
12304 Views

What is a food chain we might see in the UK?

A food chain demonstrates what different species of animals present in an ecosystem eat, and are eaten by. The start of the food chain is a producer - an organism which makes 

CT
Answered by Caroline T. • Biology tutor
11956 Views

Describe the formation of a waterfall

As a river moves through its upper course, it creates multiple erosional features such as waterfalls. The river moves over varying rock types, some harder and more resistant to erosion than others. The so...

JS
Answered by Jamie S. • Geography tutor
3580 Views

What is the difference between the present perfect and the imperfect?

Present Perfect

  • Finished past action: Il a cuisiné.

  • An action which lasted a certain amount of time: Elle a étudié au lycée pendant ...

EM
Answered by Esther M. • French tutor
1756 Views

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