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Sketch the graph of x^2 - y^2 = 16

Before attempting to re-arrange the equation, we take an organic approach to looking at asymptotes:1) What happens to y when x=0 and when x -> infinity? What happens to x when y=0 and when y -> infi...

Answered by Maths tutor
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Q15 from Senior Mathematical Challenge 2018: A square is inscribed in a circle of radius 1. An isosceles triangle is inscribed in the square. What is the ratio of the area of this triangle to the area of the shaded region? (Requires Diagram))

Radius = 1, therefore diameter = 2Let x be the length of one side of the square.Using Pythagoras,x2 + x2 = 222x2 = 4x = sqrt(2)Area of isosceles triangle = side...

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Answered by Thomas H. Maths tutor
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Solve e^(2x) = 5e^(x) - 6, giving your answers in exact form

Solve e2x = 5ex - 6e2x - 5ex + 6 = 0(ex)2 - 5ex<...

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Answered by Thomas H. Maths tutor
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A curve C is mapped by the equation ( 1+x)(4-x). The curve intersects the x-axis at x = –1 and x = 4. A region R is bounded by C and the x-axis. Use calculus to find the exact area of R.

First draw the curve. Figure out and write the integration problem. Integral4-1 (1+x)(4-x) dx.Expand integral4-1 4 + 3x - x2 dx.= 4...

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Answered by Vishesh D. Maths tutor
3817 Views

Describe and explain the change in the shape of the graph y=x^2 and y=x^2 + 2.

The graph is translated by two in the positive y-axis direction. For example, for the equation y=x2, taking the x-axis values of 0,1,2 and 3, y= 02,12, 2

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Answered by Matthew S. Maths tutor
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