Show that
Hence, or otherwise, work out
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Show that
Hence, or otherwise, work out
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Given
find the value of the positive constant k.
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A curve passes through point and has a gradient of .
Find the gradient of the curve at point .
Find the equation of the tangent to the curve at point .
Give your answer in the form .
Determine the equation of the curve .
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A point lies on the curve that has a gradient of .
Find the gradient of the curve at point .
Find the equation of the tangent to the curve at point .
Give your answer in the form .
Determine the equation of the curve .
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The diagram below shows part of the graph of
Write down the values of x where .
Show that
Evaluate
Write down the area of the region labelled R.
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The following diagram shows an arch that is tall and wide. The arch crosses the -axis at the origin, , and at point , and its vertex is at point . The arch may be represented by a curve with an equation of the form , where all units are measured in metres.
Find
the coordinates of
the coordinates of
Find the cross-sectional area under the arch.
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A trough has a cross-sectional area shown by the shaded region of the diagram below, where the and values are in centimetres. The curved bottom of the trough has an equation in the form . Point is the origin, and points are the vertices of a rectangle. Point , the deepest point of the trough, is situated on the -axis.
Determine the value of .
Find the cross-sectional area of the trough.
The length of the trough is 1.2 m.
Find the volume of the trough. Give your answer in .
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The following diagram shows part of the graph of . The shaded region is bounded by the -axis, the -axis and the graph of .
Write down an integral for the area of region
Find the area of region R.
The three points and define the vertices of a triangle.
Find the value of , the -coordinate of , given that the area of the triangle is equal to the area of region .
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