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Differentiate with respect to x: (6x + 7)e^x

Product Rule: dy/dx (uv) = u'v + uv' Let u = 6x+7 and v = e^x. Using simple disintegartion, u' is 6 and v' is e^x. Therefore, answer is: 6e^x + (6x +7)e^x
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Answered by Aisha R. • Maths tutor
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In a triangle ABC, side BC = 8.1 cm, side AC = 7 cm, and angle ACB = 30 degrees. What is the area of the triangle?

Initially, one might think to use area = 1/2 x base x height, however drawing the triangle immediately shows that this is not possible here. We then think to use the formula for area using two adjacent sides...
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Answered by Ellie B. • Maths tutor
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Aled has three concrete slabs. Two of the slabs are square, with each side of length x metres. The third slab is rectangular and measures 1 metre by (x +1) metres. The three concrete slabs cover an area of 7m^2. Show that 2x^2 + x – 6 = 0. Find x.

For the first part of the question, we can firstly assume that the... area of slab 1 + area of slab 2 + area of slab 3 = total area, which we know to be 7m^2Knowing that to work out the area of a square we u...
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Answered by Nathan J. • Maths tutor
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How do I integrate cos^2x with respect to x?

This can be a very tricky question if you do not know how to approach it. Our first instinct may be to try a substitution, but this gets us nowhere. In fact, the trick is to make use of the identity cos2x = ...
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Answered by Raiad S. • Maths tutor
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Point P on the curve, x = 2tan( y+ π/12), has a y-coordinate of π/4. Find an equation for the normal to the curve at P.

Step 1 - Firstly, we need to find the x-coordinate of point P. This will allow us to find the normal equation required in the question. To find the x-coordinate, we plug in the value of y given in the questi...
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Answered by Andrew M. • Maths tutor
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