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Solve the equation 2ln2x = 1 + ln3. Give your answer correct to 2dp.

LHS: because alnx = lnx a , 2ln2x = ln(2x) 2 = ln4x 2 Now, because ln and e are inverse functions, we take both sides to the power of e. Therefore: e ln4x^2 = e 1 + ln3 4x 2 = e 1 + ln3 x 2 = (e 1 + ln3 ) / ...
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Answered by Shiv S. • Maths tutor
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What is Newton's Third Law and what is an example of it?

Newton's Third Law looks at what happens when two objects interact with each other. The definition of Newton's Third Law is, "When one body exerts a force on a second body, the second body simultaneousl...
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Answered by Maxwell O. • Physics tutor
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Integrate ⌠( xcos^2(x))dx

We must first use trigonometric identities to simplify cos 2 (x). We can use the formula cos(A+B) = cos(A)cos(B) - sin(A)sin(B) , where A=x and B=x , so that we get cos(2x) = cos 2 (x) - sin 2 (x) = 2cos 2 (...
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Answered by Daniel A. • Maths tutor
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A uniform plank of wood of mass 32 kg and length 4.0 m is used to cross a ditch. In the ditch is a rock, which is used to support the plank horizontally 0.80 m from one end. The other end is supported by the bank. Calculate the rock's supporting force.

We need to calculate moments about a point through which one of the forces is acting. I choose the bank support point. At this point, moments are caused by the weight of the plank acting at its centre of mas...
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Answered by Ricardo S. • Physics tutor
13477 Views

A curve C has equation y = (2 - x)(1 + x) + 3 . A line passes through the point (2, 3) and the point on C with x-coordinate 2 + h . Find the gradient of the line, giving your answer in its simplest form.

First we find the y coordinate which is a function of x: x = 2+ h so y = (2 - 2 - h)(1 + 2 + h) + 3 = -h 2 - 3h + 3 Now for the gradient, the line passes through points (2,3) and (2 + h, -h 2 - 3h + 3) dx = ...
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Answered by Ricardo S. • Maths tutor
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