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What is a logarithm?

Logarithms, written in the form log x y, are another type of mathematical 'operation', just like addition or multiplication. Subtraction as the opposite of addition, division is the opposite of multiplicatio...
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Answered by Laurie H. • Maths tutor
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A cannon at ground level is firing at a fort 200m away with 20m high walls. It aims at an angle 30 degrees above the horizontal and fires cannonballs at 50m/s. Assuming no air resistance, will the cannonballs fall short, hit the walls or enter the fort?

solving horizontally, use v=s/t, where s=200, v=25(3) 1/2 . Hence t=s/v=8/(3) 1/2 (where t is the time when the ball would reach the fort if it does not reach the ground)Solivng vertically, s=?, u=25, v is i...
Answered by • Maths tutor
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Use Integration by parts to find ∫ xsin3x dx

∫ xsin3x dx takes the form of any integral ∫ (u)(dv/dx) dx. ∫ (u)(dv/dx) dx = uv - ∫ (v)(du/dx) dx Taking u=x and dv/dx= sin3x. The equation can be re-written in the form uv - ∫ (v)(du/dx) dx. Therefore, ∫ x...
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Answered by Safiyyah V. • Maths tutor
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A circle has equation: (x - 2)^2 + (y - 2)^2 = 16. It intersects the y-axis (y > 0) at point P and the x-axis (x < 0) at point Q. Find the equation of the line connecting P and Q and of the line perpendicular to PQ passing through the circle's centre.

(x - 2) 2 + (y - 2) 2 = 16 x = 0 --&gt; 4 + (y - 2) 2 = 16 --&gt; y - 2 = ±2sqrt{2} --&gt; y = 2 ± 2sqrt{2} --&gt; P(0,2 + 2sqrt{2})y = 0 --&gt; (x - 2) 2 + 4 = 16 --&gt; x - 2 = ±2sqrt{2} --&gt; x = 2 ± 2sq...
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Using the factor theorem, factorise x^4 - 3x^3 - 3x^2 + 11x - 6

Well the question states that it wants you to use the factor theorem so it would be a good idea to write down the factor theorem to remind ourselves.&quot;A polynomial f(x) has a factor (x - a) if and only i...
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Answered by Kester G. • Maths tutor
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