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Solve the simultaneous equations “x^2+y^2=4” and “x=2-y”. What does this tell us about the circle centred on the origin, with radius 2, and the straight line with y-intercept 2 and gradient -1?

In order to solve the pair of simultaneous equations, we must find a single set of values for x and y which fulfils both at once. By substituting “x=2-y” into “x 2 +y 2 =4”, we obtain a single equation conta...
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Answered by Aaron D. • Maths tutor
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What is the difference between a longitudinal and a transverse wave?

First it's important to remember that a wave isn't an object that is moving. When a wave moves through a substance the particles of the substance move side to side or backwards and forwards around their orig...
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Answered by Maya B. • Physics tutor
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What is the length of the hypotenuse in the right angled triangle to one decimal place? (a=5cm, b=4cm)

Step 1. Use the formula a 2 +b 2 =c 2 Step 2. Square a and b to find a 2= 25 and b 2 =16 Step 3. Add a 2 and b 2 to find c 2 =41 Step 4. Find the square root of c 2 is sqrt(41)=6.403 Step 5. Round 6.403 to 6...
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Answered by Eleanor R. • Maths tutor
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What is the difference bewteen a gerund and a gerundive?

Technically speaking, a gerund is a verbal noun and a gerundive is a verbal adjective. Gerunds and gerudnives both look very similar - the key feature in the words is a 'nd'. For example: amandi, vivendo, po...
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Answered by Dharaa P. • Latin tutor
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Prove the quadratic formula for ax^2 + bx + c = 0, where a is non 0 and a,b and c are reals.

By completing the square: ax^2 + bx + c = 0 => x^2 + (bx)/a + c/a = 0 (divide both side by a, since a is non-zero) => (x + b/(2a))^2 + c/a - (b/(2a))^2 = 0 (If this is not immediately clear, try expand...
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Answered by ShenZhen N. • Maths tutor
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