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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 “x2+y2=4”, we obtain a ...

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Answered by Aaron D. • Maths tutor
11974 Views

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 a2+b2=c2

Step 2. Square a and b to find a2=25 and b2=16

Step 3. Add a2 and b2 to find c

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Answered by Eleanor R. • Maths tutor
3906 Views

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...

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Answered by ShenZhen N. • Maths tutor
9232 Views

Evaluate the indefinite integral: ∫ (e^x)sin(x) dx

Note: for what’s about to come, ' denotes derivative with respect to x. Method 1 (integration by parts): let I = (e^x)sin(x) dx let u = sin(x)...

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Answered by ShenZhen N. • Maths tutor
12426 Views

How do I find the area under a curve between two points?

Assuming you know the equation of the line, this could possibly be done in several ways. If you are able to integrate the equation of the line definitely using your current knowledge, then do this between...

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Answered by Reece R. • Maths tutor
4852 Views

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