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Frank, Mary and Seth shared some sweets in the ratio 4:5:7. Seth got 18 more sweets than Frank. Work out the total number of sweets they shared.

The ratio 4:5:7 is a way of comparing the size of the shares received by Frank, Mary and Seth. It helps to pretend that we are sharing the sweets between some equally-sized boxes: each box has the same nu...

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Answered by Richard N. Maths tutor
28293 Views

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
11146 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
3505 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
8631 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
11832 Views

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