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Three identical isosceles triangles are joined together to make a trapezium. Each triangle has base b cm and height h cm. Work out an expression, in terms of b and h for the area of the trapezium.

Formula for the Area of a triangle: A = (base x height)/ 2
Here we have three identical triangles.
Therefore the formula for the Area of the three triangles: A = (b x h) x 3 / 2 = A of trapeziu...

MC
Answered by Megan C. Maths tutor
8498 Views

Solve the differential equation csc(x)*dy/dx=exp(-y), given that y(0)=0. (Typical Math HL paper 3 question, Calculus optional topic)

Firstly, we need to grasp the problem, and understand what the question is asking us to do. We are given a differential equation, and we are required to solve for y, i.e. write y as a function of x: y(x)=...

KG
Answered by Khariton G. Maths tutor
1626 Views

Explain how integration via substitution works.

The function in terms of x should be broken down into two easier to integrate functions, like so f(x) = g(h(x)). if we say that u=h(x) is our substitution then we can integrate in terms of u now, however ...

DF
Answered by Daniel F. Maths tutor
2884 Views

Solve this set of linear equation to find x and y: 1. 8x + 2y =48 2. 7x +3y =47

Write out the two equations and label them 1 and 28x + 2y =487x+ 3y= 47The first aim is to get one variable (ie x or y) on both lines to equal each other. The easiest way to do this (keeping the numbers m...

RT
Answered by Rachel T. Maths tutor
2703 Views

Express 6sin(2x)+5cos(x) in the form Rsin(x+a) (0degrees<x<90degrees)

Expand sin(2x) to 2sin(x)cos(x) so you have 6(2sin(x)cos(x))sec(x). cos(x) and sec(x) cancel out so the expression becomes 12sin(x) + 5cos(x). compare this to the expanded version of Rsin(x+a) which is Rs...

JR
Answered by Jacob R. Maths tutor
4182 Views

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