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Expand and simplify (5a-2b)(3a-4b)

=(5a x 3a) + (5a x -4b) + (3a x -2b) + (-2b x -4b) =15a^2 - 20ab - 6ab + 8b^2 =15a^2 - 26ab + 8b^2
PI
Answered by Paul I. • Maths tutor
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How to find the derivative of arctan(x)

Let y = arctan(x). Then x = tan(y). Differentiate using the chain rule and rearrange: d(x)/dx = d(tany)/dx So 1 = sec^2(y) * dy/dx dy/dx = 1/sec^2(y) But from identity sin^2(y) + cos^2(y) = 1 We can derive, ...
MR
Answered by Matthew R. • Maths tutor
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How do I do this question: A small stone is projected vertically upwards from the point A with speed 11.2 m/s. Find the maximum height above A reached by the stone.

[Draw Diagram] We are given the inital velocity u=11.2m/s and we know the acceleration due to gravity is 9.8m/s^2. We need to find the distance 's'. When the stone is at its highest point the velocity will b...
LW
Answered by Luke W. • Maths tutor
6465 Views

Solve the simultaneous equations: x^2 + y^2 = 29 and y - x = 3

To solve these equations we need to eliminate one of the variables, so make y the subject of the second equation: y = x + 3. Now y can be substituted into the first equation: x^2 + (x+3)^2 = 29. Expanding (x...
TG
Answered by Trisha G. • Maths tutor
4740 Views

Solve 3(x-2) = 21

To begin, understanding the basica concept of algebra and multiplication using brackets needs to be covered as I have met quite a few children who have been used to these equations but are still unsure about...
NF
Answered by Nicole F. • Maths tutor
4243 Views