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Simplify √32 + √18 giving your answer in the form of a√2.

√32 + √18 = 4√2 + 3√2 = 7√2
KS
Answered by Kavi S. • Maths tutor
9492 Views

A stone, of mass m , falls vertically downwards under gravity through still water. The initial speed of the stone is u . Find an expression for v at time t .

Ma = mg - Lmv 2) dv/dt = g-Lv 3)-1/L *(ln(g -Lv)/(g - Lu)) = t 4) g - Lv/ g - Lu = e -Lt 5) Rearrange to.... v = 1/L *(g-(g - Lu) e -Lt ) Missed some steps as it was relatively long, can perform this fully i...
JW
Answered by Joseph W. • Maths tutor
4563 Views

What is the cosine rule and how do I use it?

The cosine rule, a 2 =b 2 +c 2 -2bccosA, where a, b, & c are the sides of a triangle and A is the angle opposite side a, is the general version of Pythagoras' Theorem and applies to any triangle, not jus...
MQ
Answered by Matt Q. • Maths tutor
7809 Views

Find the derivative of f(x)= ln(|sin(x)|). Given that f(x) has a value for all x, state why the modulus is required.

The derivative can be found by using the chain rule. i.e. let g(x) = |sin(x)|, so f(x)=ln(g(x)), hence df/dx = df/dg * dg/dx df/dg = 1/g, dg/dx = |cos(x)| so df/dx = |cos(x)|/|sin(x)| For the second part, it...
LK
Answered by Luke K. • Maths tutor
13122 Views

What is implicit differentiation and how do I do it?

Implicit differentiation involves differentiating expressions for which it is difficult to rearrange into y in terms of x. It is important to note which variable is being differentiated by the other as, for ...
NO
Answered by Nicholas O. • Maths tutor
7253 Views