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Find the exact solution of the equation in its simplest form: 3^x * e^4x = e^7.

First take natural logs of both sides, giving us: ln(3 x * e 4x ) = ln(e 7 ). The RHS can be simplified using the definition of natural logs, so ln(e 7 ) = 7. We can then apply the product rule for logs (ln(...
HM
Answered by Hugo M. • Maths tutor
6021 Views

Explore some of the ways in which poets express change.

A key example of a poet expressing change comes in Carol Ann Duffy's ' Originally' from her 1990 collection The Other Country. In the poem, Duffy utilises imagery such as that of the turning wheels to sugges...
IM
6032 Views

What is a dialect and what is an accent?

An accent is commonly associated with sounds of a particular variety, so pronunciation. A dialect is commonly associated with the lexis and grammar of a variety e.g. the non-standard 'I were' in some Mancuni...
PS
3487 Views

Express x^2-7x+2 in the form (x-p)^2+q where p and q are rational. Hence or otherwise find the minimum value of x^2-7x+2

For the first part, use the 'complete the square method', which gives (x-7/2) 2 -49/4+2, simplified to (x-7/2) 2 -41/4. To find the answer for the second part, set x=7/2 so that the bracketed part becomes 0,...
CW
Answered by Connaire W. • Maths tutor
5439 Views

An isotope of 238,92-Uranium decays into a stable isotope of 206,82-Lead through a series of alpha and beta decays, how many of each does it go through?

This is a good example of where simplification can make an otherwise tricky question a lot easier. It is easy to get confused trying to work out different isotopes and the extra products of the decays, but a...
NM
Answered by Nathan M. • Physics tutor
6336 Views