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Given h(x) = 9^x + 9 and g(x) = 10*3^x, find {x | h(x) < g(x)}.

This question is asking to find the values for x, such that h(x) is strictly less than g(x). We can write this as 9^x + 9 < 103^x and solve for x as follows. 9^x + 9 < 103^x => 3^(2x) - ...

Answered by Carlo M. • Maths tutor

3712 Views

Prove the following identity: (1+cos⁡(x)+cos⁡(2x))/(sin⁡(x)+sin⁡(2x) )=cot⁡(x)

Straight away we notice that two trigonometric terms on the left hand side have 2x but there are no 2x on the right hand side therefore we realise that this question will require double angle formulae. If...

Answered by Jessica B. • Maths tutor

18863 Views

Given 1/2 + 1 + 2 + 2^2 + ... + 2^10 = a*2^b + c, find the values of a,b,c.

Consider the Left-Hand-Side (LHS) of the equation first. LHS: 1/2 + 1 + 2 + 2^2 + ... + 2^10. We identify this as a geometric series by noticing that dividing any term u_(n+1) by the preceding term n the ...

Answered by Carlo M. • Maths tutor

3977 Views

How can the central bank affect economic activity using monetary policy

A particular economy can go through many downturns and upturns in what is called the business cycle. A central bank may wish to dampen these fluctuations by using one of two tools. The first one is changi...

Answered by Martin S. • Economics tutor

3231 Views

What is the difference between osmolarity and osmolality?

First of all, it is important to define osmosis. If you have two solutions separated only by a semi-permeable membrane, and one solution is more concentrated than the other, then water will move from the ...

Answered by Kelly W. • Biology tutor

12547 Views