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Given sinhx = 0.5(e^x - e^-x), express its inverse, arcsinhx in terms of x.

The first step is to write sinhx in its exponential form and set it equal to y, this will make rearranging easier. Then multiply everything by e^x and rearrange to form a quadratic, in terms of e^x. Express ...
KA
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A buffer was made by mixing 20cm3 of 0.05M NaOH and 20cm3 of 0.25M propanoic acid. Calculate the pH. Ka=1.34x10^-5

pH is calculated using the equation pH=-log[H+]. The concentration of H+ ions, therefore, needs to be calculated. The amount of each substance can be calculated by multiplying the concentration by the volume...
MC
Answered by Michael C. • Chemistry tutor
14220 Views

How do I decide whether to use the perfect or the imperfect tense?

The perfect and imperfect tenses are both used to describe a past tense in French. The imperfect tense is often a more descriptive tense and is used to set the scene and 'frame' the more punctual perfect ten...
DW
Answered by Daniel W. • French tutor
6059 Views

The finite region bounded by the x-axis, the curve with equation y = 2e^2x , the y-axis and the line x = 1 is rotated through one complete revolution about the x-axis to form a uniform solid. Show that the volume of the solid is 2π(e^2 – 1)

The volume of revolution, V, is given as 2π∫ydx Substituting in the equation and limits gives as follows: V = 2π∫2e^2x dx between 0 and 1 Integrating this gives V = 2π[e^2x] between 0 and 1 Applying the limi...
MC
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Edexcel C1 2015 Q10. A curve with equation y = f (x) passes through the point (4, 9). Given that f′(x)=3x^(1/2)-9/(4x^(1/2))+2. Find f(x), giving each term in its simplest form.

I would go through a similar example of integration with the student using the whiteboard and would explain the use of integration, and would then get them to do the above question, giving them hints when ne...
IA
Answered by Issy A. • Maths tutor
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