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Express 9^(3x + 1) in the form 3^y , giving y in the form ax + b, where a and b are constants.

9^ (3x + 1) We know that 3 to power of 2 equals 9. 3x3 = 3^2 = 9, = 3^ (2 * [3x + 1]) We simply the term because 2 * [3x + 1] = 6x + 2 = 3^ ( 6x + 2) This term is in the form of 3^ y, so we know that y = 6x ...
WL
Answered by William L. • Maths tutor
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Describe the Free fantasia style used by C.P.E Bach in the late 18th Century.

Free Fantasia as a style became highly popular in the late 18 th Century, with C. P. E. Bach being a prominent composer withint this style. However, he wrote very little upon this style and rarely discussed ...
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Answered by Thomas H. • Music tutor
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A tunnel has height, h, (in metres) given by h=14-x^2 where x is the horizontal distance from the centre of the tunnel. Find the cross sectional area of the tunnel. Also find the maximum height of a truck passing through the tunnel that is 4m wide.

Firstly, solve 0=14-x^2 to find the horisontal distance to the edges of the tunnel. x1=sqrt(14), x2= -sqrt(14). Integrate h=14-x^2 between x1 and x2 28*sqrt(14) -(2(sqrt(14)^3))/3. This is the required area ...
JG
Answered by James G. • Maths tutor
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How does the 3D dash and wedge notation work?

To make life easier we often treat molecules as flat - for example we draw methane on a page as a carbon with 4 hydrogens bonded to it at perfect 90 degree angles. This isn't really the case. Electron-electr...
DM
Answered by Dario M. • Chemistry tutor
7896 Views

Express 3(x^2) - 12x + 5 in the form a(x - b)^2 - c.

Starting with a(x - b)^2 - c, if we expand the bracket we get: a(x^2 - 2xb + b^2) -c Since we need to end up with the coefficient on x^2 being 3 and in the expression above x^2 is only multiplied by a, this ...
LH
Answered by Lucy H. • Maths tutor
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