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Solve the inequality 5x + 3 ≤ 3x − 6.

x ≤ -4.5
MD
Answered by Martina D. • Maths tutor
5177 Views

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
5261 Views

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
8684 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
10915 Views

Make x the subject of the equation. y = 4( 2 + x )/ (6x -1)

First lets times both sides by (6x -1) y(6x - 1) = 4(2 + x) now lets expand the brackets 6xy - y = 8 + 4x now lets move all the ones with x as a factor onto one side of the equation and the rest on the other...
OO
Answered by Oliver O. • Maths tutor
5886 Views