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Solve for x 2x +3 + (4x-1)/2 = 10

2x +3 + (4x-1)/2 = 10 The divisor (2) is the biggest problem right now so we need to get it on its own... (4x-1)/2 = 10-2x-3 Equation has been rearranged! 4x-1 = 2(10-2x-3) Now we can eliminate the divisor b...
SH
Answered by Shannon H. • Maths tutor
6010 Views

Use the substitution u=3+(x+4)^1/2 to find the integral of 1/(3+(x+4)^1/2) dx between 0 and 5.

We will call the integral I, so I = integral of 1/(3+(x+4) 1/2 ) dx between 0 and 5. First substitute u=3+(x+4) 1/2 into the equation to get I = integral of 1/u dx between 0 and 5 Next we want to change the ...
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Answered by Calum B. • Maths tutor
4495 Views

Find the centre and radius of the circle with equation: x^2 + y^2 -4x +8y = 5, and determine whether the point (7,-4) lies on the circle.

First we complete the square on the equation of the circle to obtain: (x-2)^2 -4 + (y+4)^2 -16 = 5. Re arrange : (x-2)^2 + (y+4)^2 = 25 General equation of a circle: (x-a)^2 + (y-b)^2 = r^2, with centre (a,b...
AS
Answered by Alec S. • Maths tutor
6817 Views

How to express one quantity as a percentage of another?

There are several ways to do this which make it particularly interesting. I would advise trying to avoid doing it by eye, this leaves you open to many clumsy mistakes. My preferred method is using equivalent...
SP
Answered by Sebastian P. • Maths tutor
3456 Views

Find the exact solutions, in their simplest form, to the equations : a) 2ln(2x + 1)-4=0 b)7^(x)e^(4x)=e^5

a) 2ln(2x + 1)-4=0 -> ln(2x + 1)-2=0 -> ln(2x + 1)=2 -> (2x + 1)=e 2 -> 2x = e 2 -1 -> x = (e 2 -1)/2 b) 7 x e 4x =e 5 -> 7 x =e 5 \ e 4x ​​​​​​​-> 7 x =e 5-4x ​​​​​​​-> ln(7 x )=5-4x...
EL
Answered by Elizabeth L. • Maths tutor
5333 Views