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Solve the simultaneous equations 5x + 2y = 4 and x - y - 5 =0

First label the equations. 1: 5x + 2y = 4 . 2: x - y - 5 = 0 . Rearrange equation 2 . 2: y = x - 5 Substitute equation 2 into equation 1 . 5x + 2( x - 5 ) = 4 . 7x = 14 . x = 2 . Substitute x = 2 into equ...

CS
Answered by Conor S. • Maths tutor
5335 Views

Integrate the function f(x)=3^x+2 with respect to x

First note that a=eln(a) and ln(ab)=bln(a)By substituting a=3x we get a=3x=eln(3^x)=exln(3), and hence f(x)=exln(3)

CC
Answered by Christian C. • Maths tutor
2937 Views

Find the maximum value of 2sin(x)-1.5cos(x)

Put the equation in the form Rsin(x-a) (=Rsin(x)cos(a)-Rcos(x)sin(a)). Looking at the original equation Rcos(a) = 2 and Rsin(a) = 1.5. Tan(a)=1.5/2 and R^2= 2^2 +1.5^2. Therefore R = 2.5 and a = 0.6435.Th...

TA
Answered by Tom A. • Maths tutor
7664 Views

Given that y = cos(3x)cosec(5x), use the product rule to find dy/dx.

Write out the product rule: if y=f(x)g(x) where f and g are functions, dy/dx = f'(x)g(x) + f(x)g'(x)
Substitute in the expressions from the question:Therefore if f(x)=cos(3x) and g(x) = cosec(5x), f'...

HL
Answered by Harry L. • Maths tutor
3444 Views

How do you expand and simplify (x − 6)(x + 2y)^2

start of by expanding the braquet which has got a power(x + 2y) (x + 2y) = X2 + 2xy + 2xy + 4Y2then simplify that => x2 + 4xy + 4y2then multiply that by (x -...

AO
Answered by Antoine O. • Maths tutor
4973 Views

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