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dx/dt = -5x/2, t>=0. Given that x=60 when t=0, solve the differential equation, giving x in terms of t.

dx/dt = -5x/2 to solve this we must firstly separate the variables ∫2/x dx = -∫5 dt t hen we solve the integrals using basic integration formulae 2lnx = -5t+c. When it comes to the exam, many students forget...
KS
Answered by Kulveer S. • Maths tutor
6381 Views

Why do I have to study maths?

Maths is very important in real life. You use it day to day from basic addition and subtraction to working out percentage discounts in shops. Some of the more complex maths like algebra is used in fields lik...
JP
Answered by Jack P. • Maths tutor
3447 Views

Expand and simplify (x-4)(2x+3y)^2

( x -4) x (2 x +3 y ) 2 (x-4) x (4x 2 +12xy +9y 2 ) 4x 3 +12x 2 y + 9xy 2 -16x 2 -48xy - 36y 2 finished.
JT
Answered by James T. • Maths tutor
3386 Views

Purple paint is made by mixing red paint and blue paint in the ratio 5 : 2 Yan has 30 litres of red paint and 9 litres of blue paint. What is the maximum amount of purple paint he can make?

the ratio given is 5:2simplify this ratio by diving 2 = 2.5 : 1 the maximum amount of blue paint is 9Lso multiply the whole ratio by 99 x 1 = 9.0L blue paint9 x 2.5 = 22.5L red paint add the two paints toget...
JL
Answered by Joseph L. • Maths tutor
18456 Views

simplify fully: (x^2+x-6)/(x^2-7x+10)

First, the numerator and denominator of the fraction need to be factorised:(x+3)(x-2)/(x-5)(x-2)The 'like' terms should then be crossed out; in the case above, it is the (x-2) brackets.(x+3) (x-2) /(x-5) (x-...
LL
Answered by Lili L. • Maths tutor
8819 Views