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If a student wishes to have a ratio of 2:7 red pens to yellow pens in their pencil case: a) if they have 50 pens total what is the maximum amount they can carry with them b) if they have 18 red and 31 yellow what is the maximum amount they can carry

a) 50 pens total. 2 + 7 = 9. Number of pens is done in 9s.  50/9 = 5r5, so multiple of 5.  Then 25 + 75 pens.    10 red and 35 yellow, 45 pens             
b) 18 red / 2 = [9]r0   31 yellow ...

HF
Answered by Henry F. Maths tutor
2927 Views

Given that dx/dt = (1+2x)*4e^(-2t) and x = 1/2 when t = 0, show that ln[2/(1+2x)] = 8[1 - e^(-2t)]

1/(1+2x) dx = 4e^(-2t) dt      Integrate both sides:   ln[2/(1+2x)] = -8e^(-2t) + c      input x = 1/2, t = 0:  ln(2/2) = -8*(1) + c        ln 1 = 0,  so c = 8ln[2/1+2x] = 8[1-e^(-2t)]

HF
Answered by Henry F. Maths tutor
3338 Views

Solve: 2 sin(2x) = (1-sin(x))cos(x) for 0<x<2*Pi and give any values of x, if any, where the equation is not valid

Double angle formula:Sin(2x) = 2sin(x)*cos(x)==> 2sin(x)*cos(x) = (1-sin(x))*cos(x)       (2sin(x)-1+sin(x))*cos(x) = 0(3sin(x) - 1)*cos(x) = 0     i) cos(x) = 0,  ii) 3sin(x) = 1 ==> sin(x) = 1/3  ...

HF
Answered by Henry F. Maths tutor
5149 Views

Solve 9x +1> 2x +3

9x - 2x> 3-17x > 2x > 2/7

SG
Answered by Suruthi G. Maths tutor
3551 Views

You are told that y is proportional to x^2 and that y=75, x=5. Find a formula for y in terms of x.

You know that y is proportional to x2, so let y=kx2 . You also know that y=75 and x=5. Substitute y=75 and x=5 into the equation y=kx2 . Therefore: 75=k multiplied by 5

AG
Answered by Anna G. Maths tutor
3345 Views

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