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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 2 5 + 7 5 pens. 10 red and 35 yellow, 45 pens b) 18 red / 2 = [9]r0 31 yellow / 7 = [4]r3 So could have 9 sets of...
HF
Answered by Henry F. • Maths tutor
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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
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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)==&gt; 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 ==&gt; sin(x) = 1/3 i) x = Pi/2, 3P...
HF
Answered by Henry F. • Maths tutor
5542 Views

Solve 9x +1> 2x +3

9x - 2x&gt; 3-17x &gt; 2x &gt; 2/7
SG
Answered by Suruthi G. • Maths tutor
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Describe how carbon dioxide helps maintain temperature on Earth

Carbon dioxide allows radiation of short wavelengths to pass through the atmosphere to the Earth and absorbs any outgoing radiation that has long wavelengths.
SG
Answered by Suruthi G. • Chemistry tutor
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