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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 ...

Answered by Henry F. • Maths tutor

2817 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)]

Answered by Henry F. • Maths tutor

3229 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 ...

Answered by Henry F. • Maths tutor

5021 Views

Solve 9x +1> 2x +3

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

Answered by Suruthi G. • Maths tutor

3477 Views

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.

Answered by Suruthi G. • Chemistry tutor

8213 Views