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A 4 metre long bar rotates freely around a central pivot. 3 forces act upon it: 7N down, 2m to the left of the pivot; 8N up, 1m to the left of the pivot; 4N up, 1m to the right of the pivot. Apply one additional force to place the bar in equilibrium.

Begin by calculating the current force and moment of the bar.Force: 8+4-7=5 (or vice versa)Moment: 72= 14 Nm anticlockwise 81= 8 Nm clockwise 4*1= 4 Nm anticlockwiseSum calculated moments: 14+4-8...

Answered by Michael A. • Physics tutor

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A house is bought for £150,000 at the start of 2005. For 3 years it loses 10% of its original value per year. After this time it loses 10% per year. What was its value at the end of 2011/start of 2012?

Original value = 150,000 10% original value =15,000 After 3 years year is 2008, house value = 150,000 - 3*(15,000) = 105,000Until start of 2012 from start of 2008, so 4 years of compound intrest. New v...

Answered by Henry F. • Maths tutor

2869 Views

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

2664 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

3025 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

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