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When a 470 micro farad capacitor is discharged through a fixed resistor R, the pd across it decreases by 80% in 45 s. Calculate the time constant of the circuit

Using the equation V=V 0 e -t/RC where RC is the time constant to be calculated: We know that the pd decreases by 80%, therefore the pd remaining, V is 0.2*V 0 . Putting this into the equation above: 0.2=e -...
PK
Answered by Peter K. • Physics tutor
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The first term of an arithmetic series is a and the common difference is d. The 12th term is 66.5 and the 19th term is 98. Write down two equations in a and d then solve these simultaneous equations to find a and d.

The first step is to recall the formula for arithmetic progressions: u(n) = a + (n-1) d We can then put all the information given in the question into this so u(12) = 66.5 = a + 11d and u(19) = 98 = a + 18d ...
EW
Answered by Eleanor W. • Maths tutor
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A curve has equation (x+y)^2=x*y^2, find the gradient of the curve at a point where x=1

Differentiating left hand side: 2(x+y)(1+dy/dx) from the chain rule 2. Differentiating right hand side: y 2 +2xy(dy/dx) from the product rule 3. Equating sides and taking out factors of dy/dx to rearrange fo...
PK
Answered by Peter K. • Maths tutor
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Find the equation of a straight line that passes through the coordinates (12,-10) and (5,4). Leaving your answer in the form y = mx + c

Finding the gradient (m): The gradient is the change in y-axis over the change in x-axis Δy = -10-4= -14 Δx = 12-5=7 Δy/Δx = -14/7 = -2 Accumilating the equation: The equation of a straight line can be deduc...
MM
Answered by Martin M. • Maths tutor
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Find the vector equation of the line of intersection of the planes 2x+y-z=4 and 3x+5y+2z=13.

The line of intersection will be parallel to both planes. We can write the equations of the two planes in 'normal form' as r.(2,1,-1)=4 and r.(3,5,2)=13 respectively. We can then read off the normal vectors ...
RS
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