bill k

Please explain step by step how and why

5e^(-i(t-15°)) + 5e^(i(t-15°))

becomes

10cos(t-15°)

Please show, step by step how:

Integral, Limits from negative infinity to positive infinity of:

[(1/2)(jω+2)e^(jωt)δ(ω+1)dω] / [(jω)^2 + jω4 +2)]

becomes

[(1/2) (-j+2)e^(jt)] / [-1 - j4 + 2]

I was just wondering if I have a device that requires a 10 V 250 mA DC power adapter is there an upper limit to how many more amps I can use? I know voltage and polarity has to be the same as the original power adapter. But as far as the current is there any difference if I put a 10 V 1000 mA adapter how about 10 V 3000 mA or 10 V 8000 mA? I'm asking because I want to buy a universal power adapter should I just buy the highest amperage possible which can then cover all lower ranges? Would there be any down side for the device or the power adapter if a device required 10 V 250 mA an I used a 10 V 8000 mA adapter? Overheating or anything?

Can someone please explain to me how we choose the voltage and capacitance of a capacitor when building a DC and AC circuit. In a full wave rectifier application for example a smoothing capacitor after the diode bridge, how would we choose the voltage and capacitance is there some rule of thumb or some formula? Let's say we have a 110 V AC to 12 V AC step down transformer, then a diode bridge, then a smoothing capacitor. What Voltage would the capacitor need to be the same as the secondary winding 12 V? 20 % higher than 12 V so 14.4 V?  OR double 24 V? And what about capacitance in this example I really have no idea how I would choose capacitance 50 nano farads, 100 nano farads, 3000 micro farads? Is there some formula? For AC capacitor applications I can't think of an example please provide one if possible. Is the capacitance that a capacitor needs to be rated at somehow equal to the current it needs to be able to pass through? Like the higher the current that must pass through the capacitor the higher the capacitance? This isn't homework or anything I'm just a hobbyist trying to understand why I see electronics with different capacitors rated at different voltages and capacitance.

Show step by step how:

Equation 1: x[(1/z) + 1] - y(1/z) - 1/z = y

Equation 2: y[(1/z) + z] - x(1/z) = -x

becomes:

y = [-z + 1]/[z(z^2 + 2z +1)]

Hint: Express equation 2 in terms of x and plug into equation 1.

Please explain step by step how to mathematically prove the following:

x + y = 100

Find the value of x and y when x = y.

Obviously the answer is 50 but how do I get that answer mathematically?

Use partial fraction decomposition

[10x^2] / [(x^2+9)(x+1)]

Use partial fraction expansion on

[-1] / [(x+1)(x^2+1)]

to get:

-1/2 1/(x+1) + 1/2 x/(x^2+1) -1/2 1/(x^2+1)

Partial Fraction Expansion

Show step by step how

[x^2 + x - 1]/[x(x + 1)^2] + 1/x

becomes

1/(x + 1)^2 + 2/(x + 1) - 1/x

using partial fraction expansion

Show step by step how:

[2x^3 + 4x^2 + 4x + 12] / [(x + 1)^2 (x^2 + 1)]

becomes:

[(-4x + 1)/(x^2 + 1)] + [6/(x + 1)] + [5/(x + 1)^2]

Using partial fraction expansion.

Show step by step how:

[-1] / [(x + 1)(x^2 + 1)]

becomes:

(-1/2)[1/(x + 1)] + (1/2)[x/(x^2 + 1)] - (1/2)[1/(x^2 + 1)]

using partial fraction expansion

INT [0 TO 2] dx INT [0 to x] f(sqrt(x^2+y^2))dy

How do you sketch the region of integration and the function sqrt(x^2+y^2)? please sketch step by step.

Hi, can someone please explain what part of mathematics covers an introduction to summation notation. Single sums, double sums, triple sums, laws, solving strategies, divergence and convergence and so on. I would like to learn as much as possible about sums starting at the very basics. Is summation notation introduced in algebra, pre-calculus, calculus? Or somewhere else? Any books you can recommend that explain summation and series well? Thanks.

Please show step by step how:

[(A + 1)*((A/(A^2 + 1)) - (1/A))] / [2+(1/A)+A]

becomes:

[-1] / [(A + 1)(A^2 + 1)]

Show step by step how:

[A[1+(1/B)]-(2/B)] / [1+(1/B)]

becomes

A-[2/(B+1)]

Write all the possible second order partial derivatives of the function of two variables f(x,y).

What are the possible combinations of plus and minus for using for digits:

For example first two would be:

+ + + +

- - - -

what other cobinations of + and - do we have?