i am having a problem with law of cosines. i am using the C^2 = A^2-2ABcosc+B^2
what do i do if i dont have a value for A?
i have tried to rearrange to find A but with no luck.
any help would be great.
i get to here usually,
2ABcosc = A^2+B^2-C^2,
i then work out 2Bcosc, as i would have those values but no A
sometimes i think square root both sides. this would remove the exponents on the right and square everything on the left but that does not work.
i am using a book called "trigonometry: essentials practice workbook with answers" by chris mcmullen. it uses only certain values that mean you do not require a calculator. the values you use are 0, 30, 45 and 90 degrees. sine, cosine and tangent for these values and only those values.
any help would be great thanks
i have a parallel rlc circuit which seems to be inductive with a 1 amp magnitude(?)
the circuit is explained in a post below about rlc circuits in parallel with complex numbers.
i havent drawn a phasor diagram. the capacitor and resistor currents are really low, in the micro amps with the inductor at 1 amp which is the supply current. so i am guessing that the phasor diagram would be the voltage pointing to 3 oclock and the current pointing toward 12 oclock, the voltage would have a magnitude of 10(volts, the supply voltage) and the current would have a magnitude of 1 amp(the supply current).
would this be correct. i have read a few things on the internet but not to sure if i have grasped the idea.
been a while!
i have just started my HND electronics course and i have to do some circuit analysis.
i have a parallel RLC circuit. three components, R = 12k ohms, L = 10mH, C = 10nF
with a 10sin(1000t) supply
i have to find the total impedance in polar form
supply current in polar form
current through each component in polar form
i written out what i have done and attached it (hopefully)
not sure about this. i think that i may have done something wrong with the angles.
no, my tutor has told me that he thinks it is wrong, though he hasnt checked his answers?
he told me he would check with other students and get back to me. i posted this question on another forum and they told me this is correct. im not sure as i am terrible at this. the question is almost exactly the same as a question posted on the internet.
this is the web site, its the first question with the answer. the only difference is the capacitor, voltage and resistor values. the whole question is identical. i followed the example changing the values as i went. so i thought that it was accurate. i just wanted to check as i have no way of knowing if this is correct. i have changed the degree that i will be studying at uni because it has less maths. thats a change in career. thats how much i drag at maths.
i just wanted to know if this is correct answer with the correct work.
i have just looked at simplification and cant seem to find anything that looks like the problem i have.
i did 1/400 on the calculator and pressed the S<>D button and got 0.0025 which i can rewrite as 25x10^-3 which is what i have to show.
i still don't understand how to do this.
im not actually sure how to work it out. i have to rearrange it somehow. is there a name for that process.
the bottom part is supposed to be the top rearranged to be able to find I
i dont know how to do this. a little hint would be good
i just had another look and i think that it is 1/50 instead, not 1/200
otherwise the rest is the same
i have a problem i have this
I = 5*10^-5/1+(2*10^-2) * s = ?
i dont know s, that shouldnt matter.
i think this equals (5*10^-3) 1/200+s
i have done this on latex but cant post it so this will probably look weird, its laplace transform.
i have to rearrange to find I
any help would be great
could someone please let me know if this is correct as I have been told that I have done this wrong though I didn't inform the person of how I did it. this is using division of conjugate complex numbers.
I have followed the method my tutor showed me and I think this is correct.
any help or a push in the write direction would be great!!!
I have a circuit with values
v1 = 20 + j0
r1 = 15 +j0
l1 = 0 +j10
c1 = 0 - j5
I have to use superposition and division of complex conjugate numbers.
the resistor, inductor and voltage source are in series. the capacitor is in parallel with the voltage source
I added the resistor and inductor, (15 + jo) + (0 + j10) = 15 + j10, find the conjugate of this 15 - j10
so then product over sum for the components that are in parallel. the inductor/resistor || capacitor
(0 - j5)*(15 - j10)
(15 + j10)*(15 - j10)
for the numerator I got
0 x 15 = 0
0 x -j10 = 0
-j5 x 15 = -j75
-j5 x -j10 = (j^2)50 = -50 minus 50 because of (j^2) = -1
so the result is -50 -j75, which im not sure about
then the second line
15 x 15 = 225
15 x -j10 =-j150
j10 x 15 = j150
j10 x -j10 = -(j^2)100, (j^2) = -1 x -100 = 100
225 -j150 +j150 +100, the middle terms cancel leaving 225 + 100 = 325
so I have, -50 -j75/325
then I divide each of the numerator by the denominator so,
-50/325 = -0.153846
-75/325 = -0.230769
I think I can use this to find polar notation r and theta(the zero with a line through)
im not sure if any of this is right though, any help would be great thanks
I have these two questions
c) Plot a graph of the kinetic energy of the mass against time. Explain your calculations and state formulae used.
d) Plot a graph of the kinetic energy of the mass against distance. Explain your calculations and state formulae used.
I have used this formula for the first one,
Ek = ½ mv2 = ½ ma2t2
Ek is proportional to t2.
this for the second
Ek = ½ mv2 , but we can substitute, giving
Ek = mgy
in not too sure how to show the graphs, but is the above formula along the right lines?
also I have to explain the use of the formula. I think this is just explain why I used it and any transposing required. if anyone knows a better answer for this one please give some advice.
taken from here, http://colourpoint.co.uk/sample_files/physics_as.pdf
this is the first part of the question,
A horizontal force of 80 N acts on a mass of 6 kg resting on a horizontal surface. The mass is initially at rest and covers a distance of 5 m in 0.92 s under the action of the force. Assuming there are no energy losses due to air resistance and therefore that the acceleration is constant:
a) Calculate the total energy expended in the acceleration, I got 11.81 acceleration
b) Calculate the coefficient of kinetic friction between the mass and the surface. Suggest materials from which the block and table might be made in order to give such results. I got 0.155
I have a question
the lengths of pins produced by a machine follow a normal distribution with mean 2.54cm and standard deviation 0.04cm. a pin is rejected if the length is less than 2.44cm or more than 2.60cm
A/ find the percentage of pins that are accepted.
B/ if it is decided that 2.5% of the pins are to be rejected because they are too long and 2.5% because they are too short, determine the new range of acceptable lengths.
for the first part I have the formula, z = x-MU / sigma, I rearranged this
sigma is 0.04cm
MU is 2.54cm
so I used this z * sigma + MU = x, z * 2.58 = ? so here I thought I would take a value from a table and divide by 2.58 until I got an accurate z value. then use that z for the rest.
if anyone could confirm this method as im not to sure? the rest I think I can get.
I have a question
a hollow steel shaft with a diameter ratio of 0.75 and a length of 4m is required to transmit 1Mw at 120rpm. the maximum shear stress is not to exceed 7 Mpa and the overall angle of twist is not to exceed 1.75degree. assume the modulus of rigidity for steel is 80Gpa.
a) determine the necessary outside diameter of the shaft so that both of the above limitations are satisfied
b) determine the actual maximum shear stress and the actual angle of twist.
first I tried finding the torque(T) using P(power) = Tw(w being 2piN( N is rotational speed in rps)) I think w is omega
I rearranged the formula to get T = P/w
so, 1000,000 / 2pi 2 the second 2 is from 120(rpm) / 60(rps) to get seconds
then, as I have degrees and would require radians I converted that
1.75 * pi / 180 = 0.0305 radians
so using a formula to find J ( the symbol for second moment of area)
the formula is J = T * L / G (theta sign), so
79577.47 * 4 / 80x10^9 * 0.0305 = 130454.87x10^-9 = J
which im not sure about. I have to find the outside diameter using D^4-d^4, D is outside diameter and d is inside diameter.
J = pi * (D^4 - d^4) / 32, this is the formula using diameter to find J, I have J and so would try to rearrange
I tried this,
D^4 - d^4 = pi * J / 32
any help would be great, I only know that diameter ratio is 0.75, the inside diameter is three quarters
If I did, d^4 = pi * J / 32, then d^4 answer would be three quarters of the D^4 answer. so if I took that and cut it into thirds that is what I would add to d^4 to get D^4???
any help would be great
s = integration sign (top number, bottom number)
i have this :
s (1, 0) (2xe^3x dx)
u = 2x
du/dx = x/2
dv/dx = e^3x
v = s 1/3 ^e3x
i really have no clue what im doing.
if someone could tell me what i do any of this it would really help
i have 2x so to integrate it, i increase the power by 1 and divide by this figure. so 2x = 2x^1, add 1 = 2x^2/2 (correct?)
is 2xe^3x treated as one number, like 2*xe^3x. one answer the lecturer wrote was 2e^3x/3, = 2/3 s e^3x dx
i am looking on the internet at the moment for any answers and coming up with nothing.
does anyone know any good sites that explain with good, easy to follow examples.
NEVERMIND, I GOT THE ANSWER THANKS ANYWAY ALL THE BEST!!!:D:D
I have this question
a rectangular sheet of metal measuring 120mm by 80mm has equal squares of size x cut from each of the corners. the remaining flaps are then folded upwards to form an open tray. draw a neat sketch of the net and prove that the volume of the tray is given by:
v = 4x^3 - 400x^2 + 9600x
a) find the value of x such that the volume is a maximum, making sure you show how you prove your value is a maximum not a minimum. work out the maximum volume of the tray.
b) verify your result for question 6a using a second method. present your alternative method in writing, ensuring you compare both ease of use and accuracy of results of the two methods.
the second bit is whats getting me. I can use the results of length and width which are 88.612mm and 48.612mm respectively. I cant include height and have to find volume.
im guessing its something to do with the cut outs.
I have maximum volume of box when x = 15.594
length = 120 -2 * 15.694 = 88.612
width = 80 -2 * 15.694 = 48.612
so I have the starting width and length, the finishing width and length and two lots of something to be taken away.
I found something close, I have 15.69499126 = x, this came from the general quadratic equation
I did this,
120 - 2 * 15.69499126 = 88.61001748
88.61001748 + 2 = 90.61001748
120 - 90.61001748 = 29.38998252
divide this by 2 to get = 14.69499126
this last number is supposed to be x but it is a whole 1 out. 14 instead of 15. I think this is correct but there is a 1 missing somewhere.
I think if I put all this together I should be able to get the correct answer giving me a final volume and height.
unless I have done something really daft here and got a knot in my brain.....again!:D
NEVERMIND, I GOT THE ANSWER THANKS ANYWAY ALL THE BEST!!!
anyway, if anyone could point me in the right direction. I would really appreciate it
I have a question im stuck on.
a beam must withstand a bending moment of 285kNm. if the maximum stress must not exceed 200Mpa, determine the elastic modulus z and select an appropriate I section from the given table. (the table is in the book that I have)
im not sure what the math formula im supposed to use.
the elastic modulus is z = I / y
I don't know what I is or Y
I have M, the maximum bending moment Nm
and, sigma which is stress in pa
so I thought M/sigma = z. 285*10^3 * 200 = 1425
im not sure if the M in Mpa is mega(1000 000) or milli or what. when I use mega the answer is really small.
a push in the right direction please