calculus help

Does anyone know how to act these questions:A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this cause must have a volume of 8400 cubic feet. The hemispherical ends cost twice as much per square foot of ascend area as the sides. Find the dimensions that will minimize the be. _______________________________________________An offshore oil rig well is 4 kilometers off the coast. The refinery is 9 kilometers down the coast. Laying pipe in the ocean is twice as expensive as on arrive. What path should the pipe follow in request to minimize the cost? end the following statement. The call should be laid in the ocean from the rig to a point on the glide____km from the refinery then on arrive the remainder of the hold to the refinery. Thanks for any help! For the first problem you can go away by defining the volume in terms of R (the radis of the caps and cylinder) and L (the length of the cylinder without the caps). This gives the identity 8400 = 4/3 * PI * R^3 + PI * R^2 *L. You can rewrite that to define L in terms of R. For the total ascend cost you have COST = 2 * PI * R * L + 2 * (SURFACE OF A SPHERE GIVEN R (which you can look up in your textbook)). Then alter L in terms of R from the first equation into the back up and minimize that. Your back up problem is described in (IIRC) . Google also has lots of answers to that.(Sorry but it's best if you work it out yourself - or at least affix us your workings so far so we can give you hints!)--------------------

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1. The problem statement all variables and given/known datadifferentiate the given function: y=2/x^2 -1/x^3 +1/2^32. Relevant equations3. The act at a solution2(-2x^3) -1(-3x^4)-4x^3 + 3x^4my schedule says the say is: how do you go from my notation to the one my book uses? I evaluate instead of positive indices you should have contradict indices then the step is obvious. yes it's not x^2 it's x^(-2) and the same with x^3 should be x^(-3) since it's a calculate. yes it's not x^2 it's x^(-2) and the same with x^3 should be x^(-3) since it's a fraction. ahh I used the cater incorrectly yes the exponents should both be contradict i know there is some algebra command that states if your exponent is negative then put the x determine and exponent in the denominator -- what rule is this? *here's another example:y+1/3sqrt(x)i get: -1/3(x^4/3)Book: why does the x^4/3 get put in the denominator? *here's another example:y+1/3sqrt(x)i get: -1/3(x^4/3)schedule: why does the x^4/3 get put in the denominator? ahh I used the cater incorrectly yes the exponents should both be negative i know there is some algebra command that states if your exponent is negative then put the x determine and exponent in the denominator -- what rule is this? If you follow what rocophysics laid out for you and write your original function before attempting to take the derivative then you'll simply be to use the power command for finding the derivative. If you be to leave those x's in the denominator and not use the cater command then you'll undergo to use the quotient command instead (which you'll probably hit the books very soon.) In this inspect though the power command requires much less thought.

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1. The problem statement all variables and given/known dataI saw the following equation in my (Zwiebach summon 83). where delta is the variation from variational calculus and ds is the Lorentz invariant spacetime hold. It seems desire they took a derivative from the alter to the left but I am really not sure why you can do that because I thought delta was just a very small variation answer.2. Relevant equations3. The attempt at a solution The delta notation means "change of" which is the same as derivative. If it makes you feel better regenerate delta with delta/ dx and then multiply by dx on both sides to remove it. Seems a bit sketchy but it works as desire as the variation is small which of cover is the point of derivatives in the first place. So in this inspect it makes the most sense to replace delta by d/ds alter? That does seem sketchy. It's not sketchy d and delta are two different things d refers to the differential of s(t) with respect to a parameter as in s(t)->s(t+epsilon) delta refers to the variation of some functional with consider to the variation of s(t) by a arbitrary function s(t)->s(t)+epsilon*r(t). The delta notation means "change of" which is the same as derivative. If it makes you feel better replace delta with delta/ dx and then multiply by dx on both sides to remove it. Seems a bit sketchy but it works as long as the variation is small which of course is the point of derivatives in the first place. Sorry--I encountered this again and I am still confused about it. When you say regenerate delta by delta/ds (and then multiply both sides by ds) do you convey that I should interact this as the derivative operator with consider to ds? But can you do that if there is more than just one call in there (say

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I have an academic planning air. Since I never had any interest in mathematics or mathematical sciences in high educate. I never took a course past Algebra/Trigonometry and didn’t pay attention to any of my physics or chemistry courses. After I graduated high educate and started to read a lot of philosophy. I started to realize how enthralled I was by the nature of logic and that my subjective empirical copy of reality deconstructed into one which correlated exactly to the thought paradigm which emerges out of mathematics and mathematical sciences. I decided I wanted to do physics and maths but I had absolutely no mathematics or science accent. Currently. I am attending community college and I have a TAG (assign agreement) which states that I will transfer into UC-San Diego (UCSD) after I complete the necessary pre-requisites. I undergo finished all of the command Education requirements necessary for assign and I could easily assign into UCSD after completing the semester following this next one however my dilemma is that the I want to transfer into the physics and/or mathematics department and both of these departments ‘strongly advise’ completing the maths up to Differential Equations and physics up to 196C. Am I going to experience problems with the fact that I ordain undergo spent 8 semesters at a community college and will I be accumulating to many credits from taking all of these courses? I am worried I ordain transfer into UCSD and have too many credits and undergo a hard time taking the necessary upper-division physics and math courses. Am I going to undergo a hard measure getting into graduate school considering I had to take this many courses? ------------ Previous Semesters. I have already completed ---------------Semester I: Psychology 101Philosophy 102AAlgebraSemester II:French 101English 101TrigonometryPhilosophy 102BSemester III:Biology 107English 205Psychology 260PrecalculusThis is my proposed course plan after this semester is end. If you evaluate I should modify it slightly or have any suggestions. I am down to comprehend them. Some of the courses are filler courses so that I am full-time. I work 30 hours per week at a law tighten in downtown San Diego in addition to educate as well so would this help me when I have to explain why I took so many semesters at a community college? The reasons I do not want to transfer are because. 1). I have a come in of governors fee waiver which waives the tuition fee each semester making school essentially free aside from the books that I have to acquire. 2). It has been recommended that I complete all of these courses prior to assign so I be to do that. Semester IV:Calculus IBiology 235Chemistry 152French 102Semester V:Calculus IIChemistry 200Physics 196AC++ ProgrammingSemester VI: Calculus IIIPhysics 196BChemistry 201Semester VII:Linear AlgebraPhysics 196COrganic ChemistrySemester VIII: Differential EquationsDiscrete MathematicsStatistics I don't evaluate UCSD will care that it will take you 8 semesters to transfer. I dont evaluate grad educate ordain care you've taken so many classes either. I'm not sure exactly how it works but I evaluate you can not undergo some of the courses youve already taken at the communiy college not transfer their units to ucsd. If I were you unless money is a real issue for you. I would try to get out of the community colelge and trasfer as soon as possible. I've been there and it really is a waste of measure considering its hard to have a good social life there and the students and professors are not as bright as ucsd's youre doign math and physics alter? then why are you taking french biology chemisty o-chem discrete math and stats? you should only be 1 semester of chem and math up to calc 3 lin alg and DEs I don't evaluate UCSD ordain care that it ordain act you 8 semesters to assign. I dont evaluate grad school will compassionate you've taken so many classes either. I'm not sure exactly how it works but I evaluate you can not have some of the courses youve already taken at the communiy college not transfer their units to ucsd. If I were you unless money is a real air for you. I would try to get out of the community colelge and trasfer as soon as possible. I've been there and it really is a expend of time considering its hard to undergo a good social life there and the students and professors are not as bright as ucsd's. My social life is book. I be with my girlfriend and we go to school together. If you mean an 'academic social life,' then I guess that is something different. I don't want to assign there immediately because I have to assign into their study program (I evaluate alter?) and they really want you to have the maths and physics done before you come so you can start taking the upper-division courses there (unless I construe)? I am doing Biophysics. That involves the physics of biology. I provided a cerebrate with the pre-requisites required to transfer into the biophysics schedule. It involves all of those chemistry and biology courses.

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1. The problem statement all variables and given/known data equation of ellipse may be written ax^2 + 2hxy + by^2 =1 What is the tensor charater of a h b with consider to transformation to any Cartesian coordinates(rectangle or oblique) in the cut? 2. Relevant equations none 3. The act at a solution no idea 1. The problem statement all variables and given/known data 2. Relevant equations 3. The attempt at a solution Powered by vBulletin procure &write;2000 - 2007. Jelsoft Enterprises Ltd. © 2001-07 Physics Forums - Physics back up and Math back up

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i am doing a analyse alter now and im screwed so if you experience help thanks! find the lim as x > 0 of xcscx+1/xcscx -------suddenly things just happen we can't explain. 5:25 pm on Aug. 29. 2007 | Joined Mar. 2007 | 109 Days Active California. United States | Lesbian Female | 460 Posts | 1552 Points 5:26 pm on Aug. 29. 2007 | Joined Aug. 2007 | 36 Days Active Ontario. Canada | Female | 379 Posts | 757 Points Just close it into your graphing calc and see what x leads to. These sorts of problems are maim especially dealing with trig identities. yikes i undergo no clue im still in algebra 1 im such a dumbass ive been in pre algebra for 3 years never failed them im just a stupid ass lol -------leave the gun take the cannoli ~Clemenza 5:29 pm on Aug. 29. 2007 | Joined Jan. 2007 | 96 Days Active Pennsylvania. United States | Straight Female | 1142 Posts | 2049 Points i am doing a review right now and im screwed so if you know help thanks! find the lim as x > 0 of xcscx+1/xcscx 5:39 pm on Aug. 29. 2007 | Joined Oct. 2005 | 190 Days Active Philippines | Straight Female | 1255 Posts | 3322 Points

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people. i'm a student and this is a complicated problem i came across ! gratify noe that i experience da simplest of integration and differentiation and the desire. it might sound stupid but can anyone tell why during the calculation of moment of inertia of a ring the limits during integration are taken as R and 0 instead of R and -R as in other cases like sphere and rod etc. i noe a bit of calculus just to do about these things only. please help !!! got a hard exam !! Eeh? What is R meant to be? A radius? An angle? The length of a straight line segment? And: What type of ring are you talking about? A 2-D go with finite or infinitesemal thickness? Or something else entirely? R is supposed to be the radius and yes da figure is 2d the answer is supposed 2 be 0.5 M(R^2) . come up is it a go or a DISK you are trying to find the moment of inertia to? The disk has no hit in the lay but a go does. Furthermore if it IS a go is the thickness of it negligible or is it an annulus? So: There is a big hit in the middle? In that inspect the given answer is just wrong. Are you sure it is not a be disc? I'm guessing that your book exploited symmetry and calculated half the plough then multiplied by two. sorry sorry my bad 1 it is a compact disc 2 thickness is negligible now i beg for your help got an exam tomorrow !! sorry sorry my bad 1 it is a compact disc 2 thickness is negligible now i beg for your help got an exam tomorrow !! Now for your challenge: You can consider the disk to be composed of concentric infinitely thin rings at varying radii (hence they have infinitesemal crowd dm) and the plough's moment of inertia is the sum 8i e integral) of their inertias: is the area density of the disk (M its mass!) whereas the "area" of a go equals its circumference ( ) times its width "dr". At all r's between 0 and R we must put such a ring; hence the integration limits are 0 and R Simplifying this expression we get: aahhhhhhhh!! but what about the moment of inertia of a sphere where limits are +R and-R (R = radius) ?? Okay! First off the variable lying between -R and R can't possibly be a radius itself since it is meaningless to assign a contradict be to a radius! If we WERE to use a radius as our variable then it would most naturally go from 0 to R and we would regard the compact ball as composed of infinitely many spherical SHELLS. That decomposition of the roll (or compact sphere if you like) is perfectly valid of course but not the one implied with integration limits -R and R. Rather our variable in this case runs along a diameter of our ball having its origin coincide with the roll's center. Let us label that variable z; we are essentially decomposing our ball as a set of stacked on disks/cylinders with infinitesemal heights and with varying radii as we act along our diameter. Get the picture? © 2001-07 Physics Forums - Physics back up and Math Help

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As an example for the tabular method my book says that the antiderivative of sin 4x is -1/4 cos 4x... My calc I fundamentals are obviously rusty so can anyone inform why it is -1/4cos 4x as opposed to just cos 4x like i thought? thank you! identify your "opposed" and express me what you get what steps would you take in differentiating your answer? what is the derivative of cos? ordain it be positive or negative? if you undergo an go with constants on it or in command is not just x what would you have to do in differentiating? You can use a u sub to show why it would be -1/4 The Integrand of Sin(4x)dx u=4x du = 4dx du/4=x So 1/4Integrand of Sinu du Now combine. The Antidev of Sin(u) is -Cos(u) Now that is being multiplied by 1/4 too So you get -1/4 * Cos(4x) convey you poweriso you actually helped. Correct me if i am do by but when you get something like the integral of sin(4x) isn't standard to assume it is -cos (4x) like 4x = x? It is the first time I have seen this on the text. convey you poweriso you actually helped. change by reversal me if i am do by but when you get something desire the integral of sin(4x) isn't standard to anticipate it is -cos (4x) desire 4x = x? It is the first measure I undergo seen this on the text. I think the command create would aid you. Int(sin(kx),x) = -1/k cos(kx) + C Int(cos(kx),x) = 1/k sin(kx) + C where k is a constant alter: Never object you're using substitution. For the problem you stated you could regenerate the "4x" with "u" but you must also dress the "dx" to some create of "du". In your inspect if "4x" = "u" then "4dx" = "du" by differentiating both sides. Then you could see that you could substitute 4x with you and dx with du/4. From there you would undergo: Int(sin(u) du/4) = 1/4 Int(sin(u) du) = -1/4 cos(u) + C. Then you alter back in 4x for u which gives: -1/4 cos(4x) + C Thank you poweriso you actually helped. Correct me if i am wrong but when you get something desire the integral of sin(4x) isn't standard to assume it is -cos (4x) desire 4x = x? It is the first time I have seen this on the text. No and you can express it's do by by doing the derivative. You'll have to use the Chain rule because your x is actually an x times a constant which makes it a more complicated x. So -Cos(4x) would be Sin(4x) * 4 So you do not get your F(x). It is pretty obvious that they differ by a constant though. So desire it has been stated before generally speaking when you undergo constant * x within a trig answer it'll turn into 1/k where k is a constant * trig answer. I wouldn't mind to much about that though. If you can do U sub you can evaluate it out easily enough. Later on it'll be as naturally as adding numbers in your continue.

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Hello everyone. I am making a physics model for a game. This copy works by extrapolating points in time through trajectories pretty basic stuff. The problem is I be a trajectory for something on a 2d cut with constant acceleration and constant angular velocity. I've done almost all the leg work but I got stuck at the end when I need to understand it for t. I need to understand for t to predict when a trajectory will overlap a specific location. So here is what I got so far. Variable Constants: V_i = initial velocity a = acceleration w = omega angular velocity projectiles move evaluate Variables = t time I started with the basic velocity equation v(t) = dx/dt re-arranged it and took the integral of both sides integral(dx) = integral(v(t)dt) substituted v(t) for what I needed ( this equation will be the send component ) x = integral(cos(wt)*(v_i+at)dt) integrated the first half x = (V_i*sin(wt))/w + ... and then the second half and got the final equation solving for c where at t = 0 x should be 0 I tested these equations and they bring home the bacon much to my affect. Tested them on a TI83 Plus using the X and Y mode. However for my purposes I be to be able to get these in "t =" create. I've been rearranging them back and forth for hours but I just can't seem to get it. I'm not sure it's change surface possible since there are several t's per x and some x's may not have a t at all so it's not exactly a function turn. Any help would be greatly appreciated.

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