mm-2219 === Subject: Intergration I am faced with a brick wall. i have an equation that i need to intergrate. However i am not able to do one step of it. i was wondering if anyone would be able to help. the equation is sin(1.570796327x-1.570796327) However i do not understand how to intergrate the 1.570796327x term. i realise that the intergral of sin is -cos but i do not know how this particular term. Any help would be greatly appreciated Kate -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Intergration Kate (kate@uq.net.au) requested help integrating: : sin(1.570796327x-1.570796327) : I do not understand how to intergrate the 1.570796327x term. : I realise that the integral of sin is -cos Excellent. You know that the Integral of Sin(x)dx is -Cos(x)+C or the Integral of Sin(y)dy is -Cos(y)+C or the Integral of Sin(z)dz is -Cos(z)+C etc. A technique called Integration by Substitution is helpful. Try to simplify the Integral of Sin(1.570796327x-1.570796327)dx by substituting y=1.570796327x-1.570796327. (Attempt to turn it into something you DO know how to do.) Of course, you cannot just replace 'dx' with 'dy'. NOT Equal!! But you CAN calculate their ratio: dy/dx = ?? (Differentiate!) So, replacing 'dx' with the appropriate multiple of 'dy', you will get a multiple of the Integral of Sin(y)dy which you CAN do! After integrating, substitute '1.570796327x-1.570796327' for the 'y' to get an answer in terms of 'x'. Done. Robert |)|/| || Burnaby South Secondary School || |orewood@olc.ubc.ca || Beautiful British Columbia Mathematics & Computer Science || (Canada) -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Intergration > I am faced with a brick wall. i have an equation that i need to intergrate. > However i am not able to do one step of it. i was wondering if anyone would > be able to help. > the equation is > sin(1.570796327x-1.570796327) That's not an equation, BTW, since it contains no = sign. Also, the decimal expression 1.570796327 is a approximation of pi/2 to 10 digits. Are you sure you're not supposed to be using pi/2 instead of this approximation? I'll just use pi/2 and if you're sure of your decimal expression just continue using that in place of my pi/2 in the following. Also, you should have dx in there (variable of integration) and some sort of integration operator. Many use INT on newsgroups. Anyway, integration is all about pattern recognition... INT sin(u)du = -cos(u) + C ...basic integration rule, or pattern You have: INT sin[(pi/2)x-(pi/2)] dx ...and you try to make this fit the pattern You can let u = (pi/2)x - (pi/2), then du/dx = pi/2 du = (pi/2)dx You have the dx factor of du there already. You need an additional factor of pi/2 to complete du (since du=(pi/2)dx). Other than this one exception (a missing factor of pi/2) you have fit the expression to the desired pattern. Pi/2 is a constant, and remember constants can freely move in and out of integrals. So multiply the integrand by pi/2, which gives you what you need to complete the pattern. Don't forget to divide by pi/2 (ie multiply by 2/pi) outside the integral to keep things balanced. IOW, you are multiplying the entire expression by 1 in the convenient form (pi/2)(2/pi), then using an integral property to move the factor of pi/2 inside the integral. So, (2/pi) * INT sin(u) du ...and now you can apply the basic integration rule. Moral--don't leave out your dx. It's quite important, especially when doing a u du substitution like this. You need to be able to determine what du corresponds to a particular u and whether or not you have it all there already, or need to do something creative to *get* it there. Multiplying and dividing by constants is one of those creative things--probably the simplest such thing) you will have to do. -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Intergration Wouldn't it be -(1/1.570796327) cos(1.570796327x-1.570796327) since (d/dx) cos (ax+b) = - a sin(ax+b) so int (sin(ax+b)) = -(1/a) cos (ax+b) Maybe you have not come to this topic in your calculus course yet. > I am faced with a brick wall. i have an equation that i need to intergrate. > However i am not able to do one step of it. i was wondering if anyone would > be able to help. > the equation is > sin(1.570796327x-1.570796327) > However i do not understand how to intergrate the 1.570796327x term. i > realise that the intergral of sin is -cos but i do not know how this > particular term. > Any help would be greatly appreciated > Kate -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Precalculus:A Graphing Approach 4ed. This fall, I will be teaching Precalculus using Demana's (to be exact: Demana, Waits, Clemens, Foley) Precalculus:A Graphing Approach 4ed. My HS does not have the complete Teacher's Resource package. In particular, we don't have the Solutions Manual. I have done without before, but it would be nice to have it. The publisher, alas, does not have any more. I have looked on the www without success. I am hoping someone on the AP Calculus list has a extra, or has moved on to a new Precalculus book, and therefore has no further need. I would, naturally, pay for a copy. used or new, I am indifferent. I would be most appreciative. Please contact me directly (samtrpt@aol.com.) to spare everyone on the list the specific details. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: examview Has anyone had any experience with test making software named ExamView? The feature list on the web site (www.examview.com) is impressive and the price seems reasonable. Any opinions you can offer - good or bad - would be appreciated. p -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: How would you solve this? === Subject: How would you solve this? Author: Indra If Anthony gives 30% of his money to Brandon, they will have the same amount of money. And, if Anthony gives $250 to Brandon, Brandon will have 20% more money than Anthony. How mush does Anthony have at the beginning? This question was given to 12 yr olds in Singapore. Best to Follow the money Assume they are using rupees (R) Anthony Brandon 100R 40R 100R- 30R 40R + 30R , or 70R 70R They now have the same. 70R -$250 70R + $250 (=1.2(70R -$250) = 84R - $300) 70R + $250 = 84R -$300 So, to get from 70R to 84R we need $550 Or, 14R = $550 which implies 100R is $3928.57 (Anthony's orig amount) Gary Tupper, Terrace BC - I have assumed the transactions are sequential. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: finding a number from a fraction of a whole number trying to configure ram settings on a computer.need to know how to -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: finding a number from a fraction of a whole number That would be 10. 166 but not 160. 1/10 of 166 is 16.6. > trying to configure ram settings on a computer.need to know how to -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: finding a number from a fraction of a whole number To find 1/16, simply divide by 16. 60 /16 = 10 SFS >trying to configure ram settings on a computer.need to know how to -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: finding a number from a fraction of a whole number >trying to configure ram settings on a computer.need to know how to We used to say, using a computer? No math background? That doesn't make sense! Age has nothing to do with it; but things change. Far less math background is needed to use a computer these days. You want 1/16 of 160; Divide 160 by 16, or, if you start with 160, how many times can you scoop out 16 until you have nothing left to scoop out? G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Inscribed circles in equliteral triangle > I don't know how to solve this problem. > In an equilateral triangle (a triangle were lenght of all sides are equal) > there are inscribed three circles which touch (tangent) each other. > The radii of circles is 3.0 cm. > How long are the sides of the triangle? Draw the picture. Add line segments from the circle centers to the sides of the triangle. Also connect the centers of the circles. Figure out the length of each piece the side is cut up into using trigonometry or what you know about rectangles. You'll probably need to use the fact that a redius of a circle is at right angles to a tangent to the circle. -- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Help us with this word problem!!!!! The fifth grades has 335 students, and the sixth grades has 264 students. All classes are the same size. What is the number of students in each class? Be Sure to show your work and label all parts. Now give me break what to do? Doesn't divide equally? Trick? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Help us with this word problem!!!!! >The fifth grades has 335 students, and the sixth grades has 264 >students. All classes are the same size. What is the number of >students in each class? Be Sure to show your work and label all >parts. >Now give me break what to do? Doesn't divide equally? Trick? If I understand the problem correctly, you are looking for a common factor of 335 and 264, presumably the greatest common factor. Since we can't split a student into a fractional part, we need only be concerned with whole number factors. Factors of 335 are 1, 5, 67, and 335. (You could have 1 class of 335 students, 5 classes of 67 students, 67 classes of 5 students, or 335 classes of 1 student each.) 264 has a larger list of factors: 1, 2, 3, 4, 6, 11, 12, 22, 24, 44, 66, 88, 132, and 264. (1 class of 264, 2 classes of 132, etc...) The only common factor for 335 and 264 seems to be 1, so as unlikely as it seems, the answer could only be that every class in the 5th and 6th grades has only 1 student. Possibilities: The problem was meant to make you realize that there are no common factors other than 1, the problem was copied down incorrectly, or perhaps I'm not understanding the wording? SFS -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Re: Inscribed circles in equilateral triangle I'd suggest you but yourself 3 rulers and 3 tennis balls, and try to picture what's going on. Then make a drawing where you connect the radii of the circles, and try to relate them to what you know about the angles and sides of the triangle. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Subject: Mental Calculation Game You can test your students or adults on their mental calculation very challenging. jamsportland -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html