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    Proportionality of triangles problem

    proportionality x1/x2=y1/y2
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    Proportionality of triangles problem

    the curve is a parabola
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    Proportionality of triangles problem

    Homework Statement Is any formulas similar to that of proportionality of the triangles to proportionality of the given figure? Homework Equations The Attempt at a Solution
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    Factoring methods with equations higher than second degree

    Can I know what method you used? and teach me to solve this kind of equations?
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    Factoring methods with equations higher than second degree

    when i used synthetic division, -1 is not a root of that equation. why should I divide the polynomial by x+1?
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    Factoring methods with equations higher than second degree

    an example: how can you factor x^3 - 2x^2 + 10x + 7 = 0 It cannot be factored using synthetic division.
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    Factoring methods with equations higher than second degree

    so what should I do if the the given cannot be factored by synthetic division? I already encountered one in differential equations and I do not know what to do.
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    Factoring methods with equations higher than second degree

    Homework Statement Can someone tell what are the other factoring methods when dealing with equations higher than the second degree. The only I is the synthetic division. Aside from that, I do not know anything. I need other factoring methods so I can deal with problems that cannot be...
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    Help with 2 integrals

    Factor first the denominator then use the partial fractions.
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    Integral of trigonometric functions

    Homework Statement How can I integrate this: \int sin (nt) sin (n \pi t) dt This actually in the Fourier series.
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    The Fourier Series

    Can 2n+1 be 2n-1 provided that n=1 to infinity? How can I know if the function can be converted in some form?
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    The Fourier Series

    Homework Statement f(x) = 1 0<t<1 = -1 1<t<2 How can I simplify this given that function(on the attachment). What I mean is that how can I write the function in any other way? In addition, How can I know if the function can be written in other form? How can I...
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    Summation with infinity

    Homework Statement what is the summation of a function where n=1 to n=infinity? For example, given a function sin[(pi)nt]. Homework Equations The Attempt at a Solution I asking how I get that I do not know what should I do
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    Fundamental Period (graph)

    ok so how I prove by mathematical statement that the period f is 2? can this be or it can only be proved by graph?
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    Fundamental Period (graph)

    thats what i am saying. f(t+2) =f(t) is given. what im trying to prove is that if k is not equal to zero, the period f is 2. how i should i plot the 1+kt?
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    Fundamental Period (graph)

    Homework Statement The elements of f(t) are 1+kt and t here are 0<t<1 the other element is 1 and t here are 1<t<2. f(t+2)=f(t) prove if k is not equal to zero, the period f is 2. i know the graph of element 1 but how should I graph the other element with k. Based from the graph...
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    The Fundamental Period

    is my last post correct?
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    The Fundamental Period

    without using the listing of multiples, will this work? lets say, find the LCM of pi/2 and 3pi/4 Using LCD pi/2 becomes 2pi/4 and 3pi/4 is still 3pi/4 By multiplying 2 and 3, it becomes 6 Then the LCM is 6pi/4 or 3pi/2
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    The Fundamental Period

    Am i correct? the multiples of pi/2 are pi/2, pi, 3pi/2, 2pi.... the multiples of 3pi/4 are 3pi/4, 3pi/2,9pi/4... so the LCM is 3pi/2.
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    The Fundamental Period

    a mistake. it should be pi/2 and 3pi/4 is 3pi/2 there LCM.
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    The Fundamental Period

    Im talking about his last post, pi/2 and 3pi/2, how it became 3pi/2. All I know about LCM is it for whole number just like the LCM of 3,5,and 15 is 30. For fraction, it is LCD.
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    The Fundamental Period

    how do I can solve for the LCM if the given is fraction?
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    The Fundamental Period

    what should I do?
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    The Fundamental Period

    how about if the function comes in many terms? for example: 1+cost+cos2t Will I get the larger period among them or use the LCM? if LCM, how do I do that?
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    The Fundamental Period

    oh i see... so you regroup the 5t+2pi+pi into (5t+pi)+2pi? how about if you dont regroup it?
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    The Fundamental Period

    so 2p will only be added to t since the part 5t determines the period? ok i understand what you said thanks...
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    The Fundamental Period

    where does pi/5 came from? what do I do to the 2pi/5 period?
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    The Fundamental Period

    Homework Statement The function is defined on (-infinity, +infinity) Find the fundamental period of sin(5t+\pi) Homework Equations The Attempt at a Solution f(x)=sin(5t+\pi) f(x)=f(x+2p) f(x+2p)=sin(5t+\pi+2p) f(x+2\pi/5)=sin(5t+\pi+2\pi/5) The period i got was...
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    Integrate dy/dx

    yes its ln but I type In. Sorry.
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    Arc Length

    ok. I do not see that. Just a u-substitution.
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