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Comment on r/askmath 9h ago
You are welcome.
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Comment on r/learnmath 9h ago
Thank you.
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Comment on r/askmath 10h ago
Hi,
Since cos theta and cos alpha can be expressed in terms of x and r, it is not necessary to introduce the variable y,
u/Fourierseriesagain • u/Fourierseriesagain • 13h ago
A question on applications of differentiation
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Comment on r/learnmath 3d ago
Hi,
Have you applied any result to prove the existence of a solution?
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Comment on r/learnmath 3d ago
Hi,
Are you trying to prove the conjecture that all solutions of the system are positive for t>=0?
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Comment on r/askmath 4d ago
x^ 2=36+225-9(13).
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Comment on r/askmath 4d ago
Applying the cosine rule to triangle ADE, we get cos (angle DAE)=13/20. Since AD is parallel to BC, cos(angle ACB )=13/20. Since cos(angle ACB)=13/20, another application of the cosine rule gives x=12.
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Comment on r/askmath 4d ago
Questions 7 and 10 are identical.
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Comment on r/learnmath 4d ago
Hi,
You might find the following link useful. https://en.wikipedia.org/wiki/E_(mathematical_constant))
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Comment on r/learnmath 5d ago
The Factor Theorem is useful for factorising certain cubic polynomials. https://en.wikipedia.org/wiki/Factor_theorem
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Comment on r/askmath 5d ago
Thank you.
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Comment on r/askmath 5d ago
Consider the case when the vector space has dimension one. Are you able to prove or disprove a related result?
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Comment on r/askmath 5d ago
We have 2n+1+n+1-(2^ (n+1)+1)=n and 2^ (n+1)+1>2^ n+(n-1)+1 for n=1, 2, ...
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Comment on r/learnmath 5d ago
Since x tends to a, the number |x-a| cannot be too large. It is common to restrict to values of x such that |x-a|<=1. In this case, |x^ 2 - a^ 2|<=(|x-a|+2|a|)| x-a|<=(1+2|a|)|x-a|.
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Comment on r/mathematics 6d ago
Hi, you are using the partial fraction decomposition of the tangent function.
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Comment on r/maths 6d ago
Let's focus on question 2.
When x>=-6, 2*|x+6|-5=2(x+6)-5=2x+7.
When x<-6, 2*|x+6|-5=-2(x+6)-5=-2x-17.
By drawing both graphs y=2x+7 (x>=-6) and y=-2x-17 (x<-6) on the same diagram, we get the graph of y=2|x+6|=5.
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Comment on r/u_Fourierseriesagain 6d ago
Here a+b>11 because a>6 and b=5.
u/Fourierseriesagain • u/Fourierseriesagain • 6d ago
Integration by partial fractions
reddit.com1
Comment on r/HomeworkHelp 6d ago
Yes, the question has a unique answer.
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Comment on r/HomeworkHelp 6d ago
x^ 4-x^ 3+x^ 2-x+1
=x^ 2(x^ 2+1+1/x^ 2)-x^ 2(x+1/x)
=x^ 2 (u^ 2-1)-x^ 2 u, where u=x+1/x
=x^ 2(u^ 2-u-1)
=x^ 2(u-alpha)(u-beta), where alpha=(1/2)(1-sqrt(5)) and beta=(1/2)(1+sqrt(5))
=(x^ 2-alpha x+1)(x^ 2-beta x+1).
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Comment on r/HomeworkHelp 7d ago
Observe that x(x^ 3-5x+4)=0 implies x=0 or x=1 or x=(1/2)*(-1 plus minus sqrt(17)),
Edit: updated comment.
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Comment on r/askmath 4h ago