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    A question about dy/dx

    I'm just a little confused about dy/dx. I read that its one entity not a fraction. Can someone please clarify why is this not a fraction? According to what I know (delta y)/(delta x) becomes equal to dy/dx as (delta x) appraches zero. If delta x apparaches to zero then delta y should alway have...
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    Short and simple question

    What exactly is an echelon matrix? I searched the web and did find some useful results but I'm still a little confused. :confused: Thanks in advance for any help. :smile:
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    E-4 Mensuration Question

    Damn I was wrong. You can definitely add the sixth level which makes the no. of max spheres 543. I was making a simple error.
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    E-4 Mensuration Question

    I worked on it and found out that maximum no. of spheres in only possible if they are placed directly on to each other. For this particular problem if the spheres are placed as you have said than there are two possibilities. Either the no. of spheres that can be packed is (81+100+81+100+81)=443...
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    E-4 Mensuration Question

    Well along the width of the base 10 spheres can fit same is the with the lenght of the base. Along the height of the box 5 sphere can fit. So the total no. of spheres is 10x10x5=500 spheres. That's what I think.
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    Estimation of Square roots

    Thanks Integral but I'm still confused... I'm just in 10th grade and I think the method there is for much senior students. Isnt there any simpler form of this method or any other simple method to find it? Any help will be appreciated.
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    Estimation of Square roots

    How can I estimate the value of sqrt. of a particular no. which is not a perfect square(e.g. 125) without using the calculator? Secondly how does the Calculator solve it? Does it use logrithms? If it does how does it solve them?
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    A ridiculous question

    It can be also done like that: By dividing both sides by 'a' we get: x^2+\frac{b}{a}x+\frac{c}{a}=0 Taking the constant term to the right side of the equation and then completing the square. This will give us the following equation...
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    How can I find the coefficient of x^12

    Thanks alot for your reply Matt. I got what you said but I'm still curious to find out how can I find the answer to it by using the method I stated above? I have done many similar questions and I know I have to find the value of r for which the power of x is 12. Is this possible?
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    How can I find the coefficient of x^12

    How can I find the coefficient of x^12 in: (2+x)^{14}(1+ \frac{2}{x})^{14} I did it like that: (2+x)^{14}(1+ \frac{2}{x})^{14} Can be written as: (4+ \frac{4+x^2}{x})^{14} Now the term T_{r+1} can be represented as: 14C_r (4)^{14-r}(\frac{4+x^2}{x})^r (How can I write 14Cr?) Dont...
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    Log base 4 64 without using a calculator

    Hes right. log_4 64 = log_4 4^3 = 3log_4 4 = 3(1) = 3
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