Recent content by AmritpalS

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    High School Other ways of expressing a derivative.

    dy/dx=2√y ? not exactly sure what you're asking..
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    How Many Integers Meet the Condition {√n - √(23×24)}² < 1?

    Notice that the square root of 23x24 is approximately the square root of 23 squared. Since asked about only integers, this approximation suffices
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    Improper Integral Solution Check: Is Your Answer Accurate?

    I meant completing the square so that the denominator is (v+1)^2 -4. Multiply by -1/-1 and you have -dv/(4-(v+1)^2) which fits the rule ∫du/(a^2-u^2)=1/2a(ln (a+u/a-u)+c
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    Improper Integral Solution Check: Is Your Answer Accurate?

    if I'm not mistaken u= (v+1) is pretty easy and it ends up fitting the arctanh rule. Seems that it'll involve an inverse hyperbolic function
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    Is the Nobel Prize Truly the Pinnacle of Achievement?

    The Nobel prize doesn't necessarily recognize the "best" in a particular field. It gives recognition to a particular scientist that has accomplished something of a high magnitude which deserves recognition.
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    Undergrad Is it possible to integrate x^2*e^(x^2)?

    Like stated above, the first expression, when integrated, will probably result in an imaginary error function in terms of a "function" for the anti-derivative. The second one is easy. ∫x(ex)dx u=x2 du=2xdx 1/2∫eudu =(1/2)eu+c =(1/2)ex2+c P.S: @HallsofIvy i love your signature
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    Initial value problem with y(0)=C

    (y^3)*(dy/dx)=(8y^4+14)*cos(x) (y^3)/(8y^4+14)dy=cos(x)dx ∫y3/(8y4+14)dy=∫cos(x)dx through integrating (did it quickly so you might want to recheck) (1/32)ln(8y4+14)+c=sin(x)+c ln(8y4+14)=32sin(x)+c 8y4+14=e32sin(x)+c solve from there substitute c for y as u did and o for x...
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    Need help with half-life of C-14 question (exponents unit)

    no what I am trying to say is the function is equal to 16/8 which is 2.. you see c(t) is the mass after a certain time period. the question asks you for the time given the c(t) value which is 1/8 the original amount
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    Need help with half-life of C-14 question (exponents unit)

    You got the wrong idea. The initial condition is a constant. Since it says the original mass is 16g, that will be your initial mass. 1/8 of the 16grams is c(t) so c(t)=16(1/8) put that into the formula: 16(1/8)= 16(1/2)^(t/H) and solve for t C(t) is the mass after a time has passed. If 16grams...
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    Confused about +- symbol use in inverse function

    ±√2 that is
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    Velocity under constant acceleration

    no finger trouble is on me
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    Velocity under constant acceleration

    sorry about that i plugged it into my calculator on radian mode. Should have just done it in my head. It is 12m/s sorry about that i guys
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    Velocity under constant acceleration

    the solution i got is 10m/s if anyone else can verify
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    Velocity under constant acceleration

    The initial velocity is what you are looking. It's not zero. the equation you want to use is ymax=((Vo^2)sin^2(theta))/2g i believe
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    Confused about +- symbol use in inverse function

    indeed it does