3 years ago

The square root of 68 is between what two consecutive whole numbers

Mathematics

1 answer:

Pavel [41]3 years ago

4 0

The two consecutive numbers are 8 and 9.

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Solve the separable differential equation dtdx=x2+164 and find the particular solution satisfying the initial condition x(0)=9

maria [59]

$\dfrac{dt}{dx} = x^2 + \frac{1}{64} \Rightarrow\ dt = \left(x^2 + \frac{1}{64}\right)dx \Rightarrow \\ \\ \displaystyle \int 1 dt = \int \left(x^2 + \frac{1}{64}\right)dx \Rightarrow \\ t = \dfrac{x^3}{3} + \frac{x}{64} + C$

C = 9 because all the x terms go away.

$t = \dfrac{x^3}{3} + \dfrac{x}{64} + 9$