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cluponka [151]
3 years ago
8

Yanni read 24 pages of

Mathematics
2 answers:
Marianna [84]3 years ago
6 0

Answer:

di gun0ifulgwuytid5

Step-by-step explanation:

DJ e57

lukranit [14]3 years ago
5 0

Answer:

36 pages

Step-by-step explanation:

If one third of the book is left to read until completion, then Yanni has read two thirds of the book so far.

24 pages is equal to two thirds, so one third will be half of this; 12 pages.

The whole book is three thirds, so 12 * 3, which is 36 pages

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y'=(t+y)^2-1

Substitute u=t+y, so that u'=y', and

u'=u^2-1

which is separable as

\dfrac{u'}{u^2-1}=1

Integrate both sides with respect to t. For the integral on the left, first split into partial fractions:

\dfrac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)=1

\displaystyle\int\frac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm dt=\int\mathrm dt

\dfrac12(\ln|u-1|-\ln|u+1|)=t+C

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\dfrac12\ln\left|\dfrac{u-1}{u+1}\right|=t+C

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\dfrac2{u+1}=1-Ce^{2t}

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Replace u and solve for y:

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y=\dfrac2{1-Ce^{2t}}-1-t

Now use the given initial condition to solve for C:

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so that the particular solution is

y=\dfrac2{1-\frac34e^{2t-6}}-1-t=\boxed{\dfrac8{4-3e^{2t-6}}-1-t}

3 0
3 years ago
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Answer:

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