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ser-zykov [4K]
3 years ago
11

rosy has 16 pencils and 24 erasers. she is putting together packets that will have an equal number of pencils and erasers in eac

h packet. If rosy uses all of the pencils and erasers, what’d the max number of packets she can make?
Mathematics
1 answer:
faust18 [17]3 years ago
4 0

Answer:48

Step-by-step explanation: you were indirectly asked for the L.C. M of 16 and 24

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\mathbf r'(t)=\langle\sin9t,\sin6t,9t\rangle


\mathbf r(t)=\displaystyle\int\mathbf r'(t)\,\mathrm dt


\mathbf r(t)=\left\langle\displaystyle\int\sin9t\,\mathrm dt,\int\sin6t\,\mathrm dt,\int9t\,\mathrm dt\right\rangle


\displaystyle\int\sin9t\,\mathrm dt=\frac19\cos9t+C_1

\displaystyle\int\sin6t\,\mathrm dt=\frac16\cos6t+C_2

\displaystyle\int9t\,\mathrm dt=\frac92t^2+C_3


With the initial condition \mathbf r(0)=\langle4,6,3\rangle, we find


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\dfrac16\cos0+C_2=6\implies C_2=\dfrac{35}6

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So the particular solution to the IVP is


\mathbf r(t)=\left\langle\dfrac19\cos9t+\dfrac{35}9,\dfrac16\cos6t+\dfrac{35}6,\dfrac92t^2+3\right\rangle

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Step-by-step explanation:

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