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Ilya [14]
2 years ago
8

Kiera already has 12 plants in her backyard and she can also grow 1 plant with every seed packet she uses. How many seed packets

does Kiera need to have a total of 24 plants in her backyard?
Mathematics
1 answer:
Elza [17]2 years ago
7 0

Answer: 12

Step-by-step explanation: 24 - 12 times 1

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Find the solution r(t)r(t) of the differential equation with the given initial condition: r′(t)=⟨sin9t,sin6t,9t⟩,r(0)=⟨4,6,3⟩
klemol [59]

\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


\dfrac19\cos0+C_1=4\implies C_1=\dfrac{35}9

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

\dfrac92\cdot0^2+C_3=3\implies C_3=3


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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Im not sure what to do here or how to start for AP calculus
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hope this help you with your question~~~~

love


meowlover

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