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timofeeve [1]
3 years ago
5

SERIOUS MATH HELP PLEAZE SHOW WORK OR AN EXPLANATION HELPPPPPPPPPPPP

Mathematics
1 answer:
Natali5045456 [20]3 years ago
4 0

Answer:

x=3

Step-by-step explanation:

x^2 = 6x - 9

Subtract 6x from each side

x^2 -6x = -9

Add 9 to each side

x^2 -6x+9 = 0

Factor  

what 2 numbers multiply to 9 and add to -6

-3*-3 = 9

-3+-3 =-6

(x-3)(x-3) = 0

Using the zero product property

x-3 =0    x-3=0

x=3 with multiplicity 2

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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

4 0
3 years ago
Izzys dog is 10 1/2 years old. Car end dog is 18 months old. How many years older is Izzys dog.
dsp73
12 months in a year. So 18 months= 1 year and 6 months. Izzys dog is 10 1/2= 10 years and six months. Then subtract 1 year and 6 months by 10 year and six months and it would be exactly 9 years older.
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PLease answer as soon as possible
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Answer:

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