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maksim [4K]
2 years ago
10

Find the 10th term, 18, 72,288,...

Mathematics
1 answer:
dusya [7]2 years ago
6 0

Step-by-step explanation:

a = 18

n = 10 th term

difference (d) = 72-10 = 62

an ( n th term ) = a + (n-1)d

a10 ( 10 th term = 18 + (10-1)62

= 18 + 9×62

= 18 + 558

10 the term = 576

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The graph shows the solution to the initial value problem y'(t)=mt, y(t0)= -4
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y'(t)=mt
\\
\\ y=\int {mt} \, dt=m \int{t} \,dt=m \frac{t^2}{2} +C \\ \\y= \frac{mt^2}{2}+C

Now find equation of the graph. It passes through the point (2,3), and intersects y-axis at -2.

y=at^2+b
\\
\\3=a\times 2^2-2
\\
\\3=4a-2
\\
\\5=4a
\\
\\a= \frac{5}{4} 
\\
\\y=\frac{5}{4} t^2-2 \\ \\y= \frac{m}{2} t^2+C
\\ \\  \frac{m}{2} = \frac{5}{4} 
\\
\\m= \frac{5}{2} 
\\
\\C=-2
\\
\\y(t_0)=-4
\\
\\-4= \frac{5}{4} t_0^2-2
\\
\\ -2= \frac{5}{4} t_0^2
\\
\\ t_0^2=- \frac{8}{5} 
\\
\\t_0=\pm \sqrt{- \frac{8}{5} }



3 0
3 years ago
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Answer:

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