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kumpel [21]
2 years ago
9

In a movie theater, the first row contains 3 seats, the second row contains 6 seats, the third row contains 9 seats, and the fou

rth row contains 12 seats.
A.) Write explicit rule for sequence
B.) Write recursive rule for sequence.
Mathematics
1 answer:
yanalaym [24]2 years ago
7 0

Answer:It's an arithmetic sequence with a common difference, d, = 4

A1 = 8

A2 = 8+4 = 12

A3 = 12+4 = 16   = 8+4(3-1) = 8+4(2) = 8+8

AN = A1 + d(N-1)

AN = 8 +4(N-1)  =  the Nth term in the sequence

Step-by-step explanation: hoped it helped

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Put the equation in standard linear form.

x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}

Find the integrating factor.

\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5

Multiply both sides by \mu.

(t+5) x'(t) + x(t) = 5(t+5)e^{5t}

Now the left side the derivative of a product,

\bigg((t+5) x(t)\bigg)' = 5(t+5)e^{5t}

Integrate both sides.

(t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt

On the right side, integrate by parts.

(t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C

Solve for x(t).

\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}

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2 years ago
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garri49 [273]

Answer:

110

Step-by-step explanation:

8x10=80

Area of triangle= 1/2 base times height

3x10=30

80+30=110

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