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IgorLugansk [536]
2 years ago
13

Find the term to term rules for 2,6,18,54,162

Mathematics
1 answer:
faltersainse [42]2 years ago
4 0

Answer:

a, ax3 =b, bx3= c , cx3=d, dx3=e

Step-by-step explanation:

2, 2×3=6, 6x3=18,18 x3 =54, 54x3= 162

Multiplication of three with previous number will give you next number in series.

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A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and
goldfiish [28.3K]

Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of

(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min

and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

\dfrac{\mathrm dS(t)}{\mathrm dt}=\dfrac8{100}-\dfrac{S(t)}{800}

Solve for S(t):

\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}

e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}

The left side is the derivative of a product:

\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}

Integrate both sides:

e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt

e^{t/800}S(t)=64e^{t/800}+C

S(t)=64+Ce^{-t/800}

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

0=64+C\impleis C=-64

and so (b) the amount of sugar in the tank at time t is

S(t)=64\left(1-e^{-t/800}\right)

As t\to\infty, the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

7 0
3 years ago
Simplify 3 to the power of 1
lina2011 [118]

3 to the power of 1 simplified, is just 3.

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3 years ago
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statuscvo [17]
I believe that x=4 would be the answer
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Mrac [35]

Answer:

97 + 312 = 409

409 is not divisible by 90.

There must be a mistake in the question.

7 0
3 years ago
WHO CAN HELP ME !!!!!!! PLEASE FINNA CRY RN​
Taya2010 [7]

Answer:

In the other polygon which is smaller you just half the size of the larger one like 12 became 5 and 6 became 3 so 14 will also be halved and the answer will be

7

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2 years ago
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