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3 years ago

Which of the following is NOT an arithmetic sequence?

Mathematics

1 answer:

Alex787 [66]3 years ago

3 0

The sequence that is NOT arithmetic would be 2,4,8,16,32 it's an exponential sequence not an arithmetic

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g Suppose that the populationy(t)of a certain kind of fish is given by the logistic modely′= 3y−2y2(a) Solve the Bernoulli equat

Ksju [112]

Answer:

y = $\frac{3}{2 + 3Ce^{-3t} }$

Step-by-step explanation:

As given , y' = 3y - 2y²

⇒y' - 3y = -2y²

Divide by y² in the above equation

⇒ $\frac{y'}{y^{2} } - \frac{3y}{y^{2} } = -\frac{2y^{2} }{y^{2} }$

⇒ $\frac{y'}{y^{2} } - \frac{3}{y } = -2$ ........(1)

Now , let $\frac{1}{y}$ = u

⇒- $\frac{1}{y^{2} } \frac{dy}{dt} = \frac{du}{dt}$

⇒- $\frac{1}{y^{2} }y' = \frac{du}{dt}$

∴ equation (1) becomes

- $\frac{du}{dt}$ - 3u = -2

⇒ $\frac{du}{dt}$ + 3u = 2

It is a linear differential equation

Now,

Integrating factor = I.F = $e^{\int\limits {3} \, dt }$ = $e^{3t}$

∴ The solution becomes

u.(I.F) = $\int\limits {2.(I.F)} \, dt$ + C

⇒u.( $e^{3t}$ ) = $\int\limits {2.(e^{3t} )} \, dt$ + C

⇒u.( $e^{3t}$ ) = $\frac{2e^{3t} }{3}$ + C

⇒u = $\frac{2}{3} + Ce^{-3t}$

As $\frac{1}{y}$ = u

⇒ $\frac{1}{y}$ = $\frac{2}{3} + Ce^{-3t}$

⇒ y = $\frac{1}{\frac{2}{3} + Ce^{-3t} } = \frac{3}{2 + 3Ce^{-3t} }$

⇒ y = $\frac{3}{2 + 3Ce^{-3t} }$

6 0

3 years ago

What is the probability of throwing 2 dice and getting the sum of 12?

Natasha_Volkova [10]

Answer:

1/36

Step-by-step explanation:

P(6,6) = 1/6 x 1/6 = 1/36

4 0

3 years ago

A. A cylinder just fits into a cube of side length 36 m Calculate the percentage

Nataliya [291]

Answer:

21.5%

Step-by-step explanation:

volume of cube: 36x36x36

volume of cylinder: πx18²x36

Cylinder percentage: (πx18²x36) / 36x36x36 = π / 4 = 0.785

percentage of empty space: 1 - 0.785 = 0.215 (21.5%)

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3 years ago

What is the simplified form of (3x + 2)(4x – 3)? Use a table.

ch4aika [34]

Answer:

Step-by-step explanation:

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3 years ago

9:39 PM A truck travels on a highway at a speed of 66 miles per hour. What is the speed of the truck in feet per second? Round y

Paul [167]

Answer:

$96.8\frac{feet}{second}$

Step-by-step explanation:

Remember that

$1\ mile =5,280\ feet$

To convert miles to feet multiply by 5,280

$1\ hour =3,600\ sec$

To convert hours to seconds multiply by 3,600

we have

$66\frac{miles}{hour}$

convert to feet per second

$66\frac{miles}{hour}=66(\frac{5,280}{3,600})=96.8\frac{feet}{second}$

7 0

3 years ago