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3 years ago

Rewrite this exponential equation as a logarithmic equation.

Mathematics

1 answer:

Mekhanik [1.2K]3 years ago

3 0

Answer:

Step-by-step explanation:

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Nastasia [14]

Answer:

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Step-by-step explanation:

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7 0

3 years ago

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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

Use Pythagorean theorem to find the missing length. (round to tenth if necessary) IS

sertanlavr [38]

11.7

Formula: a^2 + b^2 = c^2

so substitute the numbers like this:

10^2 + 6^2 = c^2

both 10^2 and 6^2 are perfect squares:

10 × 10= 100 and 6 × 6= 36

100 + 36= c^2

add:

100 + 36 =

136 = c^2

now in order to get rid of the squared, you put it into a radical:

√136 = √c^2

note: whatever you do on one side, you do to the other

it's easier to use the calculator for this so put √136 and you're gonna get 11.66

since it's asking you to round it to the nearest tenth:

11.66 = 11.7

sorry if the explanation is kinda long ✋ i tried explaining it better in the end but i failed

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3 years ago

ANSWER THESE ASAP Carla got a ride from her mom to school on 13 of 20 school days in November. Which is NOT equivalent to the fr

Artyom0805 [142]

question 1: 35%

question 2: 0.23

question 3: 9/20

question 4: 1,360 mL

question 5: 1,994 yds

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3 years ago

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horsena [70]

For the Jet one the answer should be 450 but its not on there

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3 years ago