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3 years ago

Distance between(-3,-5) and (-4,6)

Mathematics

1 answer:

Citrus2011 [14]3 years ago

4 0

Just use the distance formula.. (-3 - -4)squared + (-5 - 6)squared

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One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the populatio

kenny6666 [7]

Answer:

Therefore , $y= \frac{Ae^{kt}}{1+Ae^{kt} }$

Step-by-step explanation:

The fraction of population who have heard rumor = y

The fraction of population who haven't heard rumor = 1-y

The rate of of spread (y'(t)) is proportional to the product of the fraction of population who have heard rumor the fraction of population who have heard rumor.

Therefore

y'(t) ∝ y (1-y)

⇒ y'(t) =k y (1-y) [ k = constant of proportional]

$\Rightarrow \frac{dy}{dt}=ky(1-y)$

$\Rightarrow \frac{dy}{y(1-y)}=k \ dt$

Integrating both sides

$\Rightarrow \int\frac{dy}{y(1-y)}=\int k \ dt$

$\Rightarrow \int \frac{dy}{y}+\int\frac{dy}{1-y}=\int k \ dt$ $[\because \frac{1}{y(1-y}=\frac{1}{y}+\frac{1}{1-y} ]$

$\Rightarrow ln \ y- ln \ |1-y| = kt +c$ [ c = arbitrary constant]

$\Rightarrow ln|\frac{y}{1-y}|=kt +c$

$\Rightarrow \frac{y}{1-y}= e^{kt+c}$

$\Rightarrow \frac{y}{1-y}= Ae^{kt}$ [ Here $e^c=A$ ]

$\Rightarrow y = Ae^{kt}(1-y)$

$\Rightarrow y = Ae^{kt}-y Ae^{kt}$

$\Rightarrow y+y Ae^{kt} = Ae^{kt}$

$\Rightarrow y(1+Ae^{kt} )= Ae^{kt}$

$\Rightarrow y= \frac{Ae^{kt}}{1+Ae^{kt} }$

Therefore , $y= \frac{Ae^{kt}}{1+Ae^{kt} }$

5 0

3 years ago

When h is one-half and j is one-third, g is 4. if g varies jointly with h and j, what is the value of g when h is 2 and j is 3?

Effectus [21]

The value of g = 144 solved by using direct proportion.

<h3>What is a direct proportion?</h3>

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol, ∝.

Given that,

h = $\frac{1}{2}$ , j = $\frac{1}{3}$ , g = 4