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2 years ago

Solve for B -(12 x 2) x (-6) = -12 x (2 x b) A. -6 B. 6 C. -12 D. 12

Mathematics

1 answer:

myrzilka [38]2 years ago

5 0

Answer:

Option A

Step-by-step explanation:

-(12 x 2) x (-6) = -12 x (2 x b)

=> -24 x -6 = -12 x 2b

=> 144 = -24b

=> b = -6

Hoped this helped.

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The population of a suburb grows at a rate proportional to the population. Suppose the population doubles in size from 3000 to 6

frozen [14]

Answer:

$P(t) = 3000e^{0.1155t}$

Step-by-step explanation:

The growth of the population can be modeled by the following differential equation:

$\frac{dP}{dt} = rP$

Where r is the growth rate, P is the population, and t is the time measures in months.

I am going to solve the above differential equation with the separation of variables method.

$\frac{dP}{P} = rdt$

Integrating both sides:

$ln P = rt + P(0)$

Where P(0) is the initial condition

We need to isolate P in this equation, so we do this

$e^{ln P} = e^{rt + P(0)}$

$P(t) = P(0)e^{rt}$

The problem states that P(0)=3000, so:

$P(t) = 3000e^{rt}$

The problem wants us to find the value of r:

It states that the population doubles in size from 3000 to 6000 in a 6- month period, meaning that P(6) = 6000. So

$6000 = 3000e^{6r}$

$e^{6r} = 2$

To isolate 6r, we apply ln to both sides.

$ln (e^{6r}) = ln 2$

$6r = 0.693$

$r = \frac{0.693}{6}$

r = 0.1155

The particular solution to the differential equation with the initial condition P(0)=3000 is:

$P(t) = 3000e^{0.1155t}$

5 0

3 years ago

Determine the value of r so that a line through the points (r,3) and (5,-4) has a slope of -1/2

CaHeK987 [17]

$\bf (\stackrel{x_1}{r}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-4-3}{5-r}=\stackrel{\stackrel{slope}{\downarrow }}{-\cfrac{1}{2}}\implies \cfrac{-7}{5-r}=\cfrac{1}{-2} \\\\\\ 14=5-r\implies 9=r$