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soldi70 [24.7K]
3 years ago
5

What is the value of 5(a + b) when a=1 and b=6 ​

Mathematics
1 answer:
lana [24]3 years ago
5 0

Answer: 35

Step-by-step explanation:

We substitute a for 1 and b for 6.

5(1+6)=5(7)=35

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The rate of change of the number of mountain lions N(t) in a population is directly proportional to 725 - N(t), where t is the t
wolverine [178]

Answer:

a) The implied differential equation is \frac{dN}{725 - N} = kdt

b) The general equation is N = 725 - C e^{-kt}

c) The particular equation is N = 725 - 325 e^{-0.49t}

d) The population when t = 5, N(5) = 697 = 700( to the nearest 50)

Step-by-step explanation:

The rate of change of N(t) can be written as dN/dt

According to the question, \frac{dN}{dt} \alpha (725 - N(t))

\frac{dN}{dt} = k (725 - N)\\\frac{dN}{725 - N} = kdt

Integrating both sides of the equation

\int {\frac{1 }{725 - N}} \, dN  = \int {k} \, dt\\- ln (725 - N) = kt + C\\ ln (725 - N) = -(kt + C)\\725 - N = e^{-(kt + C)} \\725 - N = e^{-kt} * e^{-C} \\725 - N = C e^{-kt}\\N = 725 - C e^{-kt}

When t = 0, N = 400

400 = 725 - C e^{-k*0}\\400 = 725 - C\\C = 725 - 400\\C = 325

When t = 3,  N = 650

650 = 725 - (325 * e^{-3k})\\325 * e^{-3k} = 75\\e^{-3k} = 75/325\\e^{-3k} = 0.23\\-3k = ln 0.23\\-3k = -1.47\\k = 1.47/3\\k = 0.49

The equation for the population becomes:

N = 725 - 325 e^{-0.49t}

At t = 5, the population becomes:

N = 725 - 325 e^{-0.49*5}\\N = 725 - 325 e^{-2.45}\\N = 696.95\\N(5) = 697

N(5) = 700 ( to the nearest 50)

6 0
3 years ago
What is 76 to the 3rd power
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Answer:

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Step-by-step explanation:

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2 years ago
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Fynjy0 [20]
You need 16 more terms not 17 because you already have 4 terms in the series so if you add those 4 terms to the other 16 terms to the series you get a total of 20 terms in total. I hope this helped.
7 0
3 years ago
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nataly862011 [7]
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3 years ago
What is the simplest form <br><br> 3/4 + 2/5
maw [93]

Answer:

1  3/20

Step-by-step explanation:

3/4 + 2/5

Get a common denominator of 20

3/4 *5/5  + 2/5 *4/4

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