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3 years ago

3. A regular hexagon has six equilateral triangles with a common

Mathematics

1 answer:

hichkok12 [17]3 years ago

8 0

Answer:

if the height of the triangle is 8 in, its side is 9.2379, and this side is also the side of the hexagon, so the perimeter is 6*9.2379 = 55.43 in

Step-by-step explanation:

As the hexagon is regular, each of those triangles will also be regular.

So if the height of one triangle is 8 inches, we can find the side of the triangle with the height formula of a regular triangle:

height = side * sqrt(3)/2

8 = side * 0.866

side = 8/0.866 = 9.2379

The side of the triangle will also be the side of the hexagon. So the perimeter of the hexagon will be:

P = 6 * 9.2379 = 55.43 inches

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During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

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

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

7 0

3 years ago

There are 60 minutes in an hour. The total number of minutes is a function of the number of hours, as shown in the table. Does t

Alexxx [7]

Answer:

Step-by-step explanation:

It represents a linear function because there is a constant rate of change.

Step-by-step explanation:

Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.

Here, number of hours represents input value and minutes represents the output value,

Now, By the given table,

The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),

Also,

⇒ The rate of change output value with respect to input value remains constant,

Hence, It represents a linear function because there is a constant rate of change.

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2 years ago

Find the slope of line a and line b from two points

Degger [83]

Answer: Line A has a slope of 3/4 and Line B has a slope of 5/6

Step-by-step explanation: Look at the attachment

5 0

3 years ago

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Triangles H J K and L M N are congruent. Triangle H J K is rotated about point H to form triangle L N M. Triangle L M N is highe

Alex

Answer:

a rotation about point H

Step-by-step explanation:

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3 years ago

Read 2 more answers

Does anyone know these answers??

densk [106]

The angles of a triangle always add up to 180°.

By simply adding the angles and checking the total, you can tell if they make a triangle or not.

Using this property, 5 won't make a triangle, 6 will.

Hope this helps! :D

7 0

3 years ago