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Assoli18 [71]
3 years ago
10

What is the surface area of this triangular prism

Mathematics
1 answer:
const2013 [10]3 years ago
6 0
The perimeter of the triangular end is 12 m, so the total rectangular area is
.. (12 m)*(8 m) = 96 m^2

There are two triangles with base 3 m and height 4 m, so their total area is
.. (3 m)*(4 m) = 12 m^2

The surface area of the figure is the sum of these 
.. 96 m^2 +12 m^2 = 108 m^2
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The population of a certain species of insect is given by a differentiable function P, where P(t) is the number of insects in th
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Answer:

\frac{dP}{dt} \ =\  \frac{1}{5}P

Step-by-step explanation:

Given

Variation: Directly Proportional

Insects = 10 million when Rate = 2 million

i.e. P = 10\ million when \frac{dP}{dt} = 2\ million

Required

Determine the differential equation for the scenario

The variation can be represented as:

\frac{dP}{dt} \ \alpha\ P

Which means that the rate at which the insects increase with time is directly proportional to the number of insects

Convert to equation

\frac{dP}{dt} \ =\ k * P

\frac{dP}{dt} \ =\ kP

Substitute values for \frac{dP}{dt} and P

2\ million = k * 10\ million

Make k the subject

k = \frac{2\ million}{10\ million}

k = \frac{2}{10}

k = \frac{1}{5}

Substitute \frac{1}{5} for k in \frac{dP}{dt} \ =\ k * P

\frac{dP}{dt} \ =\  \frac{1}{5}* P

\frac{dP}{dt} \ =\  \frac{1}{5}P

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