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EleoNora [17]
3 years ago
7

What is the value of cosΘ given that (-2, -3) is a point on the terminal side of Θ?

Mathematics
1 answer:
Alona [7]3 years ago
3 0
<u>Answer</u>
-3/√13

<u>Explanation</u>
We are going to take angle ∅ to be at the origin (point (0,0)). 
The point at (-2, -3) means, 2 units to the left (negative side of x-axis) and 3 units downwards (negative side of y-xis). 
This will make a right triangle with a hypotenuse of √(2²+3²) = √13

The angle ∅ is in the 3rd quadrant where cosine is negative. 

cosine = adjacent/hypotenuse

The exact answer for cos ∅ = -2/√13
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Answer:

\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})

Step-by-step explanation:

The logistic differential equation is as follows:

\frac{dP}{dt} = rP(1 - \frac{P}{K})

In this problem, we have that:

K = 1200, which is the carring capacity of the population, that is, the maximum number of people allowed on the beach.

At 10 A.M., the number of people on the beach is 200 and is increasing at the rate of 400 per hour.

This means that \frac{dP}{dt} = 400 when P = 200. With this, we can find r, that is, the growth rate,

So

\frac{dP}{dt} = rP(1 - \frac{P}{K})

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166.67r = 400

r = 2.4

So the differential equation is:

\frac{dP}{dt} = rP(1 - \frac{P}{K})

\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})

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3 years ago
What is <br> 7w(-8 + 3w) and <br> 6q(-4 + 8q)
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If you are looking to simplify these equations, here is how you would go about doing so.

7w(-8+3w)

Use a property called the Distributive Property, which means multiplying the number outside of the bracket by each number inside of the brackets.

Here is how this would look:

7w(-8+3w)

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Now,

6q(-4+8q)

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Hope this helps.

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