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aalyn [17]
3 years ago
6

In the diagram below, AC is perpendicular to BD. Find the value of N.

Mathematics
1 answer:
timurjin [86]3 years ago
8 0
Hi there!

In order to find the value of N, we'll need to set the value of the angle containing the variable n equal to 90. This is because in perpendicular lines, all angles are equal to 90.

WORK:
5n - 25 = 90
5n = 115
n = 23
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Answer:

Below, you can see the graph of the function:

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green: k = 2

orange: k = 0.

Now let's find the values of k such that our function does not have local maxima nor local minima.

First, remember that for a given function f(x), the local maxima or minima points are related to the zeros of the first derivate of f(x).

This means that if:

f'(x0) = 0.

Then x0 is a maxima, minima or an inflection point.

Then if a function is such that the f'(x) ≠ 0 , ∀x, then this function will not have local maxima nor minima.

Now we have:

f(x) = x + cos(k*x)

then:

f'(x) = 1  - k*sin(k*x)

This function will be zero when:

1 = k*sin(k*x)

1/k = sin(k*x)

now, remember that -1 ≤ sin(θ) ≤ 1

then if 1/k is smaller than -1, or larger than 1, we will not have zeros.

And this will happen if -1 < k < 1.

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Answer:  see below

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2) When determining the equation of a hyperbola you need the following:

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3) The equation of a hyperbola is:

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