Answer:
Below, you can see the graph of the function:
f(x) = x + cos(k*x)
for different values of k, as follows:
red: k = 1
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.
Look at the picture.
1)|AM| = |MB| = x
|AN| = |NC| = y
|BC| = 2y - 2x = 2(y - x)
|MN| = y - x
Therefore |BC| = 2|MN|
2)|AM| = |MB| = x
|AN| = |NC| = y
|BC| = 2y - 2x = 2(y - x)
|MN| = y - x
Therefore |BC| = 2|MN|
The answers would be (0,10) , (20,0) , and (100,100)
Answer:
(x, y) ⇒ (-x, y)
Step-by-step explanation:
When you're looking for a rule that transforms one figure to the other, the first step is to look at the figures. You want to identify their orientation (order of vertices) and the relative locations of corresponding vertices.
Here, vertices VWX are in <em>clockwise</em> order. The corresponding vertices V'W'X' are in <em>counterclockwise</em> order. For that to happen, there must be a reflection involved.
The y-axis goes through the midpoints of VV', WW' and XX'. This means the y-axis is the line of reflection. The coordinates of V'W'X' have the same y-values as their originals, but their x-values have changed sign.
The algebraic rule for these two figures is ...
(x, y) ⇒ (-x, y) . . . . . . reflection over y-axis; sign of x changes
__
<em>Additional comment</em>
No rotation is involved here.
The rule (x, y) ⇒ (x, y+10) means the y-coordinate has had 10 added to it. That causes a translation upward by 10 units. This <em>is</em> the algebraic rule.
Assuming the keypad has all 26 letters and the numbers 1-9 there are 2106 possible codes
9x9x26=2106
