A swimmer would be able to swim across a 25-meter pool in about 1/5 of a minute.How fast can a swimmer go
1 answer:
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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.
Answer:
(0, 7)
Step-by-step explanation:
The point that crosses the y-axis is called the y-intercept of the line.
We are given an equation of the line and we need to determine the y-intercept. This can be done by determining the constant in the equation.
What are constants?
Constants are such terms that include only numbers. There should be no variables in constants.
<u>We know that:</u>
The constant we can see in the equation is "7". Therefore, the y-intercept is 7.
Note: The y-intercept of the line must have an x-coordinate of 0.
<u>Therefore,</u>
⇒ Coordinates of y-intercept: (x, y) ==> (0, 7).