Dante runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes?
1 answer:
<h2>Answer: 2.8 miles</h2>
Step-by-step:
We can write it in the proportion
where x is our number of miles trying to find
We now cross multiply or use the butterfly method which I will demonstrate both
<h3>Cross Multiply</h3>We multiply the numerator with the dominator
so
and
or
Now for the
<h3>Butterfly Method </h3>You would do 7 times 24 divided by 60 or
Then simplify
so 2.8 miles in either method
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Answer:
The correct option is;
Step-by-step explanation:
The given information is that m(x) = x² - 17·x
The above equation can be written in the form;
y = x² - 17·x
Therefore;
0 = x² - 17·x - y
From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;
By comparison to the equation,0 = x² - 17·x - y, we have;
a = 1, b = -17, and c = -y
Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;
Which can be simplified as follows;
And further simplified as follows;
Interchanging x and y in the function of the inverse, m⁻¹(x), we have;
We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;
m'(x) = 2·x - 17 = 0
x = 17/2
Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;
m''(x) = 2 > 0, therefore, the point is a minimum point on the graph
Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;
to increase m⁻¹(x) above the minimum.