Help with pre algebra
2 answers:
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Answer:
A
Step-by-step explanation:
We are given a right triangle with a base of <em>x</em> feet and a height of <em>h</em> feet, where <em>x</em> is constant and <em>h</em> changes with respect to time <em>t</em>.
The angle in radians is defined by:
And we want to find the relationship that describes dθ/dt and dh/dt.
So, we will differentiate both sides with respect to <em>t</em> where <em>x</em> is a constant:
Differentiate. Apply the chain rule on the left. Again, remember that <em>x</em> is just a constant, so we can move it outside the derivative operator. Therefore:
Since we know that tan(θ)=h/x, <em>h</em> is the opposite side of our triangle and <em>x</em> is the adjacent. Therefore, by the Pythagorean Theorem, our hypotenuse will be:
Since secant is the ratio of the hypotenuse to adjacent:
So:
By substitution, we have:
By multiplying both sides by the reciprocal of the term on the left:
Therefore:
Our answer is A.