A kite is flying 70 feet above the ground and is attached to a string tied to a stake on the ground. The angle of elevation form
1 answer:
If you draw a diagram of this, your given values of the resulting triangle give you the sides opposite and adjacent of the angle. The formula that uses these sides is tangent.
The tangent of an angle is equal to the ratio of the opposite side over the other non-hypotenuse side (adjacent).
Therefore;
Where x is the length of the string in feet.
The tangent of an angle is equal to the ratio of the opposite side over the other non-hypotenuse side (adjacent).
Therefore;
Where x is the length of the string in feet.
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Answer:
a)
b)
Step-by-step explanation:
The first step to solve this question is finding the roots of the derivative of x.
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots such that
, given by the following formulas:
In this question:
So
Finding the roots:
Simplifying by -3
So
Then
So the function can be divided in three intervals.
They are:
Less than -1
Between -1 and 5
Higher than 5
In which it increases and which it decreases?
Less than -1
Lets find the derivative in a point in this interval, for example, -2
Positive.
So in the interval of , the function increases.
Between -1 and 5
Will choose 0.
Negative.
So in the interval of , the function decreases.
Higher than 5
Will choose 6.
Positive
So in the interval of , the function increases.
(a) Find the interval on which f is increasing.
Using interval notation
b) Find the interval on which f is decreasing.