Given that triangle ABC is right angle triangle. CD is altitude such that AD=BC
ABC is a right angle triangle so apply Pythogorean theorem
(Given that AD = BC)
(Given that AB=3)
...(i)
ADC is a right angle triangle so apply Pythogorean theorem
...(ii)
Plug value (ii) into (i)
Hence final answer is
Piecewise Function is like multiple functions with a speific/given domain in one set, or three in one for easier understanding, perhaps.
To evaluate the function, we have to check which value to evalue and which domain is fit or perfect for the three functions.
Since we want to evaluate x = -8 and x = 4. That means x^2 cannot be used because the given domain is less than -8 and 4. For the cube root of x, the domain is given from -8 to 1. That meand we can substitute x = -8 in the cube root function because the cube root contains -8 in domain but can't substitute x = 4 in since it doesn't contain 4 in domain.
Last is the constant function where x ≥ 1. We can substitute x = 4 because it is contained in domain.
Therefore:
The nth root of a can contain negative number only if n is an odd number.
Answer
(1) The train travels 4 miles per gallon.
(2) The slope of the graph is
Explanation:
(1) The miles that train travels per gallon is given by
Dividing, we have,
Thus, the train travels 4 miles per gallon.
(2) To determine the slope, let us consider two points from the graph.
The coordinates are and
Thus, substituting the coordinates in the slope formula, we get,
Simplifying, we have,
Thus, the slope of the graph is