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Answer: The sailboat is at a distance of 15 km from the port.
Step-by-step explanation: Given that a sail boat leaves port and sails 12 kilometers west and then 9 kilometers north.
We are to find the distance between the sailboat from the port in kilometers.
Since the directions west and north are at right-angles, we can visualize the movement of the sailboat in the form of a right-angled triangle as shown in the attached figure.
The sailboat moves leaves the port at P and reach O after sailing 12 km west. From point O, again it moves towards north 9 km and reach the point S.
PS = ?
Using the Pythagoras theorem, we have from right-angled triangle SOP,
Thus, the sailboat is at a distance of 15 km from the port.
Answer:
1)
Minimum is a 4th Degree
2)
Positive; Even
3)
Step-by-step explanation:
Part 1)
The minimum degree of our function will be 4.
Looking at the graph, we know that the graph crosses the x-axis at -4 and -1. Since it <em>crosses through</em> the x-axis at these two points, these two factors must have an odd multiplicity.
So, it can be anything 1, 3, 5, 7, etc.
However, we will choose the lowest one, 1.
Next, we know that the graph <em>bounces off</em> at 3.
So, it must have an even multiplicity. In other words, 2, 4, 6, 8, etc.
We choose the lowest one, 2.
Therefore, the minimum degree of our function will be 1+1+2 or 4.
Part 2)
The degree of our polynomial is (and will always be) even. Therefore, both ends of the graph will go in the same direction.
Recall the simplest even polynomial, the parent quadratic function. When the leading coefficient is positive, both of the ends go straight up.
This applies to all polynomials with even degrees.
Therefore, since the arms of the graph is going straight up towards positive infinity, the leading coefficient of our graph must be positive.
Part 3)
This is similar to Part 1.
We can see that the graph touches the x-axis at -4, -3, and 1. So, the zeros of the function is:
We know that it<em> passes through</em> . So, these two factors must have an odd multiplicity.
However, since the graph <em>bounces off</em> , this factor must have an even multiplicity.
And we're done!