The area of a square is 15.1 unit squared. Estimate the length of the sites. Explain how you estimate it?
1 answer:
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Answer:
Step-by-step explanation:
The domain of all polynomials is all real numbers. To find the range, let's solve that quadratic for its vertex. We will do this by completing the square. To begin, set the quadratic equal to 0 and then move the -10 over by addition. The first rule is that the leading coefficient has to be a 1; ours is a 2 so we factor it out. That gives us:
The second rule is to take half the linear term, square it, and add it to both sides. Our linear term is 2 (from the -2x). Half of 2 is 1, and 1 squared is 1. So we add 1 into the parenthesis on the left. BUT we cannot ignore the 2 sitting out front of the parenthesis. It is a multiplier. That means that we didn't just add in a 1, we added in a 2 * 1 = 2. So we add 2 to the right as well, giving us now:
The reason we complete the square (other than as a means of factoring) is to get a quadratic into vertex form. Completing the square gives us a perfect square binomial on the left.
and on the right we will just add 10 and 2:
Now we move the 12 back over by subtracting and set the quadratic back to equal y:
From this vertex form we can see that the vertex of the parabola sits at (1,-12). This tells us that the absolute lowest point of the parabola (since it is positive it opens upwards) is -12. Therefore, the range is R={y|y ≥ -12}
Answer:
The distance of the helicopter from the bristol is approximately 1<u>2.81 miles</u>
Step-by-step explanation:
Given:
Helicopter flies 10 miles east of bristol.
Then the helicopter flies 8 miles North before landing.
To find the direct distance between the helicopter and bristol.
Solution:
In order to find the distance of the helicopter from the bristol before landing, we will trace the path of the helicopter
The helicopter is first heading 10 miles east of bristol and then going 8 miles due north.
On tracing the path of the helicopter we find that the direct distance of the helicopter from the bristol is the hypotenuse of a right triangle formed by enclosing the path of the helicopter.
Applying Pythagorean theorem to find the hypotenuse of the triangle.
Taking square root both sides.
Thus, the distance of the helicopter from the bristol is approximately 12.81 miles
