A teacher writes the function f(x)=3x^2-18x+27 on the board. How many times does the graph of the teacher's function intersect t
1 answer:
Answer:
Once. at (3,0)
Step-by-step explanation:
It is handy to have a graphing calculator for this kind of question.
Otherwise work it out.
All the terms are multiples of 3, so simplify.
then factor (x -3)(x-3)
Set each equal to 0 and solve for x.
x - 3 = 0 x = 3
OH ! they are identical! So there is only One value for x that will produce an output of 0.
So it intersects (touches) only once.
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The bird is 17 feet above the tree.
<u>Explanation:</u>
We need to think of this in terms of right triangles. If Wendy is 60 feet from a tree, the base of the right triangle is 60 feet. The height of the tree is the height of the right triangle. The angle of elevation is the one from the ground at her feet to the top of the tree and then to the bird. Let's start with the top of the tree first.
She's 60 feet away, we have the angle of elevation as 25 degrees, and we are looking for the height of the tree. In regards to the angle, the base of 60 is adjacent, and the height of the tree is opposite. The tangent ratio is height / base.
Let x be the height of the tree.
So,
x is approximately 28 feet
Since, Wendy's eyes are 5 feet above the ground, the height of the tree becomes
28 + 5 = 33 feet
<u>For bird</u>
Let y be the height of the bird in the air
y is approximately 45 feet
Since, Wendy's eyes are 5 feet above the ground, the height of the tree becomes
45 + 5 = 50 feet
To know how far above the tree that bird is
50 - 33 = 17 feet
Therefore, the bird is 17 feet above the tree.
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