Use the information in the diagram to determine the height of the tree to the nearest foot.
1 answer:
Answer:
The correct option is A. The height of tree is 60 ft.
Step-by-step explanation:
From the given figure it is noticed that the building is creating a right angle triangle from a point and the tree divides the hypotenuse and base in two equal part.
According to midpoint theorem of triangle: In a triangle, if a line segment connecting the midpoints of two sides, then the line is parallel to third side. The length of line segment is half of the length of third side.
Using midpoint theorem of triangle, we can say that the length of tree is half of the building.
Therefore correct option is A. The height of tree is 60 ft.
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1. As you can tell from the function definition and plot, there's a discontinuity at x = -2. But in the limit from either side of x = -2, f(x) is approaching the value at the empty circle:
Basically, since x is approaching -2, we are talking about values of x such x ≠ 2. Then we can compute the limit by taking the expression from the definition of f(x) using that x ≠ 2.
2. f(x) is continuous at x = -1, so the limit can be computed directly again:
3. Using the same reasoning as in (1), the limit would be the value of f(x) at the empty circle in the graph. So
4. Your answer is correct; the limit doesn't exist because there is a jump discontinuity. f(x) approaches two different values depending on which direction x is approaching 2.
5. It's a bit difficult to see, but it looks like x is approaching 2 from above/from the right, in which case
When x approaches 2 from above, we assume x > 2. And according to the plot, we have f(x) = 0 whenever x > 2.
6. It should be rather clear from the plot that
because sin(x) + 3 is continuous at x = 0. On the other hand, the limit at infinity doesn't exist because sin(x) oscillates between -1 and 1 forever, never landing on a single finite value.
For 7-8, divide through each term by the largest power of x in the expression:
7. Divide through by x². Every remaining rational term will converge to 0.
8. Divide through by x² again:
9. Factorize the numerator and denominator. Then bearing in mind that "x is approaching 6" means x ≠ 6, we can cancel a factor of x - 6:
10. Factorize the numerator and simplify:
where the last equality holds because x is approaching +∞, so we can assume x ≠ -1. Then the limit is
Answer:
and
Step-by-step explanation:
Blue:
The inequality for the blue line is
Yellow
The inequality for the yellow line is
This means that the correct answer is the third option,
and