2. A tree casts a shadow 25m long. At the same time, a signpost next
1 answer:
Answer:
The height of the tree is 14.85 m
Step-by-step explanation:
The length of the shadow cast by the tree = 25 m
The length of the shadow cast by the signpost = 6 m
The height of the signpost = 3.5 m
Therefore, by similar triangles, we have;
Let θ, represent the angle formed by the line extending a line from the tip of the shadow, to the tip of the object and let x represent the height of the tree, we have
Tan(θ) = Opposite/Adjacent = Height of the object/(The length of the shadow)
∴ Tan(θ) = 3.5/6 = x/25
x = 25 × 3.5/6 = 14.58
The height of the tree = x = 14.85 m
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9514 1404 393
Answer:
(A) -7
Step-by-step explanation:
The function is continuous if you can draw its graph without lifting your pencil. In this case, that means each of the piecewise function definitions must have the same value at x=3.
x^2 +2 = 6x +k . . . . . must be true at x=3
3^2 +2 = 6(3) +k . . . . substitute 3 for x
9 +2 -18 = k . . . . . . . . subtract 18
k = -7 . . . . . . . simplify
