Answer: The height of the tree is 21 feet.
Step-by-step explanation:
Here we can assume that the angle at which the sun impacts the photographer and the tree to be the same angle.
Then we can think in both cases as triangles rectangles, where the height is a cathetus, and the shadow is the other cathetus.
Then we will have a relationship like:
Tg(angle) = shadow/height
height = shadow/Tg(angle)
Now, because for both triangles we have the same angle, then Tg(angle) will be the same number for both cases, and we can just think of it as constant K
Tg(angle) = K
Then we have the equation:
Height = Shadow/K
We know that the photographer is 6ft tall, and his shadow is 2 ft long, we can replace those two things in the above equation and find the value of k:
6ft = 2ft/K
K = 2ft/6ft = (1/3)
Now we know that the shadow of the tree is 7ft long, then the height will be:
height = 7ft/(1/3) = 7ft*3 = 21ft
The tree is 21 ft tall.
Answer:
110
Step-by-step explanation:
Alright, imma help you. Imma work on it on a piece of paper. :D
Answer:
The answer is "
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Step-by-step explanation:
Please find the complete question in the attached file.
Calculating the difference of 
dividing the value by 
Answer:
x = {nπ -π/4, (4nπ -π)/16}
Step-by-step explanation:
It can be helpful to make use of the identities for angle sums and differences to rewrite the sum:
cos(3x) +sin(5x) = cos(4x -x) +sin(4x +x)
= cos(4x)cos(x) +sin(4x)sin(x) +sin(4x)cos(x) +cos(4x)sin(x)
= sin(x)(sin(4x) +cos(4x)) +cos(x)(sin(4x) +cos(4x))
= (sin(x) +cos(x))·(sin(4x) +cos(4x))
Each of the sums in this product is of the same form, so each can be simplified using the identity ...
sin(x) +cos(x) = √2·sin(x +π/4)
Then the given equation can be rewritten as ...
cos(3x) +sin(5x) = 0
2·sin(x +π/4)·sin(4x +π/4) = 0
Of course sin(x) = 0 for x = n·π, so these factors are zero when ...
sin(x +π/4) = 0 ⇒ x = nπ -π/4
sin(4x +π/4) = 0 ⇒ x = (nπ -π/4)/4 = (4nπ -π)/16
The solutions are ...
x ∈ {(n-1)π/4, (4n-1)π/16} . . . . . for any integer n
