What is the nth term to: 27,25,23,21,19
2 answers:
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Answer:
The proportion that can be used to estimate the height of the tree is option;
A.
Step-by-step explanation:
The given parameters in the question are;
The medium through which the person looks at the top of the tree = A mirror
The angle formed by the person and the tree with the ground = Right angles = 90°
The distance of the person from the mirror, d₁ = 5 ft.
The height of the person, h₁ = 6 ft.
The distance of the tree from the mirror, d₂ = 12 ft.
The angle formed by the incident light from the tree on the mirror, θ₁ = The angle of the reflected light from the mirror to the person, θ₂
Let 'A', 'B', 'M', 'T', and 'R' represent the location of the point at the top of the person's head, the location of the point at the person's feet, the location of the mirror, the location of the top of the tree and the location of the root collar of the tree, we have;
TR in ΔMRT = The height of the tree = h, and right triangles ΔABM and ΔMRT are similar
The corresponding legs are;
The height of the person and the height of the tree, which are AB = 6 ft. and TR = h, respectively
The distances of the person and the tree from the mirror, which are BM = 5 ft. and MR = 12 ft. respectively
∴ The angle formed by the incident light from the tree on the mirror, θ₁ = ∠TMR
The angle of the reflected light from the mirror to the person, θ₂ = ∠AMB
Given that θ₁ = θ₂, we have;
tan(θ₁) = tan(θ₂)
∴ tan(∠TMR) = tan(∠AMB)
From tan(∠TMR) = tan(∠AMB), we have;
The height of the tree, h = 14.4 ft.
Therefore, from the proportion the height of the tree can be estimated.
<h3>Answer: 14 feet</h3>
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Explanation:
Check out the diagrams below.
We'll start with the left diagram (marked "before") which is a right triangle with the horizontal leg of 25 feet and hypotenuse 65 feet.
Use the pythagorean theorem to find the vertical side x.
a^2 + b^2 = c^2
25^2 + x^2 = 65^2
625 + x^2 = 4225
x^2 = 4225 - 625
x^2 = 3600
x = sqrt(3600)
x = 60
The top of the ladder is 60 feet high when placed against the wall in this configuration.
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If the upper end is moved down 8 feet, then x-8 = 60-8 = 52 feet is the new height of the ladder. Refer to the "after" in the diagram below.
Like earlier, we'll use the pythagorean theorem to find the missing side.
a^2 + b^2 = c^2
y^2 + 52^2 = 65^2
y^2 + 2704 = 4225
y^2 = 4225 - 2704
y^2 = 1521
y = sqrt(1521)
y = 39
The horizontal distance from the ladder base to the wall is now 39 feet.
Earlier it was 25 feet, so it has increased by 39-25 = 14 feet.
The proportion that Alexandra can use to find r is 9 cups of water and 4 cups of dry rice
If Alexandra uses 12 cups of water and 6 cups of dry rice to make 18 cups of cooked rice, this can be expressed as:
To get the proportion "r" for the amount of dry rice to use to make 4 cups of cooked rice, we can write:
Divide both expressions:
Hence the proportion that Alexandra can use to find r is 9 cups of water and 4 cups of dry rice
Learn more on proportions here: brainly.com/question/19994681