Answer:
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Step-by-step explanation:
The height of tree is 8 feet
<h3><u>Solution:</u></h3>
Given, Micah places a mirror on the ground 24 feet from the base of a tree
At that point, Micah's eyes are 6 feet above the ground
And he is 9 feet from the image in the mirror.
To find : height of tree = ?
Let "n" be the height of tree
From the question, we can see there is a directly proportional relationship between heights and distances.
Proportional relationships are relationships between two variables where their ratios are equivalent.


Hence, the height of the tree is 8 feet
Answer:
Width = 12 feet
Step-by-step explanation:
Given that,
Area of a rectangle is 168 square feet.
The ratio of the width to the length is 6:7.
Let the length is 7x and width is 6x.
According to question,
Area = 168 sq feet
l×b=168 sq feet
7x × 6x = 168
42x² = 168
x² = 4
x = 2
Length = 7x = 7(2) = 14 feet
Breadth = 6x = 6(2) = 12 feet
So, the width of the rectangle us 12 feet.
Let

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

So, the base case is ok. Now, we need to assume
and prove
.
states that

Since we're assuming
, we can substitute the sum of the first n terms with their expression:

Which terminates the proof, since we showed that

as required