A lookout tower is 16 meters tall. Its shadow is 12 meters long. Close by, there is a wooden column that is 4 meters tall. How l
ong is the wooden column's shadow?
Write your answer as a whole number or a decimal. Do not round.
Write your answer as a whole number or a decimal. Do not round.
1 answer:
Answer:
3 metres
Step-by-step explanation:
If we draw this out, we'll see that there are actually two similar right triangles (see attachment), which means that we can set up a proportion.
The height of the lookout tower corresponds to the height of the wooden column, while the shadow of the lookout tower corresponds to the shadow of the wooden column. We can then write:
(height of lookout tower) / (shadow of tower) = (height of column) / (shadow of column)
16 / 12 = 4 / x , where x is the shadow / unknown we want to find
Cross-multiply:
16x = 48
x = 3
The answer is thus 3 metres.
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The linear inequality of the graph is: -x + 2y + 1 > 0
<h3>How to determine the linear inequality?</h3>First, we calculate the slope of the dashed line using:
Two points on the graph are:
(1, 0) and (3, 1)
The slope (m) is:
This gives
m = 0.5
The equation of the line is calculated as:
So, we have;
This gives
Multiply through by 2
Now, we convert the equation to an inequality.
The line on the graph is a dashed line. This means that the inequality is either > or <.
Also, the upper region of the graph that is shaded means that the inequality is >.
So, the equation becomes
2y > x - 1
Rewrite as:
-x + 2y + 1 > 0
So, the linear inequality is: -x + 2y + 1 > 0
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<u>Complete question</u>
Find a linear inequality with the following solution set. Each grid line represents one unit. (Give your answer in the form ax+by+c>0 or ax+by+c 0 where a, b, and c are integers with no common factor greater than 1.)
