Absolute value of any number is always positive because it represent distance and distance will always positive.
To place chimney at least 30 feet , the distance along the width of the roof (x) will be x = 17.5 feet or x = 2.5 feet.
Since, The height of the roof is described by the function f(x)=−4/3|x−10| + 40
Since, minimum height is 30 feet.
So , substitute f(x)=30 in above expression.
30=−4/3|x−10| + 40
4/3|x−10| = 10
|x−10|=30/4
|x−10| = 7.5
Taking positive case,
x−10 = 7.5
x = 17.5 feet
Taking negative case,
x−10 = - 7.5
x = 10 - 7.5
x = 2.5 feet
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<h3>
Answer: 5 < x < 21</h3>
Explanation:
Let x be the length of the third side. We can't find the exact value of x, as we don't have enough info, but we can find possible values for x.
The lower boundary for x is 13-8 = 5. It must be larger than this value.
At the same time, x must be smaller than 13+8 = 21 as well.
So x > 5 and x < 21 becomes 5 < x < 21
In short, x is between 5 and 21. It cannot equal either endpoint.
