Y ≥ |x+2| + 5, solve in a graph
2 answers:
Answer: see the graph in the figure attached.
Explanation:
1) To solve graphically, draw the function |x + 2| + 5 and shade the region above the two lines.
You can see that graph in the figure attached.
2) You can figure out th is solution by solving the inequality in two parts.
i) First part, take x + 2 ≥ 0
⇒ y ≥ x + 2 + 5
⇒ y ≥ x + 7
Therefore, draw the line y = x + 7 and shade the region above the line.
ii) Second part, take x + 2 < 0 ⇒ | x + 2| = - x - 2
⇒ y ≥ - x - 2 + 5
⇒ y ≥ - x + 3
Therefore, draw the line y = - x + 3 and shade the region above the line.
4) The solution is the intersection of the two shaded regions, which is the one shown in the graph attached.
Explanation:
1) To solve graphically, draw the function |x + 2| + 5 and shade the region above the two lines.
You can see that graph in the figure attached.
2) You can figure out th is solution by solving the inequality in two parts.
i) First part, take x + 2 ≥ 0
⇒ y ≥ x + 2 + 5
⇒ y ≥ x + 7
Therefore, draw the line y = x + 7 and shade the region above the line.
ii) Second part, take x + 2 < 0 ⇒ | x + 2| = - x - 2
⇒ y ≥ - x - 2 + 5
⇒ y ≥ - x + 3
Therefore, draw the line y = - x + 3 and shade the region above the line.
4) The solution is the intersection of the two shaded regions, which is the one shown in the graph attached.
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This means that in our case:
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We divide by 36 and take the root of both sides to obtain:
Note that the square root can be written as an exponent of 1/2 and so we can further simplify the above to obtain:
Let's leave that for the moment and look at the formula for arc length. The formula is
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As a note for a function x in terms of y simply switch each dx in the above to dy and vice versa.
As you can see from the formula we need to find dy/dx and square it. Let's do that now.
We can use the chain rule: bring down the 3/2, keep the parenthesis, raise it to the 3/2 - 1 and then take the derivative of what's inside (here
Looking at the formula for ds you see that dy/dx is squared so let's square the dy/dx we just found.
This means that in our case:
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