Liam is constructing a square in which two of its vertices are points A and B. He has already used his straightedge and compass
to construct the lines and arcs shown.
What should Liam do for his next step?
A. Place the point of the compass on point A and draw any arc above it.
B. Use the straightedge to draw a horizontal line that contains point E.
C. Use a straightedge to draw AE¯¯¯¯¯.
D. Place the point of the compass on point B and draw an arc that intersects BE¯¯¯¯¯, using AB as the width for the opening of the compass.
What should Liam do for his next step?
A. Place the point of the compass on point A and draw any arc above it.
B. Use the straightedge to draw a horizontal line that contains point E.
C. Use a straightedge to draw AE¯¯¯¯¯.
D. Place the point of the compass on point B and draw an arc that intersects BE¯¯¯¯¯, using AB as the width for the opening of the compass.
1 answer:
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Answer:
Part 1)
See Below.
Part 2)
Step-by-step explanation:
Part 1)
The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:
We want to verify that the expression:
Is the linear approximation for the function:
At <em>x</em> = 0.
So, find f'(x). We can use the chain rule:
Simplify. Hence:
Then the slope of the linear approximation at <em>x</em> = 0 will be:
And the value of the function at <em>x</em> = 0 is:
Thus, the linear approximation will be:
Hence verified.
Part B)
We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.
In other words:
By definition:
Therefore:
We can solve this by using a graphing calculator. Please refer to the graph shown below.
We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.
In interval notation:
