Answer:
First, plug-in x and y as 3sinθ-2 and 3cosθ+4 into the equation, respectively:
Then, +2 and -2 cancel out and +4 and -4 cancel out as well, leaving you with:
We can factor out 3^2 = 9 from both equations:
We know from a trigonometric identity that 
, meaning we can reduce the equation to:
And therefore, we have shown that (x+2)^2 + (y-4)^2 = 9, if x=3sinθ-2 and y=3cosθ+4.
Hope this helped you.
Problem 2
Plot point L anywhere that isn't on segment JK. Draw a line through point L. I find it helps to make the lines parallel.
Next, use a compass to measure the width of segment JK. Keeping this same width, transfer the nonpencil end of the compass to point L. Draw an arc that crosses the line through L.
Mark this intersection point M. Lastly, use a pen or marker to form segment LM and erase everything else of that line.
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Problem 3
The ideas of the previous problem will be used here. We copied segment JK to form congruent segment LM. So JK = LM.
The same steps will be used to form segment GN where GN = EF. In other words, segment GN is a perfect copy of segment EF.
If you repeat these steps again, you'll get another segment of the same length. This segment goes from point N to point H. So NH = GN = EF
Then we can say,
GH = GN + NH
GH = EF + EF
GH = 2*EF
Answer:
y = 5/3x + 31/3
=
5
3
x
+
31
3
Step-by-step explanation:
We want to calculate the following
Using the properties of exponents, we have that
So we have
So, if factor 10^-4 on the right side, we have
Note that
Then,
So we have that
You can make 5 full scarves in total.
