Find the mean and median weights of these cats.
1 answer:
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Answer:
Step-by-step explanation:
I'll show you how to do the first one; the other are exactly the same, so pay attention.
The formula for arc length is
where θ is the central angle's measure. It just so happens that the measure of the central angle is the same as the measure of the arc it intercepts. Our arc shows a measure of 40°; this measure is NOT the same as the length. Measures are in degrees while length is in inches, or cm, or meters, etc. Going off that info, our central angle measures 40°. Filling in the formula and using 3.1415 for π:
. I'm going to reduce that fraction a bit (and I'll use the same reduction in the Area of a sector coming up next):
which makes
AL = 2.09 units. Now for Area of the Sector. The formula is almost identical, but instead uses the idea that the area of a circle is πr²:
where θ is, again, the measure of the central angle (which is the same as the measure of the arc it intercepts). Filling in:
which simplifies a bit to
. As you can see, the 9's cancel each other out, leaving you with
units²
The error is when she added 4 to both sides.
Instead, she should divide both sides by -4 to undo the multiplication. Specifically, the multiplication between the -4 term and the (x-2)^2 term.
This is one possible correction of what her steps could look like.
In the third step, I'm dividing both sides by -4. In the sixth step, I'm applying the square root to both sides to undo the squaring operation. Then two steps later, I'm adding 2 to both sides to undo the "-2", which helps fully isolate x.
The only solution is x = 2, so it's the only x intercept. You can verify this answer by plugging x = 2 back into the original equation at the very top. You should end up with y = 0.
Note: The term "root" is another name for "x intercept".