HELP!!! Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 cos 3θ
2 answers:
Response:
The graph exhibits symmetry concerning the x-axis.
Step-by-step outline:
- Symmetry about the polar axis (x-axis) is observed when replacing (r,θ) with (r,-θ), resulting in an equation identical to the original.
- For the y-axis, replacing (r,θ) with (-r,-θ) gives the same equation as the original.
- For symmetry around the pole (origin), a switch of (r,θ) to (-r,θ) must yield the same original equation.
We have the following equation:
- When substituting (r,θ) with (r,-θ), the result is:
( Since, we are aware that:
)
Therefore, the graph is symmetric with respect to the x-axis.
- For when we substitute (r,θ) with (-r,-θ)
In this case, we see that the graphs are not equivalent upon performing this substitution.
Consequently, the graph lacks symmetry concerning the y-axis.
- Upon substituting (r,θ) with (-r,θ), we find:
Again, it's clear that the resulting graphs do not equate.
Thus, the graph does not exhibit symmetry with respect to the pole (origin).[TAG_63]]
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Answer:
Ben could have sold a maximum of 6 turkey sandwiches.
Step-by-step explanation:
Turkey sandwiches are priced at $2.50, while veggie wraps cost $3.50 at the snack stand.
Our goal is to determine the largest number of turkey sandwiches Ben might have sold.
4 veggie wraps were sold (y).
Thus, the inequality is: 2.50x + 3.50(4) < 30
2.50x + 14 < 30
- 14 - 14
2.50x < 16
Ultimately, Ben could sell a maximum of 6 turkey sandwiches.