Two possible plans for a new bathroom are shown. Is there a value of x for which the perimeters are equal? Show your work. Expla
in the reasoning.
2 answers:
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We have the following parameters
the general equation of a circle with center (0,0) is the following,
Let's use the following tigonometric identity,
solving for cos and sin in the equations we are given,
replace,
Since we have two different numbers in the denominator, this is not a circle equation but an elipse, of the form,
where,
a is the vertex and,
b is the covertex
thus, in the x axis, the vertex is 7 and the y-axis the covertex is 5
Now, let's determine the direction by replacing
when Θ = 0 , then x = 7*cos0 = 7*1 = 7 , and y = 5*sin0 = 5*0 = 0
when Θ = 90° or π/2 , then x = 7*cos90° = 7*0 = 0 , and y = 5sin90° = 5*1 = 5
If we draw this, we can see that the direction is counterclockwise as in the bottom right image.
