Describe in words the surface whose equation is given. (assume that r is not neg

elchatosarapage 2021-11-19 Answered
Describe in words the surface whose equation is given. (assume that r is not negative.) \(\displaystyle\theta={\frac{{\pi}}{{{4}}}}\)
a) The plane \(\displaystyle{y}=−{z}\) where y is not negative
b) The plane \(\displaystyle{y}={z}\) where y and z are not negative
c) The plane \(\displaystyle{y}={x}\) where x and y are not negative
d) The plane \(\displaystyle{y}=−{x}\) where y is not negative
e) The plane \(\displaystyle{x}={z}\) where x and y are not negative

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Expert Answer

Jennifer Hill
Answered 2021-11-20 Author has 190 answers
Step 1
It represents line equation in XY- plane whose equation if given by \(\displaystyle{x}={y}\) where x and y are not negative
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Jick1984
Answered 2021-11-21 Author has 410 answers
Step 1
Since \(\displaystyle\theta\) is the angle of x, y plane measured counter clock-wise from the \(\displaystyle+{x}-{a}\xi{s}.\)
This equation represents all points located at an angle of \(\displaystyle{\frac{{\pi}}{{{4}}}}\) to \(\displaystyle+{x}-{a}\xi{s}\).
This represents half plane. Since cosine and sine have same values at \(\displaystyle{\frac{{\pi}}{{{4}}}}\) in this case, \(\displaystyle{x}={y}\).
It means option (c) is the correct answer.
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