Describe in words the surface whose equation is given. \phi = \frac{\pi}{4} (select the correct answer) 1)the top half of the right circular cone with

ankarskogC 2021-06-07 Answered

Describe in words the surface whose equation is given.

ϕ = \frac{π}{4}

(select the correct answer)
1)the top half of the right circular cone with vertex at the origin and axis the positive z-axis
2)the plane perpendicular to the xz-plane passing through z = x, where

x \geq 0

3)the plane perpendicular to the xy-plane passing through y = x, where

x \geq 0

4)the base of the right circular cone with vertex at the origin and axis the positive z-axis
5)the plane perpendicular to the yz-plane passing through z = y, where

y \geq 0

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Expert Answer

Ayesha Gomez

Answered 2021-06-08 Author has 104 answers

The answer is pretty simple:

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Jeffrey Jordon

Answered 2021-09-30 Author has 2027 answers

The speherial coordinates are

$x = R \cos θ \sin ϕ = \frac{R \cos θ}{\sqrt{2}}$

$y = R \sin θ \sin ϕ = \frac{R \sin θ}{\sqrt{2}}$

$z = R \cos ϕ = \frac{R}{\sqrt{2}}$

$x^{2} + y^{2} = \frac{R^{2}}{2} = z^{2}$

$z^{2} = x^{2} + y^{2}$

this is coneat vertex origin and axis as z-axis

$z^{2} = x^{2} + y^{2} \Rightarrow z = \sqrt{x^{2} + y^{2}}$ (upper) and $z = - \sqrt{x^{2} + y^{2}}$ (lower)

$z = \sqrt{x^{2} + y^{2}}$ (upper) we have only upper part of cone

if $ϕ = \frac{3 π}{4}$ represents lower part of cone correction option is 1

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