3 years ago

Math order of operations

Mathematics

1 answer:

Novosadov [1.4K]2 years ago

6 0

Answer:

Step-by-step explanation:

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Circle O has a circumference of approximately 250n ft.

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Step-by-step explanation:

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2 years ago

(6) (Bonus) Determine the Cartesian equation of the surface with spherical coordinate equation rho = 2 cos θ sin φ − 2 sin θ sin

KonstantinChe [14]

Answer:

Hence, the sphere has a radius of $\sqrt{3}$ and is centered at the point (1,-1,1)

Step-by-step explanation:

We have the equation

$\rho=2cos\theta cos\phi-2sin\theta sin\phi+2cos\phi$

We have to take into account the relation between coordinates

$\rho=\sqrt{x^2+y^2+z^2}\\x=\rho cos\theta sin\phi\\y=\rho sin\theta sin\phi\\z= \rho cos\phi$

by substituting we have:

$\rho=2[\frac{x}{\rho}-\frac{y}{\rho}+\frac{z}{\rho}]\\\\\rho^2=2x-2y+2z\\\\x^2+y^2+z^2=2x-2y+2z$

We have to complete squares:

$(x^2-2x+1)+(y^2+2y+1)+(z^2-2z+1)-1-1-1=0\\\\(x-1)^2+(y+1)^2+(z-1)^2=3$

Hence, the sphere has a radius of $\sqrt{3}$ and is centered at the point (1,-1,1)

hope this helps!!

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2 years ago