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CaHeK987 [17]
3 years ago
6

Write the equation in spherical coordinates. (a) 4x2 − 3x + 4y2 + 4z2 = 0

Mathematics
1 answer:
spayn [35]3 years ago
6 0
4x^2-3x+4y^2+4z^2=0
here we shall proceed as follows:
x=ρcosθsinφ
y=ρsinθsinφ
z=ρcosφ
thus
4x^2-3x+4y^2+4z^2=
4(ρcosθsinφ)^2-3(ρcosθsinφ)+4(ρsinθsinφ)^2+4(ρcosφ)
but
ρ=1/4cosθsinφ

hence we shall have:
4x^2-3x+4y^2+4z^2
=1/4cosθsinθ(cosθ(4-3sinφ))+4sin^2(φ)

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GIVEN THAT TITAN HAS A RADIUS OF 2575 KM WHICH IS COVERED BY 600 KM ATMOSPHERE. WHAT
Ber [7]

Answer:

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Step-by-step explanation:

The radius to the top of the atmosphere as a fraction of the moon's radius is ...

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The ratio of the moon's volume with atmosphere to the moon's volume without is the cube of this, or 1.87456

Then the ratio of the atmosphere's volume to the moon's volume is ...

  (1.87456 -1)/1 = 0.87456

Atmospheric haze is about 87.4% of the moon's volume.

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We have assumed that the desired ratio is to the solid moon's volume, not the volume of moon and atmosphere together. The latter ratio would be 0.875 to 1.875 or about 46.7%.

3 0
4 years ago
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7 0
3 years ago
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Where are the asymptotes of f(x) = tan(4x − π) from x = 0 to x = pi over 2 ?
vladimir1956 [14]
tan(4x- \pi )= \frac{sin(4x- \pi )}{cos(4x- \pi )}

The asymptotes are where the graph is undefined. Since: tan(x) =sin(x)/cos(x)
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4x - π = π/2
4x = π/2 + π
4x = 3π/2
x = 3π/8

4x - π = 3π/2
4x = 3π/2 + π
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This ones outside the interval (5π/8 > π/2) , try -π/2

4x - π = -π/2
4x = -π/2 + π
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4 0
4 years ago
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kolezko [41]
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4 0
4 years ago
A governor of state A earns $53,280 more than the governor of state B. If the total of their salaries is $284,680 find the salar
Sedbober [7]

Answer:

Step-by-step explanation:

Let us take the salary of state B as 'x'

Salary of state A = 53280 + x

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Therefore, 53280 + x + x =284680

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= x = 249400/2

x = 124700

Salary of state B = 124700

Salary of state A = 177980

7 0
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