Answer:
d³y/dx³ = (-2xy² − 3x³ − 4xy²) / (8y⁵)
Step-by-step explanation:
d²y/dx² = (-2y² − x²) / (4y³)
Take the derivative (use quotient rule and chain rule):
d³y/dx³ = [ (4y³) (-4y dy/dx − 2x) − (-2y² − x²) (12y² dy/dx) ] / (4y³)²
d³y/dx³ = [ (-16y⁴ dy/dx − 8xy³ − (-24y⁴ dy/dx − 12x²y² dy/dx) ] / (16y⁶)
d³y/dx³ = (-16y⁴ dy/dx − 8xy³ + 24y⁴ dy/dx + 12x²y² dy/dx) / (16y⁶)
d³y/dx³ = ((8y⁴ + 12x²y²) dy/dx − 8xy³) / (16y⁶)
d³y/dx³ = ((2y² + 3x²) dy/dx − 2xy) / (4y⁴)
Substitute:
d³y/dx³ = ((2y² + 3x²) (-x / (2y)) − 2xy) / (4y⁴)
d³y/dx³ = ((2y² + 3x²) (-x) − 4xy²) / (8y⁵)
d³y/dx³ = (-2xy² − 3x³ − 4xy²) / (8y⁵)
Answer:

☥ 
- Write the equation of a line in slope - intercept form that has a slope of -2 and passes through the point ( - 1 , 8 ).
☥ 
☪ 
- Slope ( m ) = -2
- Given point = ( - 1 , 8 )
☪ 
- Equation of a line in slope - intercept form ( i.e y = mx + c )
Let the point ( -1 , 8 ) be ( x₁ , y₁ )
☪ 

plug the known values :
↦ 
↦ 
Distribute -2 through the parentheses :
↦ 
Transpose 8 to right hand side and change it's sign
↦ 
↦ 
And we're done !
Hope I helped!
♡ Have a wonderful day / night ツ
~TheAnimeGirl ♪
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Answer:
Rational
Step-by-step explanation:
A terminating decimal is a rational number.
A repeating decimal is a irrational number.
Since 8.27 terminates, it is rational.
I would say age of a plant to its height is a function while the others are not.