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)
We will take one given at a time, the common place is "Detroit", so we will take it as a reference.
1- Detroit is colder than Boston, this means that:
Temperature in Detroit < Temperature in Boston .........> I
2- Detroit is warmer that <span>Minneapolis, this means that:
Temperature is </span><span>Minneapolis < Temperature in Detroit .........> II
From I and II, we can conclude that:
</span><span>Minneapolis has the lowest temperature, followed by Detroit and then Boston.
Comparing this to the choices, we will find that the correct choice is:
</span><span>2. Minneapolis's temperature < Detroit's temperature < Boston's temperature</span>
Answer:
Discount = 14.3% (rounded up to one decimal place)
Step-by-step explanation:
The regular price of an item is $84
Discount = $12
Percentage discount = (Discount ÷ regular price) × 100
Percentage discount = 
× 100 = 14.3% (rounded up to one decimal place)
