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:
Step-by-step explanation:
The diagram for the question is attached below
perimeter of the triangle is 28 feet
area of a square is 144 feet
Area of the square is side^2
take square root on both sides
side = 12
side of the square = 12
side is the diameter of the semicircle
Diameter = 12 , so radius = 12 divide 2 = 6
circumference of semicircle = 
one side of the rectangle is calculated in the perimeter of triangle and other side is calculated using circumference
perimeter of other two side = 2(12)= 24
Total perimeter = 
Your salary in x years is modeled an the exponential growth
The equation that determines your salary in x years is y = 45000(1.05)^x
<h3>How to model the salary growth?</h3>
The model of the exponential growth is given as:
y = a(1 + r)^x
From the question, we have:
Initial salary, a = 45000
Raise, r = 5%
So, the equation becomes
y = 45000(1 + 5%)^x
Evaluate the sum
y = 45000(1.05)^x
Hence, the equation that determines your salary in x years is y = 45000(1.05)^x
Read more about exponential functions at:
brainly.com/question/11464095
Answer:
B. 6.000000 g
Step-by-step explanation:
The reason why its B is due to it having more 'sigs' than 'figs'
Hope this helped <3
The radius is always half of the diameter so it would be 20 inches
