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)
Parent function: y =x3 ; shift
4 units to the left
-3(x-14)+9x=6x+24
-3x+42+9x=6x+24
-3x+9x-6x=-24-42
0=-18
the formula for area=l*w
you know one side is 1.1w (w representing the unknown side) and the area is 3.3w squared. now you need to plug in the numbers you know into your formula which would look like this: 3.3w squared is equal to 1.1w times w. now you need to solve for w by multiplying 1.1w and w to get 1.1w squared. now you are going to divide 1.1 w squared on both sides which gives you w equals 3
Final answer: w=3
Answer:
0.15 miles per minute
Step-by-step explanation:
You want the rate 4.5 miles in 30 minutes expressed in terms of miles per minute.
<h3>Unit rate</h3>
To find miles per minute, divide miles by minutes.
speed = miles/minutes = (4.5 mi)/(30 min) = 0.15 mi/min
Samantha can walk 0.15 miles per minute.
