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:
y = 3/5x + 3
Step-by-step explanation:
→ Write down in y = mx + c
y = 3/5x + c
→ Substitute in coordinates
0 = -3 + c
→ Find c
c = 3
→ Rewrite
y = 3/5x + 3
Answer: 12
Step-by-step explanation:
For this counting question, we need to figure out the possible choices for each selection.
For main protein, there are four options, so we can make four slots
_ _ _ _
For beans, there's three options, so we can make three slots
_ _ _
Doing some casework, we know that 4*3 = 12, which is the answer.
Answer:
Step-by-step explanation:
Let's make this simple. Since we are given a ratio, that is the method we will use (as opposed to being told that the coordinate of the point that partitions the directed segment is one-third of the way from the first point to the second point. That's a different method). There is a formula for each of the coordinates we are looking for and they are:
and 
where
a = 4 (from the ratio),
b = 3 (from the ratio),
x1 = 1, y1 = -6,
x2 = 8, y2 = 8 (those are from the endpoints of the directed segment). Filling in to find x first:
which simplifies down to
and then y:
which simplifies down to
so the coorinates are (5, 2).
