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)
Here, 3x + 2y = 12
2x + 2y = 10
Subtract 2nd from 1st equation,
x = 2
Now, substitute in 2nd,
2(2) + 2y = 10
2y = 10 - 4
y = 6/2
y = 3
In short, Your Answer would be: (2, 3)
Hope this helps!
Answer:
a. 1/6
Step-by-step explanation:
for a, there is only one side that has three
Answer: ($8.96 / 7) * 5 or $6.40
Step-by-step explanation: You need to find the price for one watermelon then multiply it by 5 to find the price of 5.
Let +n+ = number of bottles of cranberry juice needed
+2n+ = number of bottles of ginger ale needed
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+3.2n+%2B+.9%2A%28+2n+%29+=+20+
+3.2n+%2B+1.8n+=+20+
+32n+%2B+18n+=+200+
+50n+=+200+
+n+=+4+
and
+2n+=+8+
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The most bottles of cranberry juice is 4
