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:
add, subtract, multiply and divide complex numbers much as we would expect. We add and subtract
complex numbers by adding their real and imaginary parts:-
(a + bi)+(c + di)=(a + c)+(b + d)i,
(a + bi) − (c + di)=(a − c)+(b − d)i.
We can multiply complex numbers by expanding the brackets in the usual fashion and using i
2 = −1,
(a + bi) (c + di) = ac + bci + adi + bdi2 = (ac − bd)+(ad + bc)i,
and to divide complex numbers we note firstly that (c + di) (c − di) = c2 + d2 is real. So
a + bi
c + di = a + bi
c + di ×
c − di
c − di =
µac + bd
c2 + d2
¶
+
µbc − ad
c2 + d2
¶
i.
The number c−di which we just used, as relating to c+di, has a spec
Answer:
It has no real solution.
Step-by-step explanation:
6p^2 − 7p + 5 = 0
For this equation: a = 6, b = -7, c = 5
6p^2+ −7p + 5 = 0
Step 1: Use quadratic formula with a=6, b=-7, c=5.
p = -b ± √b^2 - 4ac/2a
p = -(-7) ± √(-7)^2 - 4(6)(5)/2(6)
p = 7 ± √-71/12
Volume of a pyramid is calculated by L×W×H÷3. Which means 81× 10× 10 ÷ 3
81 × 10 × 10 = 8100 ÷ 3
So the answer is 2700.
D. I would best guess, hey have a nice thanksgiving week. Hope they gave you a whole week of school out like mine did :) if you go to school
