Answer:
x^2 -10x+25
Step-by-step explanation:
(x-5)^2
Rewriting
(x-5)(x-5)
FOIL
first: x*x = x^2
outer: x* -5 = -5x
inner: -5*x = -5x
last: -5 * -5 = +25
Add them together
x^2 -5x-5x+25
Combine
x^2 -10x+25
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:
7/4
Step-by-step explanation:
Answer:
Complement: 67°
Supplement: 157°
Step-by-step explanation:
Complementary angles = 90°
90-23=67°
Supplementary angles = 180°
180-23=157°
Answer:
(-5.77, 6.46)
Step-by-step explanation:
15x + 9y = 45 ----------- i
9x + 8y = 12----------------ii
Multiply equation i by 9 the coefficient of x in equ ii
And equation ii by 15 the coefficient of x in equ I
9 x 15x + 9y = 45 ----------- i
15 x 9x + 8y = 12----------------ii
135x+81y = 405
135x+120y= 180
Subtract equation ii from I
135x-135x+81y-(+120y)= 405-180
-39y=225
y = 225/-39 = -5.77
Insert the value of y in equ i
15x + 9y = 45
15x+9(-5.77) = 45
15x-51.92=45
15x = 45+51.92
15x= 96.92
x = 96.92/15= 6.46
(x,y) = (-5.77, 6.46)
x = 6.92/15
