Answer:
x^2 -8x -5 = -3
x^2 -8x -2 = 0
We complete the square by:
1) Moving the "non X" term to the right:
x^2 -8x = 2
2) Dividing the equation by the coefficient of X²
The coefficient of x is 1 so we don't do anything
3) Now here's the "completing the square" stage in which we:
• take the coefficient of X
that is -8
• divide it by 2
-8 ÷ 2 = -4
• square that number
-4*-4 = 16
• then add it to both sides of the equation.
x^2 -8x +16 = 2 +16
That becomes
(x -4)^2 = 18
we take the square root of both sides:
(x -4) = sqr root (18)
x1 = sqr root (18) +4
AND
(x+4) = sqr root (18) -4
x1 = sqr root (18) +4 = 4.2426406871 + 4 = 8.2426406871
x2 = sqr root (18) -4 = = 4.2426406871 - 4 = .2426406871
Step-by-step explanation:
Answer:
30 degrees.
Step-by-step explanation:
The sum of the external angles = 360 degrees.
So 2x + 4x + 8x + 10x = 360
24x = 360
x = 15.
So the smallest exterior angle = 2*15
= 30 degrees.
The formula for a circumference is c = 2(3.14)r
The picture shown is the diameter, half of a diameter is the radius. The radius is 6
So,
c = 2(3.14)6
c = 37. 7
~
Answer:
x ≥ 117
Step-by-step explanation:
Let suppose Pₙ denoted the structural damage that is probable with n cans
Pₙ = P {X₁+ ....... + Xₙ ≥ w}
= P {X₁+ ....... + Xₙ-w ≥ 0 }
So weight of the ith can denoted by Xi
From CLT , ΣXi is normal with 3n and variance 0.09
w is independent of Xi and normal
So
ΣXi-w is also normal
then mean and variance are
E [ ΣXi - w] = 3n -400
Var (ΣXi-w) = var (ΣXi) +Var (w)
= 0.09n +1600
So Pₙ = P{ X₁ +X₂ +.... +Xₙ -w-(3n-400) /underroot 0.09n +1600 ≥ -(3n-400)/ understoot (0.09n +160v)
this can be simplified to≈ P₀ { Z ≥ 400 - 3n / undersoot (0.09n+1600)}
P{Z ≥ 1.28 } ≈ .1
on simplifying x ≥ 117
1st number = x-5
2nd number = x
3rd number = 3x-15
Total = 80
x-5+x+3x-15=80
5x-20=80
5x=100
x=20
The numbers are 20, 15, 45
