Answer:
α² +β² = 3 4/9
Step-by-step explanation:
Assuming α and β are solutions to the equation, it can be factored as ...
(x -α)(x -β) = 0
Expanding this, we get ...
x² -(α +β)x +αβ = 0
Dividing the original equation by 3, we find ...
x² +(1/3)x -5/3 ≡ x² -(α+β)x +αβ ⇒ (α+β) = -1/3, αβ = -5/3
We know that the square (α+β)² can be expanded to ...
(α +β)² = α² +β² +2αβ
α² +β² = (α +β)² -2αβ . . . . . . subtract 2αβ
Substituting the values for (α+β) and αβ, we find the desired expression is ...
α² +β² = (-1/3)² -2(-5/3) = 1/9 +10/3 = 31/9
α² +β² = 3 4/9
Answer:
The correct answer is last option 78.5%
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where r is the radius of circle
Area of square = a²
Where 'a' is the side length of square
<u>To find the area of circle</u>
Here r = 10 cinches
Area = πr²
= 3.14 * 10²
= 3.14 * 100 = 314
<u>To find the area of square</u>
Here a = 20 inches
Area = a²
= 20²
= 400
<u>To find the probability percentage</u>
Probability = area of circle/Area of square
= (314/400)*100
78.5 %
Answer:
r= 10
Step-by-step explanation:
30 - 20 = 10
