Answer:
13% chance
Step-by-step explanation:
Area of backyard = length * width
A = 30 ft * 20 ft
A = 600
Area of bathtub = π
A = π *
A = 78.54
Probability of arrow landing in tub can be found by dividing Area of the bathtub by the area of the backyard, and then multiplying by 100 for a percentage
Prob. = 78.54/600
Prob. = 0.13
Prob. = 0.13 * 100
Prob. = 13%
Answer:
k = - , k = 2
Step-by-step explanation:
Using the discriminant Δ = b² - 4ac
The condition for equal roots is b² - 4ac = 0
Given
kx² + 2x + k = - kx ( add kx to both sides )
kx² + 2x + kx + k = 0 , that is
kx² + (2 + k)x + k = 0 ← in standard form
with a = k, b = 2 + k and c = k , thus
(2 + k)² - 4k² = 0 ← expand and simplify left side
4 + 4k + k² - 4k² = 0
- 3k² + 4k + 4 = 0 ( multiply through by - 1 )
3k² - 4k - 4 = 0 ← in standard form
(3k + 2)(k - 2) = 0 ← in factored form
Equate each factor to zero and solve for k
3k + 2 = 0 ⇒ 3k = - 2 ⇒ k = -
k - 2 = 0 ⇒ k = 2