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
Answer:
Speed of sound is 340 meter per second.
Step-by-step explanation:
Let the speed of sound = x meter per second.
It is given that,
The new mode of travel has the speed 170 meter per second, which is 50% less than the speed of sound.
So, we get,
x - 50%x = 170
i.e. x - 0.5x = 170
i.e. 0.5x = 170
i.e. x = 340 meter per second
Hence, the speed of sound is 340 meter per second.
The slope-intercept form:
m - slope
b - y-intercept → (0, b)
We have the points (-4, -6) and (2, 6). Substitute:
Put the coordinates of the point (2, 6) to the equation of a line:
<h3>Answer: y = 2x + 2</h3>
Answer:
a) 0.3246
b) 0.0043
Step-by-step explanation:
- For player 1 ; Probability of winning = P(W) = 1/3
- Probability of loosing; P(winning) + P( Loosing) = 1
a) To find Find P(N <= 10) = P(2)+P(3)+P(4)+P(5)+P(6)+P(7)+P(8)+P(9)+P(10)
= (1/3)^2 + (1/3)^2 x 2/3 + (1/3)^2 x (2/3)^2 + (1/3)^2x (2/3)^3 + (1/3)^2 x (2/3)^4
X (1/3)^2 x (2/3)^5 + (1/3)^2 x (2/3)^6 + (1/3)^2 x (2/3)^7 + (1/3)^2 x (2/3)^8
= 0.3246
b) Find P(N = 10) = (1/3)^2 x (2/3)^8 = 0.0043
Answer:
√4 * √15.
Step-by-step explanation:
√60
=√(4 * 15)
= √4 * √15
