Answer:
B
Step-by-step explanation:
The vertex is the turning point of the parabola.
First find the zeros by equating y to zero, that is
(x - 6)(x + 12) = 0
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 12 = 0 ⇒ x = - 12
The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros, thus
= 
= 
= - 3
Thus the x- coordinate of the vertex is x = - 3 → B
Answer:
5.7 I pretty sure
Step-by-step explanation:
it wold be this 0.000032518
Answer:
40kg
20kg
10kg
Step-by-step explanation:
The computation of the food each one is getting as follows
Total weights of all dogs
= 20 kg + 10 kg + 5kg
= 35 kg
And, the food is 70 kg
So, each one is getting
for 20 kg
= 70 ÷ 35 × 20
= 40 kg
For 10 kg
= 70 ÷ 35 × 10
= 20 kg
And, for 5 kg
= 70 ÷ 35 × 5
= 10 kg
Step-by-step explanation:
(a) ∫₋ₒₒ°° f(x) dx
We can split this into three integrals:
= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx
Since the function is even (symmetrical about the y-axis), we can further simplify this as:
= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx
The first integral is finite, so it converges.
For the second integral, we can use comparison test.
g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.
We can show that g(x) converges:
∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).
Therefore, the smaller function f(x) also converges.
(b) The width of the intervals is:
Δx = (3 − -3) / 6 = 1
Evaluating the function at the beginning and end of each interval:
f(-3) = e^(-9/2)
f(-2) = e^(-2)
f(-1) = e^(-1/2)
f(0) = 1
f(1) = e^(-1/2)
f(2) = e^(-2)
f(3) = e^(-9/2)
Apply Simpson's rule:
S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]
S ≈ 2.5103
