Answer:
Step-by-step explanation:
2x² + 9x = -7
2x² + 9x + 7 = 0
When we multiply we should get 2*7 = 14 and when we add we should get 9. Find the factors of 14 ---> 1,2,7,14. Factors are 2,7 as when we multiply we get 14 and we we add, get 9
2x² + 2x + 7x + 7 = 0
2x( x + 1) + 7 (x + 1) = 0
(x + 1)(2x + 7) = 0
Answer:£149
Step-by-step explanation:
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each number sign is a flower. he planted 10 flowers.
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
500+ 500 is 1,000, 500 represents 1 so times that by two and you get 1,000
