Answer:
The matched options to the given problem is below:
Step1: Choose a point on the parabola
Step2: Find the distance from the focus to the point on the parabola.
Step3: Use (x, y).
Find the distance from the point on the parabola to the directrix.
Step4: Set the distance from focus to the point equal to the distance from directrix to the point.
Step5: Square both sides and simplify.
Step6: Write the equation of the parabola.
Step by step Explanation:
Given that the focus (-1,2) and directrix x=5
To find the equation of the parabola:
By using focus directrix property of parabola
Let S be a point and d be line
focus (-1,2) and directrix x=5 respectively
If P is any point on the parabola then p is equidistant from S and d
Focus S=(-1,2), d:x-5=0]
80.8, 40.4, 20.2, 10.1 (the numbers are going in half.)
1024, 512, 256, 128. (also going in half.)
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
This gives you the answer and the step by step instructions to get the answer
Answer:
The correct answer is the first solution set.
Step-by-step explanation:
If we substitute -20 into the equation we get
-20+17≤-3
-3≤-3
So,the inequality is right.
We can check the second one
14+17≤-3
31≤3 The inequality is false.
We can check the last one
-20+17≤-3
-3≤3 It works however there is a difference between the first one and the last one and that is the sign.For the first one there x≤-20 meaning the greatest number x can be is -20.For the last one x≥-20 which means -20 is the least value x can be.
If we substitude -21 into the equation we get
-21+17≤-3
-4≤-3
The inequality is false because -4 is not smaller than -3.
So,the right answer is the first solution set.
