HELP PLEASE?! Determine a radical function that starts at the point (-4,2) and goes to the right and decreases. The domain is al
l x>-4 and the range is all y<2. Explain how you determined you function.
1 answer:
Answer:
f(x) = -√(x-4) + 2
Step-by-step explanation:
(a) Start with the basic function: f(x) = √x.
This would be the top half of a horizontal parabola opening to the right (always positive).
(b) The range is y < 2. This includes negative numbers, so the function must be f(x) = -√x.
(c) The function starts at x = -4. We must shift it four units to the left. We do that by adding four units to x. The function must be f(x) = -√(x + 4). The domain is x > -4.
(d) The function starts at y = 2. We must shift it up two units. We do that by adding two units to y. The function must be f(x) = -√(x+4) + 2. The range is y < 2.
The figure below is the graph of f(x) = -√(x+4) + 2.
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Answer:
The coordinates of the explosion is (3300, -2750)
Step-by-step explanation:
I have plot the points and attached to thus answer for easy understanding.
Now, from the question, since station A is the first to hear the explosion, we'll make it the foci of the parabola in the graph I attached and it will be horizontal since the distance between station C and A is much more than that between station B and A. Thus, the reason why station C will have to be the other foci with the hyperbola centred at the origin.
Now, sound travels at a speed of 1100 ft/s and station B is located 1100 ft from station A. Thus, the explosion would likely have occurred at a point on the line x = 3300ft . Since station A is 3300ft from centre C = 3300,hence C² = 3300² = 10,890,000. Since it takes 4 seconds longer for the sound to reach station C than A, the sound has traveled 4(1100)= 4400 ft.
Thus, 4400 = d1 = d2 = 2a
So,2a = 4400 and so, a =2200
a² = 2200² = 4,840,000 where d1 is the distance from station C to the explosion and d2 is the distance from station A to the explosion. To find b², let's use the equation ;
c² = a² + b² and so; b² = c² - a² = 10,890,000 - 4,840,000 = 6,050,000
Equation of hyperbola is given as;
(x²/a²) - (y²/b²) = 1
Plugging in the values of a² and b², we obtain ;
(x²/4,840,000) - (y²/6,050,000) = 1
Since we have deduced that the explosion must occur on the line x= 3300, we'll put in 3300 for x to obtain ;
(3300²/4,840,000) - (y²/6,050,000) = 1
2.25 - 1 = (y²/6,050,000)
y² = (1.25 x 6,050,000)
y² = 7562500
y = √7562500
y = ± 2750
Due to the fact that the explosion will occur at a point further from station B than from station A, the explosion will take place in quadrant 4. Thus, we will take the negative value of y which is - 2750.
So explosion will occur at the coordinate (3300, -2750)
