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dimulka [17.4K]
3 years ago
12

write an equation for a circle with a diameter that has endpoints at (-4, -7) and (-2, -5). round to the nearest tenth if necess

ary.
Mathematics
1 answer:
andrezito [222]3 years ago
3 0

Answer:

The answer to your question is          (x + 3)² + (y + 6)² = 2

Step-by-step explanation:

Endpoints (-4, -7) and (-2, -5)

Process

1.- Find the length of the radius

   d = \sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }

   d = \sqrt{(-2 + 4)^{2}+ (-5 + 7)^{2}  }

   d = \sqrt{2^{2} + 2^{2} }

   d = \sqrt{4 + 4}

   d = \sqrt{8}

   Radius = \frac{\sqrt{8} }{2} = \sqrt{2}

2.- Find the center

Xm = \frac{-4 - 2}{2} = \frac{-6}{2} = -3

Ym = \frac{-7 - 5}{2} = \frac{-12}{2} = -6

Center = (-3, -6)

3.- Write the equation

                                   (x - h)² + (y - k)² = r²

                                   (x + 3)² + (y + 6)² = (\sqrt{2})²

                                   (x + 3)² + (y + 6)² = 2

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1. what is the period of the function f(x) shown in the graph?
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Problem 1)

Answer: pi/2

-------------------------------

Place your pencil at (0,3) which is a good starting point, since x = 0 is often a good starting point. Trace along the curve until you reach back up at y = 3 again. So you'll go down and then back up until you reach (pi/2, 3). The difference in x values is pi/2-0 = pi/2. Every pi/2 units, the graph curve repeats itself over and over infinitely. 

Note: this is not the only way to determine the period. You can start at any point really. It helps to start at a min or max value, or at x = 0. In this case, it happened to be both. 

===========================================================
Problem 2)

Answer: See figure 2 (attached image)

-------------------------------

Point A is at (0,0)
Point B is at approximately (1.57,-2) which is exactly (pi/2,-2)

===========================================================
Problem 3)

Answer: See figure 3 (attached image)

===========================================================
Problem 4)

Answer: Choice B
The graph is horizontally compressed by a factor of 2 and shifts up 1 unit

-------------------------------

The jump from x to 2x will have the period go from 2pi to pi. The graph curve repeats itself more and more often (twice as often). Therefore we have an accordion squeeze effect going on, or think of it like a spring being pressed down. We have horizontal compression along the x axis.

Adding 1 to the end shifts every point upward 1 unit. Overall, this gives the visual the entire curve itself is shifted up 1 unit.

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Problem 5)

Answer: f(x) = 5.05*sin((pi/12)x)+5.15

-------------------------------

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d = 5.15 is the midline, which is the starting height at x = 0

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===========================================================
Problem 6)

Answers are:
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B) The radius of the Ferris wheel is 30 ft

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C is false because the height at t = 0 is 34 ft, but the lowest point is at height h = 4

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