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alexandr1967 [171]
4 years ago
15

Write the equation of a circle with center at (3, -2), which also passes through the point (0, 2).

Mathematics
1 answer:
Airida [17]4 years ago
3 0

\text{The equation of acircle:}\\\\(x-h)^2+(y-k)^2=r^2\\\\(h;\ k)-center\\r-radius\\\\\text{We have center}\ (3,\ -2)\to h=3\ \text{and}\ k=-2.\\\\\text{The radius is the distance between the points} (3,\ -2)\ \text{and}\ (0,\ 2).\\\\\text{The formula of a distance between two points:}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\text{Substitute:}\\\\d=\sqrt{(2-(-2))^2+(0-3)^2}=\sqrt{4^2+(-3)^2}=\sqrt{16+9}\\\\=\sqrt{25}=5\\\\Answer:\ \boxed{(x-3)^2+(y-(-2))^2=5^2\to\boxed{(x-3)^2+(y+2)^2=25}}

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I've been having problems with this for a while...
Rina8888 [55]
Like all problems that involve images within the question, we should definitely try to draw this out. In the picture above, I have done this.

Now, we can see that this is just a simple proportion problem. For every 2.5 cm of height of the flower, we are 2 cm from the opening, or aperture. For every 20 cm of height, how far are we? We can set up the problem like this:

20 ............2.5
-------- = ---------
...x ............. 2

where x is the unknown distance to the aperture from the flower. Now, we just need to get x by itself. A typical way of solving something like this is by doing "butterfly multiplication" which is really just a shortcut haha. Anyway, I can rewrite that equation ^ as:

20×2 = 2.5 × x

Then, to solve for x, we would divide both sides by 2.5. (If you don't know why that is, please let me know and I'll elaborate).

We would then have:

20×2
------- = x
2.5

Which then simplifies to:

x = 16

Try using the same logic for your second question, and if you get stuck, I'd be happy to help! please let me know if any of this doesn't make sense. :)

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8 0
3 years ago
Find the product. -7(8 + k)
Alecsey [184]
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6 0
3 years ago
The Ferris Wheel has a radius of 20 feet, and its center is 40 feet above the ground. ​
almond37 [142]

Answer:

  • The lowest point = 20 ft
  • The highest point = 60 ft
  • The diameter of the wheel = 40 ft

Step-by-step explanation:

<h3>Given</h3>
  • The radius = 20 ft
  • Distance from the ground to the center = 40 ft
<h3>To find</h3>
  • The lowest point
  • The highest point
  • The diameter of the wheel
<h3>Solution</h3>
  • The diameter = 2*radius = 2*20 ft = 40 ft
  • The lowest point = distance to the center - radius = 40 ft - 20 ft = 20 ft
  • The highest point = the lowest point + diameter = 20 ft + 40 ft = 60 ft
8 0
3 years ago
A store sells flower arrangements at a cost of $28 each. Which statements are true regarding the price of the arrangements? Sele
SashulF [63]

Answer:

10%=$25.20

25%=$21.00

35%=$18.20

Step-by-step explanation:

A mark-down in price of 10% is the same as 90% of the original price. 90% can be expressed as 0.9. $28.00(0.9)=$25.20. This same explanation holds true for the 25%/35% mark-down: $28.00(1-0.25)=$21.00; $28.00(1-0.35)=$18.20. Additionally, if you try this with the 40%/50% mark-downs it doesn‘t work.

7 0
3 years ago
Read 2 more answers
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