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nordsb [41]
2 years ago
5

Find the equation of a circle with a center at (7,2) and a point on the circle at (2,5)?

Mathematics
1 answer:
monitta2 years ago
4 0

Answer:

(x-7)^2+(y-2)^2=34

Step-by-step explanation:

We want to find the equation of a circle with a center at (7, 2) and a point on the circle at (2, 5).

First, recall that the equation of a circle is given by:

(x-h)^2+(y-k)^2=r^2

Where (<em>h, k</em>) is the center and <em>r</em> is the radius.

Since our center is at (7, 2), <em>h</em> = 7 and <em>k</em> = 2. Substitute:

(x-7)^2+(y-2)^2=r^2

Next, the since a point on the circle is (2, 5), <em>y</em> = 5 when <em>x</em> = 2. Substitute:

(2-7)^2+(5-2)^2=r^2

Solve for <em>r: </em>

<em />(-5)^2+(3)^2=r^2<em />

Simplify. Thus:

25+9=r^2

Finally, add:

r^2=34

We don't need to take the square root of both sides, as we will have the square it again anyways.

Therefore, our equation is:

(x-7)^2+(y-2)^2=34

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The price of 10 citrons and 7 fragrant wood apples is 55 units. The price of 7 citrons and 10 fragrant wood apples is 64 units.
a_sh-v [17]

Price of one citron = 5 units

Price of one fragrant = 5/7 units = 0.71 units

Further explanation:

Let x be the price of one citron and

y be the price of one fragrant

Then according to given statement

10x+7y = 55         Eqn 1

7x+10y = 64          Eqn 2

Multiplying equation 1 by 7

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This will be equation 3.

Multiplying equation 2 by 10

10(7x+10y) = 10(64)\\70x+100y=640

This will be equation 4.

Subtracting equation 3 from equation 4

70x+100y - (70x+49y) = 640-385\\70x+100y-70y-49y = 255\\51y = 255\\\frac{51x}{51} = \frac{255}{51}\\x = 5\\Putting\ x=5\ in\ equation\ 1\\10(5)+7y = 55\\50+7y = 55\\7y = 55-50\\7y = 5\\\frac{7y}{7} =\frac{5}{7}

So,

Price of one citron = 5 units

Price of one fragrant = 5/7 units = 0.71 units

Keywords: Linear Equations, Solving system of linear equations

Learn more about linear equations at:

  • brainly.com/question/13168205
  • brainly.com/question/1357167
  • brainly.com/question/1542444

#LearnwithBrainly

5 0
3 years ago
Expertsss/aceee plzzz helpppp quickkklyyyy
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1+5

2+4

3+3

4+2

5+1


 5 ways

6*6 = 36

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Step-by-step explanation:

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