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kari74 [83]
3 years ago
13

Find the radius and center of the circle given by the equation below. (x – 6)2 + (y + 4)2 = 7

Mathematics
2 answers:
valentina_108 [34]3 years ago
4 0
Center will be (6,-4) and the radius will be square root of 7
Nat2105 [25]3 years ago
4 0

Answer:

Center (6 , -4) and radius  √7.

Step-by-step explanation:

Given  : (x – 6)² + (y + 4)² = 7

To find  : Find the radius and center of the circle .

Solution : We have given that (x – 6)² + (y + 4)² = 7

We can write this equation as (x – 6)² + (y + 4)² = (√7)².

Standard form of circle (x – h)² + (y - k)² = (r)².

Where, (h , k) center coordinates , r  =radius .

On comparing with standard equation :

h = 6, k = -4 and r = √7.

Therefore, Center (6 , -4) and radius  √7.

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Mariulka [41]

Given:

The equation is,

2\log _3x-\log _3(x-2)=2

Explanation:

Simplify the equation by using logarthimic property.

\begin{gathered} 2\log _3x-\log _3(x-2)=2 \\ \log _3x^2-\log _3(x-2)=2_{}\text{      \lbrack{}log(a)-log(b) = log(a/b)\rbrack} \\ \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \end{gathered}

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\begin{gathered} \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \\ \frac{x^2}{x-2}=3^2 \\ x^2=9(x-2) \\ x^2-9x+18=0 \end{gathered}

Solve the quadratic equation for x.

\begin{gathered} x^2-6x-3x+18=0 \\ x(x-6)-3(x-6)=0 \\ (x-6)(x-3)=0 \end{gathered}

From the above equation (x - 6) = 0 or (x - 3) = 0.

For (x - 6) = 0,

\begin{gathered} x-6=0 \\ x=6 \end{gathered}

For (x - 3) = 0,

\begin{gathered} x-3=0 \\ x=3 \end{gathered}

The values of x from solving the equations are x = 3 and x = 6.

Substitute the values of x in the equation to check answers are valid or not.

For x = 3,

\begin{gathered} 2\log _3(3^{})-\log _3(3-2)=2 \\ 2\log _33-\log _31=2 \\ 2\cdot1-0=2 \\ 2=2 \end{gathered}

Equation satisfy for x = 3. So x = 3 is valid value of x.

For x = 6,

\begin{gathered} 2\log _36-\log _3(6-2)=2 \\ 2\log _36-\log _34=2 \\ \log _3(6^2)-\log _34=2 \\ \log _3(\frac{36}{4})=2 \\ \log _39=2 \\ \log _3(3^2)=2 \\ 2\log _33=2 \\ 2=2 \end{gathered}

Equation satifies for x = 6.

Thus values of x for equation are x = 3 and x = 6.

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