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3 years ago

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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3 years ago

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Ulleksa [173]

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Step-by-step explanation:

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3 0

3 years ago

A geometric series has second term 375 and fifth term 81 . find the sum to infinity of series .

Eduardwww [97]

Answer: $\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}$

<u>Step-by-step explanation:</u>

a₁, 375, a₃, a₄, 81

First, let's find the ratio (r). There are three multiple from 375 to 81.

$375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}$

Next, let's find a₁

$a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625$

Lastly, Use the Infinite Geometric Sum Formula to find the sum:

$S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}$

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3 years ago