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katovenus [111]
3 years ago
10

Find center radius 3x squared + 3y squared + 30x - 42y- 141=0

Mathematics
1 answer:
almond37 [142]3 years ago
8 0
<u>Center and Radius</u>
3x² + 3y² + 30x - 42y - 141 = 0
x² + y² + 10x - 14y - 47 = 0
x² + 10x + y² - 14y - 47 = 0
x² + 10x + 25 + y² - 14y - 49 = 0
x² + 10x + 25 + y² - 14y - 49 = 47
x² + 10x + 25 + y² - 14y + 49 = 47 + 25 + 49
x² + 10x + 25 + y² - 14y + 49 = 121
(x + 5)² + (y - 7)² = 121
center: (-5, 7)
radius: 11



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Answer:

140

Step-by-step explanation:

The arithmetic series is 5, 7, 9, 11, ........., 23.

First u have to determine the no. of terms that can be done by using

Tₙ = [a + (n - 1)d]

Tₙ-------nth term

a---------first term

n---------no.of terms in the series

d---------common difference

here a = 5,d = 2.

let it contain n terms Tₙ= [a + (n-1)d]

Substitute Tₙ, a, and d in the equation

23 = 5 + (n - 1)2

Subtract 5 from each side.

18 = (n-1)2

Divide each side by 2

(n - 1) = 9

Add 1 to each side

n = 9 + 1 = 10

The sum of the arithmetic sequence formula: Sₙ= (n/2)[2a+(n-1)d]

Substitute Sₙ, a, n and d in the equation

Sₙ= (10/2)[2(5) + (10-1)2]

Sₙ= (5)[10 + (9)2]

Sₙ= 5[10 + 18]

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Therefore the sum of the arithmetic sequence is 140.

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