Given the equation (x−13)2+y2=64, identify the center and radius. Do not enter any spaces when typing your answers.

Mathematics

1 answer:

Darya [45]3 years ago

3 0

Answer:

centre = (13,0)

radius = 8

Step-by-step explanation:

The standard equation of the circle is

(x-x0)^2 + (y-y0)^2 = r^2 ...............(1)

where

(x0,y0) is the centre,

r is the radius.

For

(x-13)^2 + y^2 = 64 ..............(2)

we rewrite (2)

(x-13)^2 + (y-0)^2 = 8^2 ...............(3)

and compare (3) with (1)

to identify

x0 = 13, y0 = 0, and r = 8

Therefore

centre = (13,0)

radius = 8

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Answer:

a) 3, 6, 9, 12, 15,..., $3\cdot n$ , b) 4, 7, 10, 13, 16,..., $3\cdot n +1$ , c) Both sequences are arithmetic.

Step-by-step explanation:

a) The sequence of natural numbers which are multiplied by 3 are represented by the function $f(n) = 3\cdot n$ , $n\in \mathbb{N}$ . Let see the first five elements of the sequence: 3, 6, 9, 12, 15,...

b) The sequence of natural numbers which are multiplied by 3 and added to 1 is represented by the function $f(n) = 3\cdot n + 1$ , $n\in \mathbb{N}$ . Let see the first five elements of the sequence: 4, 7, 10, 13, 16,...