If the pattern continues, how many stars will be in the Stage 15 figure?
1 answer:
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Answer:
(x + 6)² + (y - 2)² = 75
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 6, 2) and r = 5, hence
(x - (- 6))² + (y - 2)² = (5 )², that is
(x + 6)² + (y - 2)² = 75
The recursive formula
means that, to compute the next value, you have to double the previous one and then add 5.
So, we start with 5. To get the second term, we double it and add five, so we have
Next, we will double 15 and add 5:
So, the answer is B, because it's the only option starting with 5,15,35.
Just to check, let's compute the last step:
Which confirms option B