Circle X with a radius of 6 units and circle Y with a radius
1 answer:
Answer:
Option C.
Step-by-step explanation:
It is given that radius of circle X is 6 units and radius of circle Y is 2 units.
Here, circle Y is smaller and circle X is larger.
If we translate the circles so they share a common center point, and after that we dilate circle Y by a scale factor of 3, then we get circle which is equal to circle X.
We know that, after dilation the figure and its image are similar.
Hence, we can say that both circles are similar.
Therefore, the correct option is C.
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Answer:
Step-by-step explanation:
As per the question,
let us consider f(x) = tan(x).
We know that <u>The Maclaurin series is given by:</u>
So, differentiate the given function 3 times in order to find f'(x), f''(x) and f'''(x).
Therefore,
f'(x) = sec²x
f''(x) = 2 × sec(x) × sec(x)tan(x)
= 2 × sec²(x) × tan(x)
f'''(x) = 2 × 2 sec²(x) tan(x) tan(x) + 2 sec²(x) × sec²(x)
= 4sec²(x) tan²(x) + 2sec⁴(x)
= 6 sec⁴x - 4 sec² x
We then substitute x with 0, and find the values
f(0) = tan 0 = 0
f'(0) = sec²0 = 1
f''(0) = 2 × sec²(0) × tan(0) = 0
f'''(0) = 6 sec⁴0- 4 sec² 0 = 2
By putting all the values in the Maclaurin series, we get
Therefore, the expansion of tan x at x = 0 is
.