1) 615 Is Rational or irrational
2 answers:
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Answer:
Step-by-step explanation:
The point P(1,0) and T are on the unit circle C and the arc length from P to T is x.
Let us assume that point P - x i.e. the point obtained by moving clock wise direction along the circle from P is T'.
Because of the symmetry of the circle about the coordinate axes, the x-coordinate of point T' will be and the y-coordinate will be
.
So, coordinates of T' are .
Here we must notice that point T' is the reflection point of T with respect to X-axis. (Answer)
Answer:
The series CONVERGES with the sum being 6.25.
Step-by-step explanation:
Given that the geometric series is 10 - 6 + 3.6 - 2.16 + ....
So the first term of the geometric progression is, = 10
The second term of the geometric progression is = -6 =
× r = 10 × r
where r is the constant ratio.
Therefore r = = -0.6
The third term of the geometric progression, = 3.6 =
× r = -6 × -0.6 = 3.6
The fourth term of the geometric progression, = -2.16 =
× r = 3.6 × -0.6 = -2.16
So the above confirms that the series is indeed a geometric progression with first term, = 10 and constant ratio, r = -0.6
Now to find if the series converges or diverges we can take sum of the series from first term to infinity.
We can already infer that the series is convergent since the constant ratio, r = -0.6 which is less than 1.
So from the formula for the sum to infinity of a geometric progression, S, we get
S =
So the series is convergent with the sum being 6.25