Please help me find the area of the triangles in the picture shown below.
2 answers:
Answer:
1) 6
2) 20
3) 45
Step-by-step explanation:
To find the area of a triangle, use the formula , where
represents the length of the base, and
represents the height. In the first triangle, the base length is 4 and the height is 3, so the area is 6. In the second triangle, the base length is 5 and the height is 8, so the area is 20. In the third triangle, the base length is 15 and the height is 6, so the area is 45.
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The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.
<h3>Find the radius of convergence R and the interval of convergence:</h3>Ratio test is the test that is used to find the convergence of the given power series.
First aₙ is noted and then aₙ₊₁ is noted.
For ∑ aₙ, aₙ and aₙ₊₁ is noted.
= β
- If β < 1, then the series converges
- If β > 1, then the series diverges
- If β = 1, then the series inconclusive
Here =
and
=
Now limit is taken,
=
=
=
=
= < 1
- 1 < < 1
- 1 - 2 < x < 1 - 2
- 3 < x < - 1
We get that,
interval of convergence = (-3, -1)
radius of convergence R = 1
Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.
Learn more about radius of convergence here:
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