Write the expression as a square of a binomial: 9/25a^6b^2-a^4b^4+25/36a^2b^6
1 answer:
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Looks like your function is
Rewrite it as
Recall that for , we have
If we replace with
, we get
By the ratio test, the series converges if
Solving for gives the interval of convergence,
We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.
Answer:
890 beads can be fitted in the triangular prism.
Step-by-step explanation:
If we can fill the spherical beads completely in the triangular prism,
Volume of the triangular prism = Volume of the spherical beads
Volume of triangular prism = Area of the triangular base × Height
From the picture attached,
Area of the triangular base =
=
By applying Pythagoras theorem in the given triangle,
AC² = AB² + BC²
(13)² = 5² + BC²
169 = 25 + BC²
BC² = 144
BC = 12
Area of the triangular base =
= 30 cm²
Height of the triangular prism = 18 cm
Volume of the triangular prism = 30 × 18
= 540 cm³
Volume of one spherical bead =
=
= 0.606 cm³
Let there are 'n' beads in the triangular prism,
Volume of 'n' beads = Volume of the prism
540 = 0.606n
n = 890.90
n ≈ 890
Therefore, 890 beads can be fitted in the triangular prism.
