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2 years ago

13. For the following sequence.

Mathematics

1 answer:

ad-work [718]2 years ago

4 0

The term rule is given by a(n) = 1/3 + (n - 1)(1/3) while the 12th term is of the series is 4.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

From the series:

First term (a) = 1/3; common difference (d) = 2/3 - 1/3 = 1 - 2/3 = 1/3

The term rule is given by:

a(n) = a + (n - 1)d = 1/3 + (n - 1)(1/3)

The 12 term is:

a(12) = 1/3 + (12 - 1)(1/3) = 4

The term rule is given by a(n) = 1/3 + (n - 1)(1/3) while the 12th term is of the series is 4.

Find out more on equation at: brainly.com/question/2972832

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kodGreya [7K]

Answer:

Hence, the ratios are given by 5:7, 25:49, 125:343.

Step-by-step explanation:

We are given two spheres such that:

Volume of small sphere $V_{s}$ = 250 $yd^{3}$

Volume of large sphere $V_{l}$ = 686 $yd^{3}$ .

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Since, the volume of a sphere = $\frac{4 \pi \times r^{3}}{3}$ , this gives us that the ratio of the radius = ∛ $V_{s}$ : ∛ $V_{l}$

i.e. The ratio of the radius = ∛125 : ∛343 = 5 : 7.

Further, as the surface area of a sphere = $4 \pi \times r^{2}$ , this gives us that the ratioof surface area = $r_{s} ^{2}$ : $r_{l} ^{2}$

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3 years ago

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ZanzabumX [31]

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3 years ago

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$(8a^{-3})^{\frac{-2}{3}} = \frac{a^2}{4}$

Solution:

Given that,

$(8a^{-3})^{\frac{-2}{3}$

We have to write in simplest form

Use the following law of exponent

$(a^m)^n = a^{mn}$

Using this, simplify the given expression

$(8a^{-3})^{\frac{-2}{3}} = 8^{\frac{-2}{3}} \times a^{ -3 \times \frac{-2}{3}}\\\\Simplifying\ we\ get\\\\(8a^{-3})^{\frac{-2}{3}} = 8^{\frac{-2}{3}} \times a^2\\\\We\ know\ that\ 8 = 2^3\\\\Therefore\\\\(8a^{-3})^{\frac{-2}{3}} =2^3^{\frac{-2}{3}} \times a^2\\\\(8a^{-3})^{\frac{-2}{3}} =2^{-2} \times a^2\\\\(8a^{-3})^{\frac{-2}{3}} = \frac{a^2}{4}$

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dem82 [27]

Answer:

This is your answer.

Step-by-step explanation:

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