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2 years ago

The first term of a geometric sequence is 10,000 and the common ratio is 0.4. What

Mathematics

1 answer:

Misha Larkins [42]2 years ago

7 0

$a = 10000$

$r = 0.4 = 4/10 = 2/5$

$a_9 = ar^8 = 10000 × 2^8/5^8$

$a_9 = 10000 × 256/(25 × 25 × 25 × 25)$

$a_9 = 6.5536$

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<h2>Answer:</h2>

$\boxed{\overline{MN}=37.96}$

<h2>Step-by-step explanation:</h2>

For a better understanding of this problem, see the figure below. Our goal is to find $\overline{MN}$ . Since:

$\angle MRS=\angle MQP=90^{\circ} \\ \\ \overline{MQ}=\overline{MR}=30mm$

and $\overline{MN}$ is a common side both for ΔMRN and ΔMQN, then by SAS postulate, these two triangles are congruent and:

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By Pythagorean theorem, for triangle NQP:

$\overline{QN}=\sqrt{\overline{NP}^2+\overline{QP}^2} \\ \\ \overline{QN}=\sqrt{10^2+21^2} \\ \\ \overline{QN}=\sqrt{541}$

Applying Pythagorean theorem again, but for triangle MQN:

$\overline{MN}=\sqrt{\overline{MQ}^2+\overline{QN}^2} \\ \\ \overline{MN}=\sqrt{30^2+(\sqrt{541})^2} \\ \\ \boxed{\overline{MN}=37.96}$

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