3 years ago

Find the missing geometric means in this sequence.

Mathematics

1 answer:

amid [387]3 years ago

3 0

What's the problem?

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Use a linear approximation (or differentials) to estimate the given number. (Round your answer to five decimal places.) 3 217

Soloha48 [4]

Answer:

$f(216) \approx 6.0093$

Step-by-step explanation:

Given

$\sqrt[3]{217}$

Required

Solve

Linear approximated as:

$f(x + \triangle x) \approx f(x) +\triangle x \cdot f'(x)$

Take:

$x = 216; \triangle x= 1$

So:

$f(x) = \sqrt[3]{x}$

Substitute 216 for x

$f(x) = \sqrt[3]{216}$

$f(x) = 6$

So, we have:

$f(x + \triangle x) \approx f(x) +\triangle x \cdot f'(x)$

$f(215 + 1) \approx 6 +1 \cdot f'(x)$

$f(216) \approx 6 +1 \cdot f'(x)$

To calculate f'(x);

We have:

$f(x) = \sqrt[3]{x}$

Rewrite as:

$f(x) = x^\frac{1}{3}$

Differentiate

$f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1}$

Split

$f'(x) = \frac{1}{3} \cdot \frac{x^\frac{1}{3}}{x}$

$f'(x) = \frac{x^\frac{1}{3}}{3x}$

Substitute 216 for x

$f'(216) = \frac{216^\frac{1}{3}}{3*216}$

$f'(216) = \frac{6}{648}$

$f'(216) = \frac{3}{324}$

So:

$f(216) \approx 6 +1 \cdot f'(x)$

$f(216) \approx 6 +1 \cdot \frac{3}{324}$

$f(216) \approx 6 + \frac{3}{324}$

$f(216) \approx 6 + 0.0093$

$f(216) \approx 6.0093$

6 0

3 years ago

The diameter of a circle is 6 inches. What is the circle's circumference?

katrin2010 [14]

Answer:

brainiest? 37.68

Step-by-step explanation:

6 x 2 = 12

12 x 3.14 = 37.68

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3 years ago

If my original price is $60, then the sale price is $45, what is the percent discount

Scorpion4ik [409]

$60 -$45= $15

$15/ $60* 100%= 25%

The percent discount is 25%~

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3 years ago

A basketball team has 9 players. In how many different ways can the coach coach select 2 players to be the captain for tonight's

diamong [38]

Its acctually 36 jnioq54hmkdbf

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Simplify the expression:<br> (2m + 1)(2) =

Dima020 [189]

4m+2

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