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2 years ago

ASAP!!!!!!!!! Please show process!!! Using law of sines!!!!!!!! Thank you so much

Mathematics

1 answer:

Flauer [41]2 years ago

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Answer:

the answers are on the picture but the numbers may be rounded

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Find the third order maclaurin polynomial. Use it to estimate the value of sqrt1.3

vodka [1.7K]

$\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}$ is the maclaurin polynomial and estimate value of $\sqrt{1.3}$ is 1.14. This can be obtained by using the formula to find the maclaurin polynomial.

<h3>Find the third order maclaurin polynomial:</h3>

Given the polynomial,

$f(x)=\sqrt{1+3x}=(1+3x)^{\frac{1}{2} }$

The formula to find the maclaurin polynomial,

$f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}$

Next we have to find f'(x), f''(x) and f'''(x),

$f'(x) = \frac{3}{2}(1+3x)^{-\frac{1}{2} }$

$f''(x) =-\frac{9}{4}(1+3x)^{-\frac{3}{2} }$

$f'''(x) = \frac{81}{8}(1+3x)^{-\frac{5}{2} }$

By putting x = 0 , we get,

$f(0)=(1+3(0))^{\frac{1}{2} }=1$

$f'(0) = \frac{3}{2}(1+3(0))^{-\frac{1}{2} }=\frac{3}{2}$

$f''(0) =-\frac{9}{4}(1+3(0))^{-\frac{3}{2} }=-\frac{9}{4}$

$f'''(0) = \frac{81}{8}(1+3(0))^{-\frac{5}{2} }=\frac{81}{8}$

Therefore the maclaurin polynomial by using the formula will be,

$\sqrt{1+3x}=f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}$

$\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}$

To find the value of $\sqrt{1.3}$ we can use the maclaurin polynomial,

$\sqrt{1.3}$ is $\sqrt{1+3x}$ with x = 1/10,

$\sqrt{1+3(1/10)}=1+\frac{3}{2} (1/10)-\frac{9}{8} (1/10)^{2} + \frac{81}{8}(1/10)^{3}$

$\sqrt{1+3(1/10)}=\frac{18247}{16000} = 1.14$

Hence $\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}$ is the maclaurin polynomial and estimate value of $\sqrt{1.3}$ is 1.14.

Learn more about maclaurin polynomial here:

brainly.com/question/24188694

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6 0

2 years ago

Read 2 more answers

I need answers to these MCAS practice questions ASAP!

Semmy [17]

I’ve attached a photo with my work ....
Hope it helps!!

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3 years ago

Find the slope of the line 25 POINTS WILL MARK BRANLIST

UNO [17]

Answer:

-7/4

Step-by-step explanation:

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3 years ago

A triangle has angle measurements of 56°, 54°, and 70°. What kind of triangle is it?

alexira [117]

Answer:

Right, I am an idiot so i might be wrong

Step-by-step explanation:

Every triangle has three angles which sum to 180 degrees.

There are three types of triangles based on the measures of its angles.

Right Triangle - Has one 90 degree angle

Acute Triangle - All angles less than 90 degrees

Obtuse Triangle - One angle greater than 90 degrees

In this example we are given 2 angles and must find the measure of the 3rd.

a + 56 + 34 = 180

a + 90 = 180

a = 90

Therefore, it is a Right Triangle.

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3 years ago

What’s the answer to this problem?

Sergio039 [100]

Answer: the answer is 0

Step-by-step explanation:

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3 years ago