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2 years ago

Does (2, -1) make this a true statement? Why or why not? 3x + 2y = 4

Mathematics

1 answer:

kvv77 [185]2 years ago

3 0

Answer: Yes

Step-by-step explanation:

So a coordinate pair is always set up (x,y) so you plug the x term in the coordinate pair into the x in the equation and the y term in for the y. 3×2 + 2×-1. Multiply them together and you end up with 4.

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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

#SPJ1

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1 year ago

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How to rename fraction

frosja888 [35]

Identify the improper fraction. The improper fraction will have a higher number on top than on the bottom. For example, 7/4.Divide the top number, or numerator, by the bottom number, the denominator, to determine how many times the denominator fits into the numerator. In the 7/4 example, the denominator fits in one time, leaving three left over.Write the amount of times the denominator fits into the numerator as a whole number. In the 7/4 example, the answer is "1."Display the leftover number as a fraction on the right side of the whole number. In the 7/4 example, the answer is "3/4," since 7 divided by 4 equals 1 with a remainder of 3. The mixed number should look like this: "1 3/4."

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2 years ago

Solve for n. 8 3/4 + n + 2 3/8 + 4 1/2 = 23 1/8 A. 7 1/2 B. 8 3/8 C. 15 5/8 D. 8 4/8

Sonbull [250]

You can change all of these to decimals and then solve or get common denominators.
8.75 + n + 2.375 + 4.5 = 23.125
15.625 + n = 23.125
Subtract 15.625 from both sides
n = 7.5

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2 years ago

322 ÷ 14 using partial quotients

Nezavi [6.7K]

What exactly are partial quotients? Normal divisions says the answer is twenty three

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3 years ago

A teacher divided students into groups of 3. Each group of 3 wrote a report that had 9 pictures in it. The students used 585 pic

jeyben [28]

So this is what i did but im not sure if its 100% correct

585 / 9 to get the number of groups = 65

then you take 65 x 3 for number of students in each group and you get the final answer of 195 students

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2 years ago

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