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juin [17]
3 years ago
13

Explain how to use the distributive property to create an expression that is equivalent to 2b + 5b

Mathematics
1 answer:
yuradex [85]3 years ago
3 0

Answer:7b

Step-by-step explanation:

2b+5b

7b

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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

6 0
1 year ago
Read 2 more answers
The formula A = Pe^rt calculates the amount an investment earning a nominal rate of r compounded continuously is worth. Show tha
8090 [49]

Answer:

t = In2/ r

Step-by-step explanation:

Given the formula : A = Pe^rt

For investment to double ;

Final amount (A) = 2 * initial investment (p)

A = 2p

Hence,

2p = pe^rt

2 = e^rt

Take the In of both sides

In2 = rt

Divide both sides by r

In2 /r = rt /r

In2/ r = t

t = In2/ r ; Hence, the proof

5 0
3 years ago
Help me anyone that great in math
pochemuha

Answer:

B) 24/35

Step-by-step explanation:

Cos(X)= Adjacent/Hypotenuse

Cos(X) = 24/25

Therefore, option B is your answer.

Hope this answers your question!!

6 0
2 years ago
Htdtdeyt5ey5jed6yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuurrrrrrrrrrrrrrrrrrrrrrrrrr
raketka [301]

Answer: ok LOL thx XD

Step-by-step explanation: BRAINLIEST PLS

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3 years ago
What is 363.3 times 3456.2
KonstantinChe [14]

Answer: 1255637.46

Step-by-step explanation: asked my teacher

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3 years ago
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