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mamaluj [8]
3 years ago
15

Find the annual interest rate. I=$16, P=$200, t= 2 years

Mathematics
1 answer:
rjkz [21]3 years ago
7 0

Answer:

The annual interest rate is 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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2 years ago
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Solve equation for the given variable
Alenkinab [10]

Answer:

p=30

Step-by-step explanation:

First, you need to subtract 10 from both sides to get 1/2p=25. You do this just because simplifying is much easier.

Then, you need to isolate p, so you divide 1/2 by both sides, which is the same thing as multiplying by 2. 1/2*2p=15*2.

Simplifying, you get p=30.

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Explain why the absolute value of a number will never be negative
aleksandr82 [10.1K]
The absolute value of a number will never be negative because absolute value is the distance from zero, so it will always be positive. For example, you can't be -6 away from 0, you are 6 away from 0.
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Q: Marci wants to prove that the diagonals of
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Answer: Option B

She should use the fact that the

opposite sides of a parallelogram are

congruent and then use the

Pythagorean theorem.

We cannot use the diagonals of square property because this is a rectangle, opposite angles will also not work, and we cannot use the diagonal property because thats what we have to prove.

Must click thanks and mark brainliest

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3 years ago
6x-7y= -2 please help me
Nana76 [90]

Answer:

X=7/6y+-1/3

Step-by-step explanation:

It will be hard for me to demonstrate the equation

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