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Andrei [34K]
3 years ago
15

What is the pythetherom

Mathematics
1 answer:
pashok25 [27]3 years ago
8 0

Answer:

The Pythagorean Theorem states: In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).  

The Pythagorean theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:  

a2 + b2 = c2

Step-by-step explanation:


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He length of a rectangle is 1 inch less than twice it's width. If the width is w inches,which expression gives the length?
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L= 2w-1 Is your answer
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Find f(-5) of f (x) = x + 1<br> 1) 4<br> 2) 5<br> 6) 6
Alex
F(-5) just means that your substituting the number -5 for every x value. So if you have x+1 this would be -5+1 which is -4
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Use the definition of a Taylor series to find the first three non zero terms of the Taylor series for the given function centere
Ket [755]

Answer:

e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...

\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n

Step-by-step explanation:

<u>Taylor series</u> expansions of f(x) at the point x = a

\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...

This expansion is valid only if \text{f}\:^{(n)}(a) exists and is finite for all n \in \mathbb{N}, and for values of x for which the infinite series converges.

\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1

\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...

\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If  $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}

\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4

\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4

\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4

Substituting the values in the series expansion gives:

e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...

Factoring out e⁴:

e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right]

<u>Taylor Series summation notation</u>:

\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n

Therefore:

\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n

7 0
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In the image, shape ABCD is similar to shape WXYZ. Find the measure of side ZW.
vladimir2022 [97]

Solution:

we are given that

In the image, shape ABCD is similar to shape WXYZ.

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As we know that when two shapes are similar then the ratios of their corresponding sides are equal.

So we can write

\frac{zw}{6}= \frac{18}{24}\\&#10;\\&#10;ZW=6*\frac{18}{24}\\&#10;\\&#10;ZW=\frac{18}{4}\\&#10;\\&#10;ZW=4.5\\

Hence ZW=4.5 Inches.

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Use Gauss's approach to find the sum. 1+3+5+7+...+1001
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1017, maybe, i hope its right, sorry if its not:)
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2 years ago
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