3 years ago

How many elements are in the intersection of the set 1,4,7,10,...,61 and the set 1,6,11,16,...,61

Mathematics

1 answer:

LekaFEV [45]3 years ago

5 0

Gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg

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Enter the coefficients of the fifth Taylor polynomial T5(x) for the function f(x) = x5−3x4+2x2+5x−2 based at b=1. T5(x)= + (x−1)

DENIUS [597]

Compute the necessary values/derivatives of $f(x)$ at $x=1$ :

$f(1)=3$

$f'(1)=2$

$f''(1)=-12$

$f'''(1)=-12$

$f^{(4)}(1)=48$

$f^{(5)}(1)=120$

Taylor's theorem then says we can "approximate" (in quotes because the Taylor polynomial for a polynomial is another, exact polynomial) $f(x)$ at $x=1$ by

$T_5(x)=\dfrac3{0!}+\dfrac2{1!}(x-1)-\dfrac{12}{2!}(x-1)^2-\dfrac{12}{3!}(x-1)^3+\dfrac{48}{4!}(x-1)^4+\dfrac{120}{5!}(x-1)^5$

$T_5(x)=3+2(x-1)-6(x-1)^2-2(x-1)^3+2(x-1)^4+(x-1)^5$

###

Another way of doing this would be to solve for the coefficients $a,b,c,d,e,g$ in

$f(x)=a+b(x-1)+c(x-1)^2+d(x-1)^3+e(x-1)^4+g(x-1)^5$

by expanding the right hand side and matching up terms with the same power of $x$ .

5 0

3 years ago

Which one is an expression of distance in si units?

Arada [10]

D.500 meters is an expression of distance in SI units.

8 0

3 years ago

What is the approximate distance between the points (-3, -4) and (-8, 1) on a coordinate grid

tatyana61 [14]

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -3 &,& -4~) 
% (c,d)
&&(~ -8 &,& 1~)
\end{array}\\\\\\ % distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{[-8-(-3)]^2+[1-(-4)]^2}\implies d=\sqrt{(-8+3)^2+(1+4)^2}
\\\\\\
d=\sqrt{25+25}\implies d=\sqrt{2\cdot 25}\implies d=\sqrt{2\cdot 5^2}\implies d=5\sqrt{2}$