Question

7. The table gives the distances in nautical miles of the visible horizon for the given heights in feet above the
earth's surface:
X= height 100 150 200 250 300 350 400
Y= distance 10.63 13.03 15.04 16.81 18.42 19.90 21.27
Find the values of y when (i) x= 160 ft and x= 410 ft.​

Answer 1

1. bet 10.63 and 13.03
2. greater then 19.90

Answer 2

Answer:

Solution of newton's backward interpolation method $y(160)=13.4573$

Solution of newton's backward interpolation method $y(410)=21.5352$

Explanation:

The intial table is attached as table1.png

The value of $x$ at you want to find the$f(x): x=160$

$\begin{aligned}&h=x_{1}-x_{0}=150-100=50 \\&p=\frac{x-x_{0}}{h}=\frac{160-100}{50}=1.2\end{aligned}$

Solution of newton's forward interpolation method $y(160)=13.4573$

The value of $x$ at you want to find the $f(x): x=410$

$\begin{aligned}&h=x_{1}-x_{0}=150-100=50 \\&p=\frac{x-x_{0}}{h}=\frac{410-100}{50}=6.2\end{aligned}$

Newton's forward difference interpolation formula is table12.png

The value of $x$ at you want to find the $f(x): x=160$

$\begin{aligned}&h=x_{1}-x_{0}=150-100=50 \\&p=\frac{x-x_{n}}{h}=\frac{160-400}{50}=-4.8\end{aligned}$

Newton's backward difference interpolation formula is table13.png

Solution of newton's backward interpolation method $y(160)=13.4573$

The value of $x$at you want to find the $f(x): x=410$

$\begin{aligned}&h=x_{1}-x_{0}=150-100=50 \\&p=\frac{x-x_{n}}{h}=\frac{410-400}{50}=0.2\end{aligned}$

Newton's backward difference interpolation formula is

Solution of newton's backward interpolation method $y(410)=21.5352$