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ch4aika [34]
3 years ago
10

Estimating a square root.

Mathematics
2 answers:
timama [110]3 years ago
8 0
The way that cheap calculators do it is with Newton's approximation.

x=√n

x^2=n

x^2-n=0

Newton's approximation is:

x-f(x)/(dy/dx)

x-(x^2-n)/(2x) which if you include the improved approximation

(2x^2-x^2+n)/(2x)

x↔(x^2+n)/(2x)

It converges very quickly to the exact answer (if there is one) with relatively few iterations...

For example:  √5 ?  take an initial guess of 2 and you get:

(x^2+5)/(2x)

2, 2.25, 2.2361, 2.2360, 2.236067977499
Digiron [165]3 years ago
5 0
I'm sorry but I'm not into square roots yet :(
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the length of a rectangle exceeds its width by 17 inches, and the area is 18 square inches. what are the length and width of the
dimaraw [331]

The length and width of the rectangle are 18 in and 1 in, respectively.

<h3>Quadrilaterals</h3>

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle can be found for the formula : b*h, where b = base and h =height.

For this question, the length exceeds its width by 17 inches - L=W+17. Here, the length is the base and the width is the height. Thus,  from the value of area given, you can find the values of the length and width of the rectangle.

A=b*h

18=(W+17)*W

18=W²+17W

W²+17W-18=0

Solving this quadratic equation, you have:

w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}

w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}

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For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.

As, the area (l*w) is 18 in², see.

18=l*w

18=l*1

l=18 in

Read more about the area of rectangle here:

brainly.com/question/25292087

#SPJ1

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