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Bad White [126]
3 years ago
8

One circular table has a diameter of 9 ft, and another circular table has a diameter of 20 ft. How much greater is the area of t

he larger table? Round to the nearest whole number.
Mathematics
1 answer:
OleMash [197]3 years ago
3 0

Answer:

180

Step-by-step explanation:

20×9=180

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In the derivation of Newton’s method, to determine the formula for xi+1, the function f(x) is approximated using a first-order T
dimaraw [331]

Answer:

Part A.

Let f(x) = 0;

suppose x= a+h

such that f(x) =f(a+h) = 0

By second order Taylor approximation, we get

f(a) + hf'±(a) + \frac{h^{2} }{2!}f''(a) = 0

h = \frac{-f'(a) }{f''(a)} ± \frac{\sqrt[]{(f'(a))^{2}-2f(a)f''(a) } }{f''(a)}

So, we get the succeeding equation for Newton's method as

x_{i+1} = x_{i} + \frac{1}{f''x_{i}}  [-f'(x_{i}) ± \sqrt{f(x_{i})^{2}-2fx_{i}f''x_{i} } ]

Part B.

It is evident that Newton's method fails in two cases, as:

1.  if f''(x) = 0

2. if f'(x)² is less than 2f(x)f''(x)    

Part C.

In case  x_{i+1} is close to x_{i}, the choice that shouldbe made instead of ± in part A is:

f'(x) = \sqrt{f'(x)^{2} - 2f(x)f''(x)}  ⇔ x_{i+1} = x_{i}

Part D.

As given x_{i+1} = x_{i} = h

or                 h = x_{i+1} - x_{i}

We get,

f(a) + hf'(a) +(h²/2)f''(a) = 0

or h² = -hf(a)/f'(a)

Also,             (x_{i+1}-x_{i})² = -(x_{i+1}-x_{i})(f(x_{i})/f'(x_{i}))

So,                f(a) + hf'(a) - (f''(a)/2)(hf(a)/f'(a)) = 0

It becomes   h = -f(a)/f'(a) + (h/2)[f''(a)f(a)/(f(a))²]

Also,             x_{i+1} = x_{i} -f(x_{i})/f'(x_{i}) + [(x_{i+1} - x_{i})f''(x_{i})f(x_{i})]/[2(f'(x_{i}))²]

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3 years ago
Select all irrational numbers. 1/8 1/2 1/4 1/10 1/16
ludmilkaskok [199]
None of them are irrational, the definition of an irrational number is a number that cannot be simplified, converted to a fraction, or has no pattern to it or is never ending. For example, a pi is an irrational number because it is never ending and has no pattern to it. Another example would be 0.21411446741354...  irrational because it has no pattern to it and cannot be converted to a fraction.
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3 years ago
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DochEvi [55]

6.4/3.5, OR about 1.83

First job is to isolate the y.

3.5y=6.4x+7

Now divide both sides by 3.5 to get the equation into y=mx+b form.

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point J (1, -3.5)

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JulijaS [17]

Answer:

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Step-by-step explanation:

The formula for slope is y2-y1/x2-x1. Take coordinate (0,-2), which is the y-intercept. We'll call that (y2,x2). Coordinate (8,-3) is (y1,x1). Put that into the formula you get, 0-8/-2-(-3). You get -8/1 which is negative 8. We now have the slope. Slope intercept form equation is y=mx+b. M is slope, so we put our slope in the equation and get, y=-8x+b. B is the y-intercept which is given. So we know that the equation to this line in slope-intercept form is y=-8x-2.

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3 years ago
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