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PtichkaEL [24]
3 years ago
5

-5.8c+4.2-3.1+1.4c combine like terms to create an equivalent expression

Mathematics
2 answers:
VMariaS [17]3 years ago
4 0
-5.8c + 4.2 - 3.1 + 1.4c = -4.4c +1.1

Hope this helps! Ask me any questions if needed :)
Vikki [24]3 years ago
3 0
<h2>Answer:</h2>

The equivalent expression to the given expression is:

                    -4.4c+1.1

<h2>Step-by-step explanation:</h2>

We are given an algebraic equation in terms of the variable c as follows:

                          -5.8c+4.2-3.1+1.4c

Now, we will first combine the like term i.e. the terms with the same variable term and the constant terms are combined altogether i.e. the expression is given as follows:

        -5.8c+4.2-3.1+1.4c=-5.8c+1.4c+4.2-3.1

On simplifying this expression we get :

                  -5.8c+4.2-3.1+1.4c=-4.4c+1.1

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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
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Answer:

Part A.

Let f(x) = 0;

suppose x= a+h

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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
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The weights are within 2 standard deviations of the mean are 8.9 lbs, 9.5 lbs and 10.4 lbs

<h3>How to determine the weights?</h3>

The given parameters are:

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The weights within 2 standard deviation is represented as:

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Substitute known values

9.5 - 2(0.5) ≤ x ≤ 9.5 + 2(0.5)

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This means that the weights are between 8.5 and 10.5 (inclusive)

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Answer:

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