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7nadin3 [17]
3 years ago
14

If six more than the product of a number and -2 is greater than 10, which of the following could be that number

Mathematics
1 answer:
laiz [17]3 years ago
7 0
To get that number in the problem, you need to translate first the word problem into mathematical expression.

We will let x as the number.
six more than the product of a number and -2 is greater than 10 can be written as  (-2x) + 6 > 10
We will now solve for x to get the number.
         (-2x) + 6 > 10
Add -6 to both sides of the equation
      -2x + 6 - 6 > 10 - 6
                  -2x > 4
Divide both sides of the equation with -2
Take note that if we divide a negative number in inequality, the inequality symbol will be change from greater than to less or from less than to greater than.
             -2x / -2< 4 / -2
                     x < -2

Therefore, the number that we are looking for is less than -2.

 

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Find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that
Bond [772]

Taylor series is f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2}  }

To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have

f(x) = ln(x)

f^{1}(x)= \frac{1}{x} \\f^{2}(x)= -\frac{1}{x^{2} }\\f^{3}(x)= -\frac{2}{x^{3} }\\f^{4}(x)= \frac{-6}{x^{4} }

.

.

.

Since we need to have it centered at 9, we must take the value of f(9), and so on.

f(9) = ln(9)

f^{1}(9)= \frac{1}{9} \\f^{2}(9)= -\frac{1}{9^{2} }\\f^{3}(x)= -\frac{1(2)}{9^{3} }\\f^{4}(x)= \frac{-1(2)(3)}{9^{4} }

.

.

.

Following the pattern, we can see that for f^{n}(x),

f^{n}(x)=(-1)^{n-1}\frac{1.2.3.4.5...........(n-1)}{9^{n} }  \\f^{n}(x)=(-1)^{n-1}\frac{(n-1)!}{9^{n}}

This applies for n ≥ 1, Expressing f(x) in summation, we have

\sum_{n=0}^{\infinite} \frac{f^{n}(9) }{n!} (x-9)^{2}

Combining ln2 with the rest of series, we have

f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2}  }

Taylor series is f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2}  }

Find out more information about taylor series here

brainly.com/question/13057266

#SPJ4

3 0
1 year ago
Solve the equation 4(3-2x)=22
jeka94
<span>4(3-2x)=22
4(3) - 4(2x) = 22
12 - 8x = 22
8x = 12 - 22
8x = -10
x = -10/8 = -5/4 
or
x = -1.25</span>
8 0
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6 0
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:Phil’s age decreased by 9 years is 14 years ?
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Answer:

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Step-by-step explanation:

Add 14 to 9 and you get 23. So then you subtract 9 from 23

8 0
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Ben wants to estimate the cost of dinner and a movie for himself and his friend. He knows the following information
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Answer:

B. $3100

Step-by-step explanation:

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5 0
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