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storchak [24]
3 years ago
5

The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in

the bank account:
x g(x)
0 $600
3 $720
6 $840

Part A: Find and interpret the slope of the function. (3 points)

Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)

Part C: Write the equation of the line using function notation. (2 points)

Part D: What is the balance in the bank account after 7 days? (2 points)

- Im so confused pleas esomeone
Mathematics
1 answer:
schepotkina [342]3 years ago
7 0

Answer:

Step-by-step explanation:

um confused

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Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of
Black_prince [1.1K]

Answer:

The first four nonzero terms of the Taylor series of \frac{7}{x + 1} around a=2 are:

f\left(x\right)\approx P\left(x\right) = \frac{7}{3}- \frac{7}{9}\left(x-2\right)+\frac{7}{27}\left(x-2\right)^{2}- \frac{7}{81}\left(x-2\right)^{3}+\frac{7}{243}\left(x-2\right)^{4}

Step-by-step explanation:

The Taylor series of the function <em>f </em>at <em>a </em>(or about <em>a</em> or centered at <em>a</em>) is given by

f\left(x\right)=\sum\limits_{k=0}^{\infty}\frac{f^{(k)}\left(a\right)}{k!}\left(x-a\right)^k

To find the first four nonzero terms of the Taylor series of \frac{7}{x + 1} around a=2 you must:

In our case,

f\left(x\right) \approx P\left(x\right) = \sum\limits_{k=0}^{n}\frac{f^{(k)}\left(a\right)}{k!}\left(x-a\right)^k=\sum\limits_{k=0}^{4}\frac{f^{(k)}\left(a\right)}{k!}\left(x-a\right)^k

So, what we need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.

  • f^{(0)}\left(x\right)=f\left(x\right)=\frac{7}{x + 1}

Evaluate the function at the point: f\left(2\right)=\frac{7}{3}

  • f^{(1)}\left(x\right)=\left(f^{(0)}\left(x\right)\right)^{\prime}=\left(\frac{7}{x + 1}\right)^{\prime}=- \frac{7}{\left(x + 1\right)^{2}}

Evaluate the function at the point: \left(f\left(2\right)\right)^{\prime }=- \frac{7}{9}

  • f^{(2)}\left(x\right)=\left(f^{(1)}\left(x\right)\right)^{\prime}=\left(- \frac{7}{\left(x + 1\right)^{2}}\right)^{\prime}=\frac{14}{\left(x + 1\right)^{3}}

Evaluate the function at the point: \left(f\left(2\right)\right)^{\prime \prime }=\frac{14}{27}

  • f^{(3)}\left(x\right)=\left(f^{(2)}\left(x\right)\right)^{\prime}=\left(\frac{14}{\left(x + 1\right)^{3}}\right)^{\prime}=- \frac{42}{\left(x + 1\right)^{4}}

Evaluate the function at the point: \left(f\left(2\right)\right)^{\prime \prime \prime }=- \frac{14}{27}

  • f^{(4)}\left(x\right)=\left(f^{(3)}\left(x\right)\right)^{\prime}=\left(- \frac{42}{\left(x + 1\right)^{4}}\right)^{\prime}=\frac{168}{\left(x + 1\right)^{5}}

Evaluate the function at the point: \left(f\left(2\right)\right)^{\prime \prime \prime \prime }=\frac{56}{81}

Apply the Taylor series definition:

f\left(x\right)\approx\frac{\frac{7}{3}}{0!}\left(x-\left(2\right)\right)^{0}+\frac{- \frac{7}{9}}{1!}\left(x-\left(2\right)\right)^{1}+\frac{\frac{14}{27}}{2!}\left(x-\left(2\right)\right)^{2}+\frac{- \frac{14}{27}}{3!}\left(x-\left(2\right)\right)^{3}+\frac{\frac{56}{81}}{4!}\left(x-\left(2\right)\right)^{4}

The first four nonzero terms of the Taylor series of \frac{7}{x + 1} around a=2 are:

f\left(x\right)\approx P\left(x\right) = \frac{7}{3}- \frac{7}{9}\left(x-2\right)+\frac{7}{27}\left(x-2\right)^{2}- \frac{7}{81}\left(x-2\right)^{3}+\frac{7}{243}\left(x-2\right)^{4}

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On a coordinate plane, 4 lines are shown. Line L M goes through (negative 5, negative 3) and (0, 3). Line N O goes through (nega
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Answer:

The slope of line LM is perpendicular to the given line.

Step-by-step explanation:

L (- 5, - 3), M (0, 3)

N (- 6, - 5) , O (0, 0)

J (- 6, 1) , K (0, - 4)

Slope of given line = -5/6

Slope of perpendicular line = 6/5

Slope of line LM

\frac{3 + 3}{0 + 5}=\frac{6}{5}

Slope of line NO

\frac{0+5}{0+6}=\frac{5}{6}

Slope of line JK

\frac{-4-1}{0+6}=\frac{-5}{6}

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Answer:

60 lb. 17 oz

Step-by-step explanation:

Just add each same values together.

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Answer:

These are all points on a graph. I'm not sure what you're asking.

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Simplify 3x + 6x 2 - 5x - x 2
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