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2 years ago

Subtract w from u, then subtract v from the result

Mathematics

1 answer:

MrRa [10]2 years ago

6 0

Answer:

2-u=y

y-v

Step-by-step explanation:

Assume that the asnwer is Y so the equatio would be.

2-u=y

y-v

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The function y = (x - 4)2 + 3 is a transformation of the function y = x?. How is the function's vertex affected by the

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Answer:

The vertex of the graph of y = x is shifted to the right 3 units and up 4 units.

The vertex of the graph of y = x?is shifted to the right 4 units and up 3 units.

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3 years ago

Find the area of the following shape. You must show all work to receive credit.

almond37 [142]

Answer:

Step-by-step explanation:

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3 years ago

Use the definition of a Taylor series to find the first three non zero terms of the Taylor series for the given function centere

Ket [755]

Answer:

$e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...$

$\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n$

Step-by-step explanation:

<u>Taylor series</u> expansions of f(x) at the point x = a

$\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...$

This expansion is valid only if $\text{f}\:^{(n)}(a)$ exists and is finite for all $n \in \mathbb{N}$ , and for values of x for which the infinite series converges.

$\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1$

$\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...$

$\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}$

$\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4$

$\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4$

$\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4$

Substituting the values in the series expansion gives:

$e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...$

Factoring out e⁴:

$e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right]$

<u>Taylor Series summation notation</u>:

$\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n$

Therefore:

$\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n$

7 0

2 years ago

Mrs. Gordon had $40 to spend on cookies and pies. She bought 4 cookies, each of which cost $3. She spent twice as much on pies a

DiKsa [7]

First, multiply $3 by 4 to get $12 spent on cookies. Then, you multiply $12 by 2 to know that the pies cost $24. You then divide the $24 by 3 to get $6 per pie. Meaning, each pie had cost $6. You add the $12 and $24 together to get $36. Finally, you subtract $36 from $40 to know that she only has $4 left.

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3 years ago

The vertices of a right triangle are (6, 2), (–2, –4), and (–2, y).

aksik [14]

The answer should be C. 2
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3 years ago

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