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2 years ago

13

Answer please tysm :D i forgot TvT

1 answer:

tiny-mole [99]2 years ago

6 0

Answer:

$f=13$

Step-by-step explanation:

$5\left(f-6\right)=35$

<u>⇒ Divide both sides by 5:</u>

<u /> $\frac{5\left(f-6\right)}{5}=\frac{35}{5}$

$f-6=7$

<u>⇒ Add 6 to both sides :</u>

<u /> $f-6+6=7+6$

$f=13$

<u>OAmalOHopeO</u>

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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

1 year ago

Scaler factor of 1/2

olasank [31]

Dilation by a scale factor of 1/2 followed by a translation of 1.5 units down.

<h3>What is dilation?</h3>

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.

Here, △ HIJ are:

IH = 3

IJ = 4

then using the scale factor = 1/2 we get

Therefore, we have:

I'H '= 1.5

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Hence, dilation by a scale factor of 1/2 followed by a translation of 1.5 units down.

Learn more about this concept here:

brainly.com/question/1011146

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1 year ago

Slope is 3, and (1,4) is on the line.

3241004551 [841]

If you are looking for the equation of the line,

Use Point Slope Form

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$

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4 0

3 years ago

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maksim [4K]

Answer: 37.56

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3756/100= 37.56

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3 years ago

Tape diagram to subtract 33-19

Tpy6a [65]

Well 33 - 19 = 14 and what do u mean tape diagram?

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3 years ago