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3 years ago

Help me plz 25 points

Mathematics

2 answers:

Leni [432]3 years ago

5 0

That’s not 25 points but ok

Sav [38]3 years ago

3 0

I don’t think that shows 25 point-

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Carl went to the store to buy items for his party.He bought two packs for plates for $3.24 and a pack of cups for $5.70. He also

Andre45 [30]

3.24 + 5.70 + 6.17 = 15.11

20.00 - 15.11 = 5.11

He got 5.11$ of change back.

7 0

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:

Taylor series 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:

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

Taylor Series summation notation:

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

Therefore:

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

7 0

2 years ago

Mr.Changs class has 28 students 4/7 of whom are girls. Which equation shows how to determine the number of girls in Mr. Chang’s

irinina [24]

I think 7 of them are girls and the rest are boys and how i got this answer is I took the 28 and divided it by 4 and got 7.

8 0

3 years ago

Two angles are supplementary if the sum of their measures is 180.

anastassius [24]

True.

two angles would be complementary if the sum of their angle measures is 90 degrees.

60 degrees and 30 degrees make a complementary angle while 90 and 90 degrees make a supplementary angle.

4 0

3 years ago

What is 4x + 2 = 7x + 9

Free_Kalibri [48]

4X=7X+7

-3X=7

X= -3/7

8 0

3 years ago

Read 2 more answers

Help me plz 25 points ​

Help me plz 25 points