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1 year ago

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Part 1: About how tall is the actual Willis Tower? About how tall is the actual Great Pyramid? Be prepared to explain your reaso

ning.

1 answer:

lesantik [10]1 year ago

3 0

100 m and 300 m based off the graph the Willis is 3x the size of the great Pyramid

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The volume of the right triangular prism is 91.8ft. The height of the prism is 10.8ft. What is the area of each base? Show your

kaheart [24]

Answer:

8.5 ft.

Step-by-step explanation:

We'll use this right triangular prism volume formula: base area x height = volume

base area = ?

length = 10.8

volume = 91.8

base area x 10.8 = 91.8

Divide both sides by 10.8

base area x 10.8/10.8 = 91.8/10.8

base area = 8.5

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2 years ago

Sole the question l2l

Feliz [49]

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2 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:

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

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1 year ago

Solve for x<br>2x+4(2x+7)=3(2x+4)??

xeze [42]

Answer
It’s x= -4 for sure

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2 years ago

Seven-eighths minus five-twelfths

Elenna [48]

The answer to your question is A, 11/24

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2 years ago

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