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2 years ago

9

GEOMETRY - I NEED HELP!!!

1 answer:

Ainat [17]2 years ago

3 0

Answer:

angle DLM= 21+50=71 degrees i think

Step-by-step explanation:

take the 2 from 2x and divide 42 by the 2 and you have your variable x solved

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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

Help! Multiplying rational expressions

Ber [7]

I worked them out on paper. I hope this helps. There’s a picture of the work.

8 0

2 years ago

Please answer this question!! (Language)

stepan [7]

It is true, the predicate is the action part of a sentence. So the object or noun would be separated by a verb.

8 0

2 years ago

Francisco’s recipe for cookies calls for 3/4 cups of sugar, 2 1/2 cups of flour and 3 eggs.If you want to use half as much sugar

LenaWriter [7]

Answer:

1.125

Step-by-step explanation:

(½ of ¾)×3

⅜×3 = 9/8 or 1 1/8 or 1.125 cups of sugar

8 0

3 years ago

BD bisects ∠ABC, m∠ABD=(7x−1)°, and m∠DBC=(4x+8)°. Find m∠ABD.

Naya [18.7K]

Answer:

m∠ABD = 20°

Step-by-step explanation:

The bisector makes angles ABD and BDC congruent, so ...

7x -1 = 4x +8

3x = 9 . . . . . . add 1-4x to both sides

x = 3

m∠ABD = (7x-1)° = (7·3 -1)°

m∠ABD = 20°

4 0

2 years ago