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2 years ago

6

Reflect the point (-1,-4) in the y-axis followed by the x-axis. What point does it end at? What quadrant is it in? Answer in a c

omplete sentence.

1 answer:

coldgirl [10]2 years ago

7 0

The top right quadrant

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Kassie recorded the favorite sport of students at her school. She surveyed 800 students. How many more students chose Baseball t

lisov135 [29]

Answer:

40 more kids chose baseball over basketball.

Step-by-step explanation:

The best way to go about this is to use benchmark percentages.

For baseball, 25% of 800 people chose that, so we can do 800/4 to get 200, so 200 students chose baseball

For basketball, we could do 800/5 but that isn't mental math, so we can do 10% of 800 is 80 and 80*2=160. So 40 more kids chose baseball over basketball.

6 0

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:

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

7 0

1 year ago

What is the area of half circle with a radius of 40 cm?<br><br> PLEASE HELPPP ILL GIVE BRAINLIEST

madam [21]

Answer:

0.5027 square meters

Step-by-step explanation:

cm2

3 0

2 years ago

What is the slope of(20, 8) (19, 10)

liq [111]

Answer:

-2

Step-by-step explanation:

8-10 = -2

20-19 = 1

-2/1 = -2

5 0

2 years ago

Read 2 more answers

What is -1 2/3 • (-5 1/4)? <br><br> -8 3/4 <br><br> -5 1/6 <br><br> 5 1/6 <br><br> 8 3/4

Paraphin [41]

Your answer is D . Hope I helped :) !

3 0

2 years ago

Read 2 more answers