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lys-0071 [83]
3 years ago
8

le" class="latex-formula">
Mathematics
2 answers:
Dmitry_Shevchenko [17]3 years ago
6 0
He right from step to step
vichka [17]3 years ago
5 0

Answer:

{p}^{4} x

Step-by-step explanation:

1) Regroup terms.

{p}^{2} p^{2} x

2) Use product rule.

{p}^{2 + 2} x

3) Simplify 2 × 2 to 4.

p ^{4} x

Therefor, the answer is p⁴x

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If you are going 50 miles per hour, how many feet per second are you traveling?
Karolina [17]
You would travel 73.333334ft per second because 50 miles/hour would make 73.333333repete foot/second. 
5 0
3 years ago
use the distributive property to remove parentheses. Simplify your answer as much as possible. 1/2(4y+7)
Anna007 [38]
1/2(4y+7)

Use the distributive property. a(b+c)= ab+ac 

1/2*4y= 2y

1/2*7= 3.5

2y+3.5 <---- simplified expression

I hope this helps!
~kaikers


7 0
3 years ago
Read 2 more answers
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
2 years ago
2. Find the volume of the prism. Round to the nearest tenth.
natita [175]

\huge\mathcal\pink{ANSWER}

\mathsf \purple{ v = \frac{1}{2} (a + b) \times h \times l}

\mathsf \pink{v =  \frac{1}{2} (5 + 12) \times 6.1  \times 16}

\mathsf \purple{v =  \frac{1}{2} (17) \times 6.1 \times 16}

\mathsf \pink{v = 8 \frac{1}{2}  \times 6.1 \times 16}

\mathsf \purple{v = 829.6 {mi}^{3} }

7 0
2 years ago
Raul and Athena make bumper stickers. They know that their fixed costs are $145 and the cost of each bumper sticker is $2. Write
alexandr1967 [171]

Answer:

145 + 2c = X

Step-by-step explanation:

Fixed cost: 145

PLUS

2 dollars per bumper sticker (c)

After you write this out, you can put this as an actual equation.

8 0
3 years ago
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