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3 years ago

Jack has "Lego pieces that are 8 inches each. If he

Mathematics

1 answer:

IRINA_888 [86]3 years ago

6 0

Answer:

4 2/3

Step-by-step explanation:

8×21=168

168÷36(1 yard in inches)=4 with a remainder of 24

24/36 can both be divided by 12 so its now been reduced to 2/3

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Consider the function f(x)equalscosine left parenthesis x squared right parenthesis. a. Differentiate the Taylor series about 0

dybincka [34]

I suppose you mean

$f(x)=\cos(x^2)$

Recall that

$\cos x=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{x^{2n}}{(2n)!}$

which converges everywhere. Then by substitution,

$\cos(x^2)=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{(x^2)^{2n}}{(2n)!}=\sum_{n=0}^\infty(-1)^n\frac{x^{4n}}{(2n)!}$

which also converges everywhere (and we can confirm this via the ratio test, for instance).

a. Differentiating the Taylor series gives

$f'(x)=\displaystyle4\sum_{n=1}^\infty(-1)^n\frac{nx^{4n-1}}{(2n)!}$

(starting at $n=1$ because the summand is 0 when $n=0$ )

b. Naturally, the differentiated series represents

$f'(x)=-2x\sin(x^2)$

To see this, recalling the series for $\sin x$ , we know

$\sin(x^2)=\displaystyle\sum_{n=0}^\infty(-1)^{n-1}\frac{x^{4n+2}}{(2n+1)!}$

Multiplying by $-2x$ gives

$-x\sin(x^2)=\displaystyle2x\sum_{n=0}^\infty(-1)^n\frac{x^{4n}}{(2n+1)!}$

and from here,

$-2x\sin(x^2)=\displaystyle 2x\sum_{n=0}^\infty(-1)^n\frac{2nx^{4n}}{(2n)(2n+1)!}$

$-2x\sin(x^2)=\displaystyle 4x\sum_{n=0}^\infty(-1)^n\frac{nx^{4n}}{(2n)!}=f'(x)$

c. This series also converges everywhere. By the ratio test, the series converges if

$\displaystyle\lim_{n\to\infty}\left|\frac{(-1)^{n+1}\frac{(n+1)x^{4(n+1)}}{(2(n+1))!}}{(-1)^n\frac{nx^{4n}}{(2n)!}}\right|=|x|\lim_{n\to\infty}\frac{\frac{n+1}{(2n+2)!}}{\frac n{(2n)!}}=|x|\lim_{n\to\infty}\frac{n+1}{n(2n+2)(2n+1)}$

The limit is 0, so any choice of $x$ satisfies the convergence condition.

3 0

3 years ago

Three siblings share two cookies equally.which choice represents how many cookies each sibling get? A.1/3 b.2/3 c.3/2 d.6 cookie

Dmitry [639]

Answer:

3/2 cookies

Step-by-step explanation:

3 divided by 2 = 3/2 = 3/2

Hope this helps!

5 0

3 years ago

What two facts can you double to find 8 x 4

amid [387]

If you double 16 you get the answer to 8*4 (Which is 32)

3 0

2 years ago

Read 2 more answers

Find x . a.21.4 b. 15.1 c. 32.7 d. 29.2

Alex73 [517]

So this is going to be using proportions, which in this case is going to be $\frac{18}{21} =\frac{25}{x}$

Firstly, cross-multiply to get $18x=525$

Next, just divide 18 on both sides, and your answer will be $x=29.2$ , or the last option.

8 0

3 years ago

How to do substitution

Brut [27]

You solve for one variable like
y-5x=2
"y=5x+2"

9x+3y=58
and you plug it in into the other equation
9x+3(5x+2)=58

You solve for x and then plug in your answer for x into the other equation
*let's imagine x=8*
then:
y-5(8)=2
and solve for y
:D

5 0

3 years ago