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3 years ago

8

Steve watched television for three over four hours are Monday and 5/6 hour on Tuesday how many longer did he watch television on

Tuesday that on Monday

1 answer:

Delicious77 [7]3 years ago

5 0

Answer:

1/12 hour

Step-by-step explanation:

Subtract 3/4 hr from 5/6 hr: use the LCD 12:

Subtract 9/12 from 10/12 hr: The difference is 1/12 hr.

Steve watched TV 1/12 hour longer on Tuesday than on Monday. That's 5 minutes.

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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

Jorge is running a race. In 2/3 of an hour, he ran 2 2/5 miles. At this rate, what distance will Jorge run in one hour?

jeka94

Answer:

321312313123

Step-by-step explanation:

because ur gay

7 0

3 years ago

Use natural logarithms to solve the equation. Round to the nearest thousandth. 3e^2x +5=27

puteri [66]

Answer:

x=0.996

Step-by-step explanation:

$3e^{2x} +5=27$

To take natural log ln , we need to get e^2x alone

Subtract 5 on both sides

$3e^{2x}=22$

Now we divide both sides by 3

$e^{2x}=\frac{22}{3}$

Now we take 'ln' on both sides

$ln(e^{2x})=ln(\frac{22}{3})$

As per log property we can move exponent 2x before ln

$(2x)ln(e)=ln(\frac{22}{3})$

The value of ln(e) = 1

$2x=ln(\frac{22}{3})$

Divide both sides by 2

$x=\frac{ln(\frac{22}{3})}{2}$

x= 0.996215082

Round to nearest thousandth

x=0.996

6 0

3 years ago

¿Qué porcentaje de personas encuestadas se comunican menos de 73 minutos?

AlekseyPX

Answer:

20%

50=100%

10=x

x=10×100=1000

1000÷50=20

3 0

3 years ago

The value of X is:<br>A)27<br>B)7<br>C)5<br>D)√21<br>E)√27

liq [111]

Answer:

E.

Step-by-step explanation:

6^2=x^2+3^2

X^2=36-9

X=

$\sqrt{27}$

3 0

2 years ago

Read 2 more answers