Ask question

Ask question

All categories

3 years ago

11

15,789,200 what place is the eight in?

2 answers:

Rasek [7]3 years ago

8 0

Its in the ten thousandth sorry if it’s wrong but that’s what I at least think it is

Mrrafil [7]3 years ago

7 0

The eight is in the ten thousandths place

You might be interested in

Find a second solution y2(x) of<br> x^2y"-3xy'+5y=0; y1=x^2cos(lnx)

rosijanka [135]

We can try reduction order and look for a solution $y_2(x)=y_1(x)v(x)$ . Then

$y_2=y_1v\implies{y_2}'=y_1v'+{y_1}'v\implies{y_2}''=y_1v''+2{y_1}'v+{y_1}''v$

Substituting these into the ODE gives

$x^2(y_1v''+2{y_1}'v+{y_1}''v)-3x(y_1v'+{y_1}'v)+5y_1v=0$

$x^2y_1v''+(2x^2{y_1}'-3xy_1)v'+(x^2{y_1}''-3x{y_1}'+5y_1)v=0$

$x^4\cos(\ln x)v''+x^3(\cos(\ln x)-2\sin(\ln x))v'=0$

which leaves us with an ODE linear in $w(x)=v'(x)$ :

$x^4\cos(\ln x)w'+x^3(\cos(\ln x)-2\sin(\ln x))w=0$

This ODE is separable; divide both sides by the coefficient of $w'(x)$ and separate the variables to get

$w'+\dfrac{\cos(\ln x)-2\sin(\ln x)}{x\cos(\ln x)}w=0$

$\dfrac{w'}w=\dfrac{2\sin(\ln x)-\cos(\ln x)}{x\cos(\ln x)}$

$\dfrac{\mathrm dw}w=\dfrac{2\sin(\ln x)-\cos(\ln x)}{x\cos(\ln x)}\,\mathrm dx$

Integrate both sides; on the right, substitute $u=\ln x$ so that $\mathrm du=\dfrac{\mathrm dx}x$ .

$\ln|w|=\displaystyle\int\frac{2\sin u-\cos u}{\cos u}\,\mathrm du=\int(2\tan u-1)\,\mathrm du$

Now solve for $w(u)$ ,

$\ln|w|=-2\ln(\cos u)-u+C$

$w=e^{-2\ln(\cos u)-u+C}$

$w=Ce^{-u}\sec^2u$

then for $w(x)$ ,

$w=Ce^{-\ln x}\sec^2(-\ln x)$

$w=C\dfrac{\sec^2(\ln x)}x$

Solve for $v(x)$ by integrating both sides.

$v=\displaystyle C_1\int\frac{\sec^2(\ln x)}x\,\mathrm dx$

Substitute $u=\ln x$ again and solve for $v(u)$ :

$v=\displaystyle C_1\int\sec^2u\,\mathrm du$

$v=C_1\tan u+C_2$

then for $v(x)$ ,

$v=C_1\tan(\ln x)+C_2$

So the second solution would be

$y_2=x^2\cos(\ln x)(C_1\tan(\ln x)+C_2)$

$y_2=C_1x^2\sin(\ln x)+C_2x^2\cos(\ln x)$

$y_1(x)$ already accounts for the second term of the solution above, so we end up with

$\boxed{y_2=x^2\sin(\ln x)}$

as the second independent solution.

6 0

4 years ago

Factor the polynomial completely

pogonyaev

I just came here for free points

8 0

3 years ago

Which trigonometric expression has a negative? value? Pls help fast!!!

Delicious77 [7]

Answer:

B. sin(5pi/4)= -(sqr2/2)

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The cost of a bag of 8 peaches is $16. You could also buy individual peaches for

Veronika [31]

Answer: The peaches sold in bags

Step-by-step explanation:

16/8=2 This means that a single peach in the bag of peaches is worth $2. This is $0.15 cheaper than buying a single peach

The unit rte for a single peach is $2.15

The unit rate for a single peach in the bag of peaches is $2

5 0

3 years ago

A bag contains 5 balls: 3 blue, 1 red, and 1 yellow. You select a ball at random 4 times, replacing the ball after each selectio

serg [7]

Answer:

$P(X=3)$

And replacing we got:

$P(X=3)=(4C3)(0.3)^3 (1-0.3)^{4-3}=0.0756$

Step-by-step explanation:

Let X the random variable of interest "number of times that we select a blue ball", on this case we now that:

$X \sim Binom(n=4, p=3/10)$

The probability is always the same since we replace the ball selected in each trial.

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want to find this probability:

$P(X=3)$

And replacing we got:

$P(X=3)=(4C3)(0.3)^3 (1-0.3)^{4-3}=0.0756$

6 0

4 years ago