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3 years ago

A number decreased by six, and then doubled

Mathematics

2 answers:

PIT_PIT [208]3 years ago

3 0

Answer:

Step-by-step explanation:

ElenaW [278]3 years ago

3 0

Answer:

a-6*2

Step-by-step explanation:

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Solution for dy/dx+xsin 2 y=x^3 cos^2y

vichka [17]

Rearrange the ODE as

$\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y=x^3\cos^2y$
$\sec^2y\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y\sec^2y=x^3$

Take $u=\tan y$ , so that $\dfrac{\mathrm du}{\mathrm dx}=\sec^2y\dfrac{\mathrm dy}{\mathrm dx}$ .

Supposing that $|y|$ , we have $\tan^{-1}u=y$ , from which it follows that

$\sin2y=2\sin y\cos y=2\dfrac u{\sqrt{u^2+1}}\dfrac1{\sqrt{u^2+1}}=\dfrac{2u}{u^2+1}$
$\sec^2y=1+\tan^2y=1+u^2$

So we can write the ODE as

$\dfrac{\mathrm du}{\mathrm dx}+2xu=x^3$

which is linear in $u$ . Multiplying both sides by $e^{x^2}$ , we have

$e^{x^2}\dfrac{\mathrm du}{\mathrm dx}+2xe^{x^2}u=x^3e^{x^2}$
$\dfrac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]=x^3e^{x^2}$

Integrate both sides with respect to $x$ :

$\displaystyle\int\frac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]\,\mathrm dx=\int x^3e^{x^2}\,\mathrm dx$
$e^{x^2}u=\displaystyle\int x^3e^{x^2}\,\mathrm dx$

Substitute $t=x^2$ , so that $\mathrm dt=2x\,\mathrm dx$ . Then

$\displaystyle\int x^3e^{x^2}\,\mathrm dx=\frac12\int 2xx^2e^{x^2}\,\mathrm dx=\frac12\int te^t\,\mathrm dt$

Integrate the right hand side by parts using

$f=t\implies\mathrm df=\mathrm dt$
$\mathrm dg=e^t\,\mathrm dt\implies g=e^t$
$\displaystyle\frac12\int te^t\,\mathrm dt=\frac12\left(te^t-\int e^t\,\mathrm dt\right)$

You should end up with

$e^{x^2}u=\dfrac12e^{x^2}(x^2-1)+C$
$u=\dfrac{x^2-1}2+Ce^{-x^2}$
$\tan y=\dfrac{x^2-1}2+Ce^{-x^2}$

and provided that we restrict $|y|$ , we can write

$y=\tan^{-1}\left(\dfrac{x^2-1}2+Ce^{-x^2}\right)$

5 0

3 years ago

Can someone explain how to get the answer for the following question ?

zhenek [66]

The answer to the question is 1-5

3 0

2 years ago

Find the value of x.

erastovalidia [21]

Answer:

60 = x

Step-by-step explanation:

180-144 = 36

36+84 = 120

180-120 = 60

7 0

3 years ago

Read 2 more answers

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 2135 miles, with a variance

stiv31 [10]

Answer:

0.36878

Step-by-step explanation:

Given that:

Mean number of miles (m) = 2135 miles

Variance = 145924

Sample size (n) = 40

Standard deviation (s) = √variance = √145924 = 382

probability that the mean of a sample of 40 cars would differ from the population mean by less than 29 miles

P( 2135 - 29 < z < 2135 + 29)

Z = (x - m) / s /√n

Z = [(2106 - 2135) / 382 / √40] < z < [(2164 - 2135) / 382 / √40]

Z = (- 29 / 60.399503) < z < (29 / 60.399503)

Z = - 0.4801364 < z < 0.4801364

P(Z < - 0.48) = 0.31561

P(Z < - 0.48) = 0.68439

P(- 0.480 < z < 0.480) = 0.68439 - 0.31561 = 0.36878

= 0.36878

3 0

2 years ago

Passes through ( 4, 2), parallel to y = x + 5

Hoochie [10]

Answer:

y = x - 2

Step-by-step explanation:

You can subtract 4 from the x and y to get where the y-intercept would be.

8 0

3 years ago

Read 2 more answers