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3 years ago

Are these answers right? if not tell me what number and the explanation thank you :)

Mathematics

1 answer:

zheka24 [161]3 years ago

7 0

Answer:

theyre correct

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

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

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4 years ago

Peppermint candies per jar

Harlamova29_29 [7]

Leaf #2 because 27 and 23 are closest to 30

4 0

3 years ago

Jamil pays $20.00 for dinner. He decides to leave a 15% tip on top. How much should he pay in total

Helga [31]

Answer:

$23.00

Step-by-step explanation:

The tip amount is $3.00, but the total is $23.00

6 0

3 years ago

Read 2 more answers

Question 7 i mark as brainliest

gogolik [260]

2 1/2 should be the answer. Adding all of the x’s up you’ll get 16.5. Since you need 19 oz take 19 and subtract 16.5 to get 2.5. Convert 2.5 into a mixed fraction and get 2 1/2

Answer C- 2 1/2

7 0

3 years ago

Torque (or moment) is the measure of turning force or twist on an object. If a mechanic is applying 12 Newton centimeters of tor

SashulF [63]

Answer:

1.0638

Step-by-step explanation:

Given the question:

If a mechanic is applying 12 Newton centimeters of torque on a bolt how many pound inches would this be?

Torque = 12 Newton centimeter

Torque which is the turning effect on an object :

1 Newton = 0.225 pound force

1 centimeter = 0.394 inch

Hence ;

1 Newton centimeter = (1 × 0.225 × 0.394) = 0.08865 pound inch

12 Newton centimeter is hence, equals :

(12 × 0.225 × 0.394) pound inch

= 1.0638 pound inch

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3 years ago