Jade bike wheels have diameter of 20 inches how far does she travel if the wheel rotate 37 times

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

The owner of a quick oil-change business charges

Mkey [24]

Answer:

the sun is actually a planet

Step-by-step explanation:

8 0

3 years ago

What is the distance from point (– 1, 3) to the line 3x – 4y = 10?

natta225 [31]

Answer:

5 units

Step-by-step explanation:

The distance from a point (m, n ) to the line Ax + By + C = 0 is given by

d = $\frac{|Am+Bn+C|}{\sqrt{A^2+B^2} }$

For the point (- 1, 3 ) , with m = - 1 and n = 3

3x - 4y = 10 ( subtract 10 from both sides )

3x - 4y - 10 = 0

with A = 3 , B = - 4 , C = - 10

d = $\frac{|3(-1)+(-4)3-10|}{\sqrt{3^2+(-4)^2} }$

= $\frac{|-3-12-10|}{9+16}$

= $\frac{|-25|}{\sqrt{25} }$

= $\frac{25}{5}$

= 5

5 0

2 years ago

Add [1/-4 3/5] [-2/6 -2/4]

brilliants [131]

Answer:

25/138

Step-by-step explanation:

1 Convert 4\frac{3}{5}4

5

3

to improper fraction. Use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

c

b

=

c

ac+b

.

\frac{1}{-(\frac{4\times 5+3}{5})}(-\frac{2}{6}-\frac{2}{4})

−(

5

4×5+3

)

1

(−

6

2

−

4

2

)

2 Simplify 4\times 54×5 to 2020.

\frac{1}{-(\frac{20+3}{5})}(-\frac{2}{6}-\frac{2}{4})

−(

5

20+3

)

1

(−

6

2

−

4

2

)

3 Simplify 20+320+3 to 2323.

\frac{1}{-(\frac{23}{5})}(-\frac{2}{6}-\frac{2}{4})

−(

5

23

)

1

(−

6

2

−

4

2

)

4 Simplify \frac{2}{6}

6

2

to \frac{1}{3}

3

1

.

\frac{1}{-(\frac{23}{5})}(-\frac{1}{3}-\frac{2}{4})

−(

5

23

)

1

(−

3

1

−

4

2

)

5 Simplify \frac{2}{4}

4

2

to \frac{1}{2}

2

1

.

\frac{1}{-(\frac{23}{5})}(-\frac{1}{3}-\frac{1}{2})

−(

5

23

)

1

(−

3

1

−

2

1

)

6 Find the Least Common Denominator (LCD) of \frac{1}{3},\frac{1}{2}

3

1

,

2

1

. In other words, find the Least Common Multiple (LCM) of 3,23,2.

LCD = 66

7 Make the denominators the same as the LCD.

-\frac{1\times 2}{3\times 2}-\frac{1\times 3}{2\times 3}−

3×2

1×2

−

2×3

1×3

8 Simplify. Denominators are now the same.

-\frac{2}{6}-\frac{3}{6}−

6

2

−

6

3

9 Join the denominators.

\frac{-2-3}{6}

6

−2−3

10 Simplify -\frac{1}{3}-\frac{1}{2}−

3

1

−

2

1

to -\frac{5}{6}−

6

5

.

\frac{1}{-(\frac{23}{5})}\times \frac{-5}{6}

−(

5

23

)

1

×

6

−5

11 Move the negative sign to the left.

-\frac{1}{\frac{23}{5}}\times \frac{-5}{6}−

5

23

1

×

6

−5

12 Invert and multiply.

-\frac{5}{23}\times \frac{-5}{6}−

23

5

×

6

−5

13 Use this rule: \frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}

b

a

×

d

c

=

bd

ac

.

-\frac{5\times -5}{23\times 6}−

23×6

5×−5

14 Simplify 5\times -55×−5 to -25−25.

-\frac{-25}{23\times 6}−

23×6

−25

15 Simplify 23\times 623×6 to 138138.

-\frac{-25}{138}−

138

−25

16 Move the negative sign to the left.

-(-\frac{25}{138})−(−

138

25

)

17 Remove parentheses.

\frac{25}{138}

138

25

7 0

3 years ago

Principal = $ 15000, rate = 10% p.a. and time<br> 21/5 years<br> PLS HELP ASAP

denpristay [2]

Answer:

Simple Interest: A=P(1+rt)

A=15000(1+(0.1*4.2))

A=$21,300

Compound Interest:A=P(1+r/n)^nt

A=15000(1+0.1/4.2)^1*4.2

A=$64,500

Step-by-step explanation:

4 0

2 years ago