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ZanzabumX [31]
3 years ago
10

Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation.

Mathematics
1 answer:
Mama L [17]3 years ago
6 0

Multiplying both sides by y^2 gives

xy^2\dfrac{\mathrm dy}{\mathrm dx}+y^3=1

so that substituting v=y^3 and hence \frac{\mathrm dv}{\mathrm dv}=3y^2\frac{\mathrm dy}{\mathrm dx} gives the linear ODE,

\dfrac x3\dfrac{\mathrm dv}{\mathrm dx}+v=1

Now multiply both sides by 3x^2 to get

x^3\dfrac{\mathrm dv}{\mathrm dx}+3x^2v=3x^2

so that the left side condenses into the derivative of a product.

\dfrac{\mathrm d}{\mathrm dx}[x^3v]=3x^2

Integrate both sides, then solve for v, then for y:

x^3v=\displaystyle\int3x^2\,\mathrm dx

x^3v=x^3+C

v=1+\dfrac C{x^3}

y^3=1+\dfrac C{x^3}

\boxed{y=\sqrt[3]{1+\dfrac C{x^3}}}

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saveliy_v [14]

Answer:

Correct option is (C).

Step-by-step explanation:

Because in figure,

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.°. scale factor will be greater than 1

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5 0
3 years ago
In an aquarium, the ratio of sharks to dolphins is 3 : 5 and the ratio of
Molodets [167]

Step-by-step explanation:

step 1: how many dolphins

there are 6 sharks

sharks to dolphins is 3 to 5

3 S to 5 D

we can divide 6 (amount of sharks known) by 3, to get what a ratio of 1 is

6 ÷ 3 = 2

so 2 sharks is = 1 part or ratio

now we can times by 5 to get a ratio of 5

5 × 2 = 10

there are 10 Dolphins

Step 2: How many starfish

repeat the steps above but for the ratio 2: 7 where 2 is the Dolfin ratio and there are 10 dolphins

put in questions answer you got

3 0
2 years ago
Read 2 more answers
7/6 * 16/6 in simplest form​
Slav-nsk [51]

Answer:

3.83333333333

Step-by-step explanation:

6 0
3 years ago
On a coordinate plane, 2 polygons are shown. Polygon A B C D has points (1, negative 6), (5, negative 6), (6, negative 2), and (
irga5000 [103]

Answer:

The correct option is;

Use a scale factor of 2

Step-by-step explanation:

The parameters given are;

A = (1, -6)

B = (5, -6)

C = (6, -2)

D = (0, -2)

A'' = (1.5, 4)

B'' = (3.5, 4)

C'' = (4, 2)

D'' = ( 1, 2)

We note that the length of side AB in polygon ABCD = √((5 -1)² + (-6 - (-6))²) = 4

The length of side A''B'' in polygon A''B''C''D'' = √((3.5 -1.5)² + (4 - 4)²) = 2

Which gives;

AB/A''B'' = 4/2 = 2

Similarly;

The length of side BC in polygon ABCD = √((6 -5)² + (-2 - (-6))²) = √17

The length of side B''C'' in polygon A''B''C''D'' = √((4 -3.5)² + (2 - 4)²) = (√17)/2

Also we have;

The length of side CD in polygon ABCD = √((6 -0)² + (-2 - (-2))²) = 6

The length of side C''D'' in polygon A''B''C''D'' = √((4 -1)² + (2 - 2)²) = 3

For the side DA  and D''A'', we have;

The length of side DA in polygon ABCD = √((1 -0)² + (-6 - (-2))²) = √17

The length of side D''A'' in polygon A''B''C''D'' = √((1.5 -1)² + (4 - 2)²) = (√17)/2

Therefore the Polygon A B C D can be obtained from polygon A''B''C''D'' by multiplying each side of polygon A''B''C''D'' by 2

The correct option is therefore;

Use a scale factor of 2.

3 0
3 years ago
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Elenna [48]

Answer:

y

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Rewrite in slope-intercept form.

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y

=

3

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x

Use the slope-intercept form to find the slope and y-intercept.

Tap for more steps...

Slope:  

3

2

y-intercept:  

(

0

,

0

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Any line can be graphed using two points. Select two  

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x

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