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4 years ago

Help me please,Thanks

Mathematics

1 answer:

Liula [17]4 years ago

6 0

Download photo math you scan you problem and it tells you the answer

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A. Find y in terms of x if

givi [52]

Answer:

A. $y(x) =\sqrt{ 2(\frac{x^5}{5} -\frac{6^5}{5})}$

B.Therefore the solution is defined on the interval:

6≤ x ≤ +∞

Step-by-step explanation:

Given differential equation is

$\frac{dy}{dx} = x^4y^{-1}$

$\Rightarrow \frac{dy}{dx} =\frac{ x^4}{y}$

$\Rightarrow y dy = x^4dx$

Integrating both sides:

$\Rightarrow\int y dy = \int x^4dx$

$\Rightarrow \frac{y^2}{2} =\frac{x^5}{5} +C$ ........(1)

Given y(0)= 6

it means y=0 when x=6

Putting x=6 and y=0 in the equation (1)

$\therefore \frac{0^2}{2} =\frac{6^5}{5} +C$

$\Rightarrow C=-\frac{6^5}{5}$

Equation (1) become:

$\Rightarrow \frac{y^2}{2} =(\frac{x^5}{5} -\frac{6^5}{5})$

$\Rightarrow y} =\sqrt{ 2(\frac{x^5}{5} -\frac{6^5}{5})}$

Therefore $y(x) =\sqrt{ 2(\frac{x^5}{5} -\frac{6^5}{5})}$

(B)

The quantity under root must greater than or equal to zero.

Therefore,

$2(\frac{x^5}{5} -\frac{6^5}{5})} \geq0$

$\Rightarrow \frac{x^5}{5} -\frac{6^5}{5}} \geq0$

$\Rightarrow \frac{x^5}{5} \geq\frac{6^5}{5}}$

$\Rightarrow x^5\geq {6^5$

$\Rightarrow \sqrt[5]{x^5} \geq \sqrt[5]{6^5}$

$\Rightarrow x\geq {6$

When x≥0 then the value of $2(\frac{x^5}{5} -\frac{6^5}{5})}$ is real other wise the value of $2(\frac{x^5}{5} -\frac{6^5}{5})}$ is imaginary.

Therefore the solution is defined on the interval:

6≤ x ≤ +∞

8 0

4 years ago

When adding 2/3 + 4/5, what step must be completed first?

trapecia [35]

Answer:

(A) Finding the least common denominator.

7 0

4 years ago

Michael has a collection of 1404 race cards.He hopes to sell the collection in packs of 36 cards,and make 633.75 when all the pa

Anna007 [38]

He should charge 16.25 for each pack

6 0

3 years ago

The maximum weight of a truck on New York State turn weight is 40 tons how many pounds is

Vikki [24]

2000 pounds=1 ton

So 2000x40= 80,000

Hope this helps if you have any issues with the answer just message me.

3 0

4 years ago

Read 2 more answers

Which expressions are equivalent to x + 2y + x + 2 ? Choose all answers that apply:

Inga [223]

Answer:

2(x+y+1)

Step-by-step explanation:

x + 2y + x + 2

= 2x + 2y + 2

= 2(x + y + 1)

Answer:

2(x+y+1)

8 0

3 years ago