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mina [271]
3 years ago
9

Simplify ⎷81x^14. Assume the variable x represents a positive real number.

Mathematics
1 answer:
kotegsom [21]3 years ago
6 0
\sqrt{81x^{14}} =\sqrt{(9x^7)^2}=9x^7
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Answer:

y=1/2-2

Step-by-step explanation:

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2 years ago
Dy/dx = 2xy^2 and y(-1) = 2 find y(2)
Anarel [89]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2887301

—————

Solve the initial value problem:

   dy
———  =  2xy²,      y = 2,  when x = – 1.
   dx


Separate the variables in the equation above:

\mathsf{\dfrac{dy}{y^2}=2x\,dx}\\\\
\mathsf{y^{-2}\,dy=2x\,dx}


Integrate both sides:

\mathsf{\displaystyle\int\!y^{-2}\,dy=\int\!2x\,dx}\\\\\\
\mathsf{\dfrac{y^{-2+1}}{-2+1}=2\cdot \dfrac{x^{1+1}}{1+1}+C_1}\\\\\\
\mathsf{\dfrac{y^{-1}}{-1}=\diagup\hspace{-7}2\cdot \dfrac{x^2}{\diagup\hspace{-7}2}+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{y}=x^2+C_1}

\mathsf{\dfrac{1}{y}=-(x^2+C_1)}


Take the reciprocal of both sides, and then you have

\mathsf{y=-\,\dfrac{1}{x^2+C_1}\qquad\qquad where~C_1~is~a~constant\qquad (i)}


In order to find the value of  C₁  , just plug in the equation above those known values for  x  and  y, then solve it for  C₁:

y = 2,  when  x = – 1. So,

\mathsf{2=-\,\dfrac{1}{1^2+C_1}}\\\\\\
\mathsf{2=-\,\dfrac{1}{1+C_1}}\\\\\\
\mathsf{-\,\dfrac{1}{2}=1+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-1=C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-\dfrac{2}{2}=C_1}

\mathsf{C_1=-\,\dfrac{3}{2}}


Substitute that for  C₁  into (i), and you have

\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}}\\\\\\
\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}\cdot \dfrac{2}{2}}\\\\\\
\mathsf{y=-\,\dfrac{2}{2x^2-3}}


So  y(– 2)  is

\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot (-2)^2-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot 4-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{8-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{5}}\quad\longleftarrow\quad\textsf{this is the answer.}


I hope this helps. =)


Tags:  <em>ordinary differential equation ode integration separable variables initial value problem differential integral calculus</em>

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3 years ago
Read 2 more answers
Tickets to a movie cost $7.25 for adults and $5.50 for students a group of friends purchased 8 tickets for $52.75 how many adult
irina1246 [14]

Answer:

The number of adults tickets and student tickets purchased is 5 and 3.

Given that,

Tickets to a movie cost $7.25 for adults and $5.50 for students.

A group of friends purchased 8 tickets for $52.75.

Here we assume the no of adult tickets and no of student tickets be x and y.

Based on the above information, the calculation is as follows:

7.25x + 5.50y = 52.75 .............(i)

x + y = 8

x = 8 - y..................(2)

Now put the x value in the equation (1)

So,  

7.25(8-y) + 5.50y = 52.75

7.25 × 8 - 7.25y + 5.50y = 52.75

58 - 1.75y = 52.75

5.25 = 1.75y

y = 3

So,  

x = 8 - 3

= 5

Therefore we can conclude that the number of adults tickets and student tickets purchased is 5 and 3.

-Hope this helps<3

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2 years ago
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