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3 years ago

When each of these functions is increasing, which type eventually grows the fastest?

Mathematics

1 answer:

kodGreya [7K]3 years ago

4 0

Answer:

Step-by-step explanation:

Exponential. you can search the graph of each types on the internet :)

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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>

7 0

3 years ago

How do you round 30,361 to the nearest dollar

alexandr402 [8]

Answer:

if that is supposed be a decimal then round tenths place which is still six

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Betty has some hair ribbons that are blue. She has 19 blue ribbons. Three times the number of blue ribbons decreased by 5 is gre

likoan [24]

Answer:

3x-5> 6x- 14

Step-by-step explanation:

Let the blue ribbons be denoted by the letter x.

Then according to the given condition

3 times the blue ribbons = 3x

Decreased by 5 = 3x-5

is greater than

6 times the blue ribbons = 6x

decreased by 14 = 6x-14

Putting in one line

3x-5> 6x- 14

Solving the inequality

3x-5> 6x- 14

Taking both sides positive as in modulus

14-5 > 6x-3x

9> 3x

9/3 > x

3> x

Again solving for inequality

3x-5> 6x- 14

Taking one side negative that is mod

3x-5> -6x + 14

3x+ 6x > 14+5

9x> 19

x > 19/9

x > 2.11

so x lies between 2 and 3

3 > x > 2.11

Now putting the values for x= 19

3x-5> 6x- 14

57-5> 114-14

52 > 100 False

Now putting the values for x= 3

3x-5> 6x- 14

9-5> 18-14

4>4 False

Now putting the values for x= 2

3x-5> 6x- 14

6-5> 12-14

1> -2 True

There are 2 blue ribbons

5 0

3 years ago

Read 2 more answers

after a lady is seated in a restaurant, she realizes that she only has $48.00. if she must pay 7% sales tax and wishes to leave

Alexeev081 [22]

Answer:

$38.84

Step-by-step explanation:

1) 48.00 x 0.07 = 3.36 (she must pay this amount)

2) 48.00 x 0.1 = 4.8 (she must tip this much)

48.00 - 4.8 + 3.36 = 39.84

She has 39.84 dollars she can use to order food with.

7 0

3 years ago

Can anyone help please?

Furkat [3]

Alternate interior angles are equal.
2x - 10 = 65 - x
2x + x = 65 + 10
3x = 75
x = 75/3 = 25
x = 25.

8 0

3 years ago