Which of the following graphs shows the solution to the system of equations y=5x-1 and y= x+3

Anarel [89]

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—————

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

I need help! please is expression equivalent

nikitadnepr [17]

No the value of functions are not same .

What is function in math?

A quantitative expression, rule, or law that describes the link between an independent variable and a dependent variable (the dependent variable).
In mathematics, functions occur widespread, and they are essential for defining physical links in the sciences.
A function is a type of rule that generates one output for a single output.
This is represented by the equation y=x2. Any inputs for x result in an output for y. Given that x is the input value, we would state that y is a result of x.

- 5 × ( -5)⁻⁹ = -5 × 1/-5⁹ ⇒ 1/5⁸ = 1/390625

[ -5 × (-5)]⁻⁹ = [25]⁻⁹ = 1/25⁹ = 1/3814697265625

No the value of functions are not same .

Learn more about function

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6 0

1 year ago

How much is three half’s plus one fifth

Maslowich

Let's make it an expression.

Three half's= 3/2 Plus= + one fifth= 1/5

We need to turn 3/2 and 1/5 so that they have the same denominator. Let's use 10.

3/2→15/10 1/5→2/10

15/10+2/10=17/10=1 7/10

So, three half's plus one fifth is 1 7/10.

7 0

3 years ago

Read 2 more answers

Select the correct answer. Which function has a domain of all real numbers? A.y=(x+2)^ 1/4 B.y=-x^ 1/2+5 C.y=-2(3x)^1/6 D.y=(2x)

BaLLatris [955]

Answer:

The answer is probably A

Step-by-step explanation:

Its domain is the only one of these that contain -2, which is a real number.

EMERGENCY CORRECTION: THIS IS WRONG AND I'M TOO ST*PID TO FIGURE OUT THE REAL ANSWER I'M SORRY

7 0

3 years ago

A dealer paid $7,000 for a car at an auction. At the dealership, a salesperson sold the car for 30% more than the auction price.

timurjin [86]

30% of $7000 is $2100
25% of $2100 is $525

7 0

3 years ago