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Nastasia [14]
3 years ago
15

Solve -3x+y=-7 by slope intercept form

Mathematics
1 answer:
marin [14]3 years ago
8 0

can u add picture?

if u dont add picture i cant solve sorry...

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Consider the following differential equation. x^2y' + xy = 3 (a) Show that every member of the family of functions y = (3ln(x) +
Veronika [31]

Answer:

Verified

y(x) = \frac{3Ln(x) + 3}{x}

y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{x}

Step-by-step explanation:

Question:-

- We are given the following non-homogeneous ODE as follows:

                           x^2y' +xy = 3

- A general solution to the above ODE is also given as:

                          y = \frac{3Ln(x) + C  }{x}

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.

Solution:-

- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

                          y' = \frac{\frac{d}{dx}( 3Ln(x) + C ) . x - ( 3Ln(x) + C ) . \frac{d}{dx} (x)  }{x^2} \\\\y' = \frac{\frac{3}{x}.x - ( 3Ln(x) + C ).(1)}{x^2} \\\\y' = - \frac{3Ln(x) + C - 3}{x^2}

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

                          -\frac{3Ln(x) + C - 3}{x^2}.x^2 + \frac{3Ln(x) + C}{x}.x = 3\\\\-3Ln(x) - C + 3 + 3Ln(x) + C= 3\\\\3 = 3

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.

- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

                         y( 1 ) = \frac{3Ln(1) + C }{1} = 3\\\\0 + C = 3, C = 3

- Therefore, the complete solution to the given ODE can be expressed as:

                        y ( x ) = \frac{3Ln(x) + 3 }{x}

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

                         y(3) = \frac{3Ln(3) + C}{3} = 1\\\\y(3) = 3Ln(3) + C = 3\\\\C = 3 - 3Ln(3)

- Therefore, the complete solution to the given ODE can be expressed as:

                        y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{y}

                           

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6 0
3 years ago
Solve for n; 1.2n + 0.68 = 5
bulgar [2K]

Answer:

n= 18 over 5

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Which 2 equations would you use to solve this system?
slega [8]

Answer:

x-y=4

and

x+y=32 is <u>your</u><u> </u><u>equation</u>

<u>d</u><u>i</u><u>f</u><u>f</u><u>e</u><u>r</u><u>e</u><u>n</u><u>c</u><u>e</u><u> </u><u>o</u><u>f</u><u> </u><u>t</u><u>w</u><u>o</u><u> </u><u>n</u><u>u</u><u>m</u><u>b</u><u>e</u><u>r</u><u> </u><u>=</u><u>x-y</u><u> </u><u>is</u><u> </u><u>equal</u><u> </u><u>to</u><u> </u><u>4</u>

<u>s</u><u>u</u><u>m</u><u> </u><u>o</u><u>f</u><u> </u><u>t</u><u>w</u><u>o</u><u> </u><u>n</u><u>u</u><u>m</u><u>b</u><u>e</u><u>r</u><u>=</u><u>x</u><u>+</u><u>y</u><u> </u><u>i</u><u>s</u><u> </u><u>e</u><u>q</u><u>u</u><u>a</u><u>l</u><u> </u><u>t</u><u>o</u><u> </u><u>3</u><u>2</u>

<u>x</u><u>-</u><u>y</u><u>=</u><u>4</u><u>.</u><u>.</u><u>.</u><u>.</u><u>.</u><u>.</u><u>.</u><u>(</u><u>1</u><u>)</u>

<u>x</u><u>+</u><u>y</u><u>=</u><u>3</u><u>2</u><u>.</u><u>.</u><u>.</u><u>.</u><u>.</u><u>.</u><u>.</u><u>(</u><u>2</u><u>)</u>

<u>a</u><u>d</u><u>d</u><u>i</u><u>n</u><u>g</u><u> </u><u>equation</u><u> </u><u>1</u><u> </u><u>a</u><u>n</u><u>d</u><u> </u><u>2</u>

<u>x</u><u>-</u><u>y</u><u> </u><u>+</u><u>x</u><u>+</u><u>y</u><u>=</u><u>4</u><u>+</u><u>3</u><u>2</u>

<u>2</u><u>x</u><u>=</u><u>3</u><u>6</u>

<u>x</u><u>=</u><u>3</u><u>6</u><u>/</u><u>2</u><u>=</u><u>1</u><u>6</u><u>a</u><u>n</u><u>s</u><u>w</u><u>e</u><u>r</u>

<u>s</u><u>u</u><u>b</u><u>s</u><u>t</u><u>i</u><u>t</u><u>u</u><u>t</u><u>i</u><u>n</u><u>g</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>y</u><u> </u><u>in</u><u> </u><u>equation</u><u> </u><u>1</u>

<u>1</u><u>6</u><u>-</u><u>y</u><u>=</u><u>4</u>

<u>1</u><u>6</u><u>-</u><u>4</u><u>=</u><u>y</u>

<u>y</u><u>=</u><u>1</u><u>2</u><u> </u><u>a</u><u>n</u><u>s</u><u>w</u><u>e</u><u>r</u>

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2 years ago
Tyrone paid $2,800 plus 7% sales tax on mountain bikes for a bike club.How much did Tyrone pay in total for the mountain bikes?
timurjin [86]
2800 x 0.07 = 196
2800 + 196 = 2996
Total paid = $2996
8 0
3 years ago
A go-karts top speed is 607,200 feet per hour. what is the speed in miles per hour?
Genrish500 [490]

Answer:115 miles/hour

Step-by-step explanation: one mile equals to 5280 feet, so 607200 divided into 5280 is 115 and as your timing don’t change you can convert only the distance

7 0
3 years ago
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