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vova2212 [387]
3 years ago
8

15 divided by 3.15 what is the unit rate

Mathematics
1 answer:
stiv31 [10]3 years ago
7 0

Answer: 4.8 i think

Step-by-step explanation: its just division

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(X^2+y^2+x)dx+xydy=0<br> Solve for general solution
aksik [14]

Check if the equation is exact, which happens for ODEs of the form

M(x,y)\,\mathrm dx+N(x,y)\,\mathrm dy=0

if \frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}.

We have

M(x,y)=x^2+y^2+x\implies\dfrac{\partial M}{\partial y}=2y

N(x,y)=xy\implies\dfrac{\partial N}{\partial x}=y

so the ODE is not quite exact, but we can find an integrating factor \mu(x,y) so that

\mu(x,y)M(x,y)\,\mathrm dx+\mu(x,y)N(x,y)\,\mathrm dy=0

<em>is</em> exact, which would require

\dfrac{\partial(\mu M)}{\partial y}=\dfrac{\partial(\mu N)}{\partial x}\implies \dfrac{\partial\mu}{\partial y}M+\mu\dfrac{\partial M}{\partial y}=\dfrac{\partial\mu}{\partial x}N+\mu\dfrac{\partial N}{\partial x}

\implies\mu\left(\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}\right)=M\dfrac{\partial\mu}{\partial y}-N\dfrac{\partial\mu}{\partial x}

Notice that

\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}=y-2y=-y

is independent of <em>x</em>, and dividing this by N(x,y)=xy gives an expression independent of <em>y</em>. If we assume \mu=\mu(x) is a function of <em>x</em> alone, then \frac{\partial\mu}{\partial y}=0, and the partial differential equation above gives

-\mu y=-xy\dfrac{\mathrm d\mu}{\mathrm dx}

which is separable and we can solve for \mu easily.

-\mu=-x\dfrac{\mathrm d\mu}{\mathrm dx}

\dfrac{\mathrm d\mu}\mu=\dfrac{\mathrm dx}x

\ln|\mu|=\ln|x|

\implies \mu=x

So, multiply the original ODE by <em>x</em> on both sides:

(x^3+xy^2+x^2)\,\mathrm dx+x^2y\,\mathrm dy=0

Now

\dfrac{\partial(x^3+xy^2+x^2)}{\partial y}=2xy

\dfrac{\partial(x^2y)}{\partial x}=2xy

so the modified ODE is exact.

Now we look for a solution of the form F(x,y)=C, with differential

\mathrm dF=\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0

The solution <em>F</em> satisfies

\dfrac{\partial F}{\partial x}=x^3+xy^2+x^2

\dfrac{\partial F}{\partial y}=x^2y

Integrating both sides of the first equation with respect to <em>x</em> gives

F(x,y)=\dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3+f(y)

Differentiating both sides with respect to <em>y</em> gives

\dfrac{\partial F}{\partial y}=x^2y+\dfrac{\mathrm df}{\mathrm dy}=x^2y

\implies\dfrac{\mathrm df}{\mathrm dy}=0\implies f(y)=C

So the solution to the ODE is

F(x,y)=C\iff \dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3+C=C

\implies\boxed{\dfrac{x^4}4+\dfrac{x^2y^2}2+\dfrac{x^3}3=C}

5 0
3 years ago
Can someone please help me? I don't know how to do this. I will mark brainliest! Thanks!
Bezzdna [24]

Answer:

So it gives you a little picture and tells you what would the question be if you had this graph.

Step-by-step explanation:

The correct answer would be B, find the area because the 4x + 3 is your length and 3x is your length, A = length * width. So the answer is B, find the area.

4 0
3 years ago
Read 2 more answers
Ms. hernandez has 100 to spend on parking and admission to the zoo. The park will cost $7 and admission tickets will cost $15.50
Firdavs [7]
Number of people < (should be smaller than or equal to but I don't have that button on my keyboard) (100-7) / 15.50

103/15.50 = 6.64516...
You can't have .645 of a person, so you must round down. Therefore, she can bring 6 people including herself.
3 0
3 years ago
The four rectangles shown have different side lengths.
RUDIKE [14]
Answer is <span>D.
A and D

A = 2(6+2) = 16
D = 2(4+3) = 16
both have perimeters = 16</span>
8 0
3 years ago
Sketch the algebra-tile shape at right on your paper. Write an expression for the
Dima020 [189]

Answer:

Part 1) P=(4x+4)\ units

Part 2)

a) P=32\ units

b) P=26\ units

c) P=13\frac{1}{3}\ units

Step-by-step explanation:

<u><em>The complete question in the attached figure</em></u>

Part 1) Write an expression for the  perimeter of the shape

we know that

The figure is composed by a larger square, a rectangle and a smaller square

1) The area of the larger square is given

A=x^2\ units^2

so

The length and the width of the larger square is x units

2) The area of the rectangle is given

A=x\ units^2

so

The length of the rectangle is x units and the width is 1 unit

3) The length and the width of the smaller square is x units

see the attached figure N 2 to better understand the problem

Find out the perimeter

The perimeter is the sum of all the sides.

so

P=(x+x+x+x+1+1+1+1)

P=(4x+4)\ units

Part 2) Find the perimeter for each of the given values of x.

a) For x=7 units

Substitute the value of x in the expression of the perimeter

P=(4(7)+4)=32\ units

b) For x=5.5 units

Substitute the value of x in the expression of the perimeter

P=(4(5.5)+4)=26\ units

b) For x=7/3 units

Substitute the value of x in the expression of the perimeter

P=(4(\frac{7}{3})+4)=\frac{40}{3}=13\frac{1}{3}\ units

8 0
3 years ago
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