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solmaris [256]
3 years ago
6

Find the solution of the problem (1 3. (2 cos x - y sin x)dx + (cos x + sin y)dy=0.

Mathematics
1 answer:
lakkis [162]3 years ago
7 0

Answer:

2*sin(x)+y*cos(x)-cos(y)=C_1

Step-by-step explanation:

Let:

P(x,y)=2*cos(x)-y*sin(x)

Q(x,y)=cos(x)+sin(y)

This is an exact differential equation because:

\frac{\partial P(x,y)}{\partial y} =-sin(x)

\frac{\partial Q(x,y)}{\partial x}=-sin(x)

With this in mind let's define f(x,y) such that:

\frac{\partial f(x,y)}{\partial x}=P(x,y)

and

\frac{\partial f(x,y)}{\partial y}=Q(x,y)

So, the solution will be given by f(x,y)=C1, C1=arbitrary constant

Now, integrate \frac{\partial f(x,y)}{\partial x} with respect to x in order to find f(x,y)

f(x,y)=\int\  2*cos(x)-y*sin(x)\, dx =2*sin(x)+y*cos(x)+g(y)

where g(y) is an arbitrary function of y

Let's differentiate f(x,y) with respect to y in order to find g(y):

\frac{\partial f(x,y)}{\partial y}=\frac{\partial }{\partial y} (2*sin(x)+y*cos(x)+g(y))=cos(x)+\frac{dg(y)}{dy}

Now, let's replace the previous result into \frac{\partial f(x,y)}{\partial y}=Q(x,y) :

cos(x)+\frac{dg(y)}{dy}=cos(x)+sin(y)

Solving for \frac{dg(y)}{dy}

\frac{dg(y)}{dy}=sin(y)

Integrating both sides with respect to y:

g(y)=\int\ sin(y)  \, dy =-cos(y)

Replacing this result into f(x,y)

f(x,y)=2*sin(x)+y*cos(x)-cos(y)

Finally the solution is f(x,y)=C1 :

2*sin(x)+y*cos(x)-cos(y)=C_1

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BlackZzzverrR [31]

Answer:

C  a1= -2

    an = an-1 +3

Step-by-step explanation:

an = -2+ (n-1)3

What is the first term?  Let n=1

a1 = -2 + 0*3

a1 = -2


The difference between the  terms is +3  (coefficient on (n-1))

The second term is the first term +3

The third term is the second term plus 3

The next term is the previous term +3

so an = an-1+ 3

5 0
3 years ago
What is the missing value in the proportion 4/5 = x/30?
ra1l [238]

Answer:

\displaystyle x = 24

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
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Step-by-step explanation:

<u>Step 1: Define</u>

<u />\displaystyle \frac{4}{5} = \frac{x}{30}<u />

<u />

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. [Multiplication Property of Equality] Cross-multiply:                                      \displaystyle 5x = 120
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4 0
3 years ago
Sandra has developed a program designed to increase reading comprehension scores in 6th graders. She randomly selects three stud
Mandarinka [93]

Answer:a small sample size

Step-by-step explanation:

From the information given in the question, we are informed that Sandra developed a program that was designed to increase reading comprehension scores in 6th graders and she then randomly selects three students and has them participate in her program.

After comparing the mean score from the students who completed her program to three students who did not participate in the program, she finds no significant difference between their mean scores, it should be noted that the reason for this will be because the sample size is small.

If a large sample size was used, this could have been different as thsi could result in a significant difference between their mean scores.

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Gnesinka [82]
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<span>x = a(y - k)^2 + h </span>

<span>There are no steps. Just look at what is inside the parentheses and compare it to (y - k) with k = -3. </span>
<span>Then look at what is added and compare it to h = -1. </span>

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Answer:

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Step-by-step explanation:

Find the perfect square of 256 since you need to sides of the same length

16 * 26 = 256

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