1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
JulijaS [17]
3 years ago
6

Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.) (tan(x) −

sin(x) sin(y)) dx + cos(x) cos(y) dy = 0
Mathematics
1 answer:
never [62]3 years ago
7 0

Answer:

f(x,y)=ln secx+cosx siny+C

Step-by-step explanation:

We are given that DE

(tanx-sinx siny)dx+cosxcosydy=0

We have to determine given DE is exact or not.

Compare it with Mdx+Ndy=0

M=tanx-sinx siny

N=cosxcosy

\frac{\partial M}{\partial y}=M_y=-sinxcosy

\frac{\partial N}{\partial x}=N_x=-sinxcosy

Therefore, M_y=N_x

If DE is exact then M_y=N_x

Hence,it is exact.

M=\frac{\partial f}{\partial x}=tanx-sinxsiny

Integrate w.r.t x on both sides

f(x,y)=\int(tanx-sinxsiny)dx

f(x,y)=lnsecx+cosxsiny+\phi(y)...(1)

By using the formula

\int tanxdx=lnsecx+C,\int sinxdx=-cosx+C

Differentiate partially  equation (1) w.r.t y

\frac{\partial f}{\partial y}=cosxcosy+\phi'(y)

By using the formula:

\frac{d(sinx)}{dx}=cosx

N=\frac{\partial f}{\partial y}=cosxcosy=cosxcosy+\phi'(y)

\phi'(y)=cosxcosy-cosxcosy=0

\phi'(y)=0

Integrate  w.r.t y

\phi(y)=C

Substitute the value

f(x,y)=ln secx+cosx siny+C

You might be interested in
On the double number line, 3 minutes corresponds to 180 beats.
harina [27]

Answer:

your answer is- toni types 270 lettre in three minutes

Step-by-step explanation:

2:180=90

3:270=90

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
What value of b will cause the system to have an infinite number of solutions?
irga5000 [103]

b must be equal to -6  for infinitely many solutions for system of equations y = 6x + b and -3 x+\frac{1}{2} y=-3

<u>Solution: </u>

Need to calculate value of b so that given system of equations have an infinite number of solutions

\begin{array}{l}{y=6 x+b} \\\\ {-3 x+\frac{1}{2} y=-3}\end{array}

Let us bring the equations in same form for sake of simplicity in comparison

\begin{array}{l}{y=6 x+b} \\\\ {\Rightarrow-6 x+y-b=0 \Rightarrow (1)} \\\\ {\Rightarrow-3 x+\frac{1}{2} y=-3} \\\\ {\Rightarrow -6 x+y=-6} \\\\ {\Rightarrow -6 x+y+6=0 \Rightarrow(2)}\end{array}

Now we have two equations  

\begin{array}{l}{-6 x+y-b=0\Rightarrow(1)} \\\\ {-6 x+y+6=0\Rightarrow(2)}\end{array}

Let us first see what is requirement for system of equations have an infinite number of solutions

If  a_{1} x+b_{1} y+c_{1}=0 and a_{2} x+b_{2} y+c_{2}=0 are two equation  

\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}} then the given system of equation has no infinitely many solutions.

In our case,

\begin{array}{l}{a_{1}=-6, \mathrm{b}_{1}=1 \text { and } c_{1}=-\mathrm{b}} \\\\ {a_{2}=-6, \mathrm{b}_{2}=1 \text { and } c_{2}=6} \\\\ {\frac{a_{1}}{a_{2}}=\frac{-6}{-6}=1} \\\\ {\frac{b_{1}}{b_{2}}=\frac{1}{1}=1} \\\\ {\frac{c_{1}}{c_{2}}=\frac{-b}{6}}\end{array}

 As for infinitely many solutions \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}

\begin{array}{l}{\Rightarrow 1=1=\frac{-b}{6}} \\\\ {\Rightarrow6=-b} \\\\ {\Rightarrow b=-6}\end{array}

Hence b must be equal to -6 for infinitely many solutions for system of equations y = 6x + b and  -3 x+\frac{1}{2} y=-3

8 0
3 years ago
Can you please help me with this problem
vagabundo [1.1K]
\bf \begin{cases}&#10;\textit{area of a circle}=\pi r^2&#10;\\ \quad \\&#10;circumference=2\pi r&#10;\end{cases}&#10;\\ \quad \\&#10;&#10;12.56=\pi r^2\implies \cfrac{12.56}{\pi }=r^2\implies \sqrt{\cfrac{12.56}{\pi }}=\boxed{r}&#10;\\ \quad \\&#10;thus&#10;\\ \quad \\&#10;circumference=2\pi \boxed{r}\implies 2\pi \boxed{\sqrt{\cfrac{12.56}{\pi }}}
8 0
3 years ago
Katrina drinks 0.5 gallons of water per day which shows how to find the number of cups of water she drinks in a week
krok68 [10]

Answer:

if she does so multiply by seven to get final answer

3 0
2 years ago
Read 2 more answers
Which figure is a unit square?
photoshop1234 [79]

Answer:

C

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • Is 20 g greater or less than 0.02 kg?
    9·1 answer
  • Solve using the system using elimination for x - y= -5 and 3x + y= 1
    11·2 answers
  • What is the discriminant of the quadratic equation 0 = –x2 4x – 2? a.–4 b.8 c.12 d.24
    7·1 answer
  • 9. A ball is thrown into the air at an initial velocity of 18 meters per second from an initial height of 10
    13·1 answer
  • А,
    7·1 answer
  • What is the remainder of f(x)=x^4-2x^3-27x^2-9x+18 when divided by binomial x+4
    12·1 answer
  • <img src="https://tex.z-dn.net/?f=%20%5Chuge%20%5Cpink%7Bwhat%20%5C%3A%20is%20%5C%3A%20cranial%7D%20%5C%5C%20%5Chuge%20%5Cpink%7
    10·1 answer
  • Can someone help me with this?
    5·1 answer
  • HELP PLEASEEE YOULL GET 15 POINTS
    7·1 answer
  • Gerry purchases 12 hamburgers at a fast food restaurant for $2.25 each. For half the amount of money, he could purchase 5 buffal
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!