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timurjin [86]
2 years ago
7

How do you know where to put the constant when finding general solutions for differential equations?

Mathematics
1 answer:
Norma-Jean [14]2 years ago
5 0
Let's suppose we want to solve y'=y with y(0)=2. Separating variables and integrating, we get

\displaystyle\int\dfrac{\mathrm dy}y=\int\mathrm dx\implies\ln|y|=x+C\implies y=e^{x+C}

Leaving the solution in this form, the initial condition gives

2=e^{0+C}=e^C\implies C=\ln2

This means the solution is y=e^{x+\ln2}.

Now if we were to write y=e^{x+C}=e^xe^C=Ce^x, then we would have found

2=Ce^0\implies C=2

so that the solution would have been y=2e^x.

But these two solutions are the same, since y=e^{x+\ln2}=e^xe^{\ln2}=2e^x. So we get the same solution regardless of where we place C, despite getting different values for C.
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What is the value of x in the equation
chubhunter [2.5K]

Well I solved it and This is what i got

3 0
2 years ago
Which statement best describes the relationship between the positions of the two players
Lena [83]

Answer:

N is M reflected across the x-axis; only the signs of the x-coordinates of M and N are different.

Step-by-step explanation:

The y-axis is vertical, and the x-axis is horizontal. If a point, or image, is reflected over the x-axis, in this case M and N, then the signs of the y-coordinates do not change, and instead the coordinates of the x-axis change.

7 0
3 years ago
The length of a rectangle is shown below: On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis two
Degger [83]

9514 1404 393

Answer:

  3.  C(−1, −5), D(2, −5)

Step-by-step explanation:

The given points are 2 -(-1) = 3 units apart horizontally, so the remaining points will need to be 18/3 = 6 units below, vertically. Translating the given points down 6 gives ...

  D = A -(0, 6) = (2, 1) -(0, 6) = (2, -5)

  C = B -(0, 6) = (-1, 1) -(0, 6) = (-1, -5)

The two points required to make a rectangle with an area of 18 square units are ...

  C(-1, -5), D(2, -5)

_____

The area of a rectangle is the product of length and width. If the area is 18 square units, and the width is 3 units, then the length must be 6 units. 3×6=18.

5 0
2 years ago
PTG has side lengths of 18 cm, 27 cm, and 13 cm. which type of triangle is PTG? The answer is obtuse.
Verizon [17]
To know what kind of triangle is it. use the pythagorean theorem:
A^2 + B^2 = C^2,
where C is the longest side of the triangle 
if it satisfies the equation then it is a right triangle
if it does not then A^2 + B^2 > C^2 so it is acute triangle
if A^2 + B^2 < C^2 it is obtuse triangle

18^2 + 13^2 ? 27^2
324 + 169 ? 729
493 < 729 so it is obtuse triangle

3 0
3 years ago
BRAINLIEST <br> Solve for X. Round to the nearest tenth.
Kryger [21]

Step-by-step explanation:

2 things to remember for problems like this :

the sum of all angles in a triangle is always 180 degrees.

the law of sines :

a/sin(A) = b/sin(B) = c/sin(C) or upside-down (whatever fuss the situation better), with the sides being always opposite of the angles.

so, now for the given problems :

4.

x/sin(90) = 12/sin(29)

x/1 = x = 12/sin(29) = 24.75198408...

rounded x = 24.8

5.

the opposite angle of x is

180 - 90 - 16 = 74 degrees.

x/sin(74) = 37/sin(90) = 37

x = 37×sin(74) = 35.56668275...

rounded x = 35.6

6.

the opposite angle of x is

180 - 90 - 58 = 32 degrees.

x/sin(32) = 22/sin(58)

x = 22×sin(32)/sin(58) = 13.74712574...

rounded x = 13.7

7.

the opposite angle of 15 is

180 - 90 - 51 = 39 degrees.

x/sin(51) = 15/sin(39)

x = 15×sin(51)/sin(39) = 18.52345735...

rounded x = 18.5

4 0
2 years ago
Read 2 more answers
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