Phương trình vi phân y'' - 2y' -3y =0 có nghiệm tổng quát là ?

please mark this answer as brainlist

Step-by-step explanation:

Let [tex]x = r\cos{\theta}[/tex] and [tex]y = r\sin{\theta}[/tex]. Substituting these into our equation, it becomes

[tex]\dfrac{r^2\cos^2{\theta}}{25} + \dfrac{r^2\sin^2{\theta}}{9} = 1[/tex]

or

[tex]9r^2\cos^2{\theta} + 25r^2\sin^2{\theta} = 225[/tex]

Let use the identity [tex]\cos^2{\theta} = 1 - \sin^2{\theta}[/tex] to express the equation in terms of sine only:

[tex]9r^2 - 9r^2\sin^2{\theta} + 25\sin^2{\theta} = 225[/tex]

which simplifies to

[tex]r^2(9 + 16\sin^2{\theta}) = 225[/tex]

Taking the square root and solving for r , we get the polar form of the equation as

[tex]r = \dfrac{15}{\sqrt{9 + 16\sin^2{\theta}}}[/tex]

Answer:

x = r\cos{\theta}x=rcosθ and y = r\sin{\theta}y=rsinθ

\dfrac{r^2\cos^2{\theta}}{25} + \dfrac{r^2\sin^2{\theta}}{9} = 1

25

r

2

cos

2

θ

+

9

r

2

sin

2

θ

=1

or

9r^2\cos^2{\theta} + 25r^2\sin^2{\theta} = 2259r

2

cos

2

θ+25r

2

sin

2

θ=225

Let use the identity \cos^2{\theta} = 1 - \sin^2{\theta}cos

2

θ=1−sin

2

θ

9r^2 - 9r^2\sin^2{\theta} + 25\sin^2{\theta} = 2259r

2

−9r

2

sin

2

θ+25sin

2

θ=225

which simplifies to

r^2(9 + 16\sin^2{\theta}) = 225r

2

(9+16sin

2

θ)=225

Taking the square root and solving for r ,

r = \dfrac{15}{\sqrt{9 + 16\sin^2{\theta}}}r=

9+16sin

2

θ

15

Answer:

x≤4 is a closed circle on 4 going left and x≥8 is a closed circle on 8 going right

Step-by-step explanation:

Not sure how to explain it.

9514 1404 393

Answer:

  A.  500 cm²

Step-by-step explanation:

The height of the piece of cardboard is the same as the height of the prism: 20 cm.

The width of the piece of cardboard is the sum of the side lengths of the prism: 7 cm + 9 cm + 9 cm = 25 cm.

The area of the cardboard is the product of its height and width.

  A = HW

  A = (20 cm)(25 cm) = 500 cm²

Answer:

that's cheating, still your indian bro will help _XD

Step-by-step explanation:

ab = 34

bc 33

ac 27

pq 27

qr 27

pr 40

Answer:

40 000

Step-by-step explanation:

4 thousands = 4000

10 x 4000 = 40 thousands = 40 000

Answer:

40,000

Step-by-step explanation:

Answer:

To find when a function is increasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is positive. Now test values on all sides of these to find when the function is positive, and therefore increasing.

Answer:

68.88m

Step-by-step explanation:

√(x²-x²)²+(y²-20)²

The 3 angles form the straight line AB. A straight line equals 180 degrees.

The 3 angles when added together need to equal 180:

2x + 65 + (x + 65) = 180

Simplify by combining like terms:

3x + 130 = 180

Subtract 130 from both sides

3x = 50

Divide both sides by 3

X = 50/3

X = 16 2/3 (16.66667 as a repeating decimal)

Now you have x if you need to solve all the angles replace x with its value and sole:

2x = 2(16 2/3) = 33 1/3

X + 65 = 16 2/3 + 65 = 81 2/3

Step-by-step explanation:

2x+65°+(x+65°)=180° ( sum of angle of straight angle )

3x+65°+65°=180°

3x=180°-130°

3x= 50°

now,

i) 2x=2*50=100°

ii) (x+65°) = 50+65 =115°

plz mark me brainiest and thanks

have a good day ahead...

(-_-)

Answer:  [tex]18\sqrt{2}\\\\[/tex]

This is the same as saying 18*sqrt(2) or you could say 18√2

============================================================

Explanation:

We'll be using this square root rule: [tex]\sqrt{A}*\sqrt{B} = \sqrt{A*B}[/tex]

So we could have this as our steps:

[tex]3\sqrt{12}*\sqrt{6}\\\\3\sqrt{12*6} \ \text{ ... Apply the rule mentioned}\\\\3\sqrt{72}\\\\3\sqrt{36*2}\\\\3\sqrt{36}*\sqrt{2} \ \text{ ... Apply the rule again, but in reverse}\\\\3*6*\sqrt{2}\\\\18\sqrt{2}\\\\[/tex]

Therefore, [tex]3\sqrt{12}*\sqrt{6} = 18\sqrt{2}[/tex]

The basic idea is to first combine the roots using that rule. From there, we factor the radicand such that we pull out the largest perfect square factor. This will allow us to break the root apart and fully simplify it.

Step-by-step explanation:

67.5 minutes of the movie that was left

Answer:

[tex] \frac{2n}{3} [/tex]

hope, I'm right

Answer:

[tex] \frac{2n}{3} [/tex]

Step-by-step explanation:

[tex] \frac{ \frac{n}{4} }{ \frac{3}{8} } = \frac{n}{4} \div \frac{3}{8} [/tex]

[tex] \frac{n}{4} \times \frac{8}{3} = \frac{n \times 8}{4 \times 3} [/tex]

[tex] \frac{n \times 2}{3} = \frac{2n}{3} [/tex] ✅

Answer:

200

Step-by-step explanation:

Answer:

32±b±90=180(being the three angle of a treangle)

32±90±b=180

122±b=180

B=180-122

b=58 answer

90±23±d=180(being three angle of the trangle)

113±d=180

d=180-113

d=78 answer

Answer

:.b=58

:.d=78

Thank you

Answer: De and Ef

Step-by-step explanation:

Answer:

12 sides

Step-by-step explanation:

its a regular polygon so we can use the formula 180(n-2)/n which finds the angle of the regular polygon, since the exterior angle is 30, the angle of the regular polygon is 180-30=150, so 180(n-2)/n=150.

Answer:

x = 2

Step-by-step explanation:

Equation: 2x + 6 = 10

2x = 4

x = 2

Answer:

let the number be x

then

2x + 6 = 10

2x = 10-6

2x = 4

x = 2

mark me as brainliest

Answer:

x=30 degree is the answer

Answer:

-2 ,2

Step-by-step explanation:

Answer:

45oz

Step-by-step explanation:

We can find the ratio of white to blue paint he needs by dividing.

10 / 4 = 2.5oz of blue paint for every ounce of white paint

Now, we can multiply to find how much blue paint he needs.

18 * 2.5 = 45oz

Best of Luck!

Answer:

D.  -3/5.

Step-by-step explanation:

6x + 10y = 8

We convert this to slope-intercept form:

Subtract 6x from both sides of the equation:

10y = -6x + 8

Divide through by 10:

y = -6/10 x +  8/10   (Slope-intercept form)

The slope is -6/10

= -3/5.

Answer:

The difference between the height of the mountain and the depth of the trench is 8,271 ft.

Step-by-step explanation:

brainliest plz?

Answer:

10boys, 17 girls

Step-by-step explanation:

10+17=27,

17-10=7

Answer: there are 17 girls in the class

Step-by-step explanation:

let the number of boys be x

and the number of girls be re[presented as 7+x

Since there are a class of 27 containing the sum of the boys and girls, we have our equation as

boys +girls =27

x+ 7+x=27

7+2x =27

2x=27-7

2x=20

x=20/2=10

Boys =x=10

girls= 7+x=7+10=17

See similar question here: https://brainly.com/question/21953702

Answer:

rational

Step-by-step explanation:

as it is of the form p/q

mark me as brainliest ❤️

Answer:

which class Of question is this

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]m = 14[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'm'...}}}\\\\(\frac{3}{7}) m=6\\\\-------------\\\rightarrow (\frac{3}{7}m)7 = 6*7\\\\\rightarrow 3m = 42\\\\\rightarrow \frac{3m=42}{3}\\\\\rightarrow \boxed{m= 14}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.