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3 years ago

Please help, will reward brainliest.

Mathematics

1 answer:

Gekata [30.6K]3 years ago

4 0

Answer:

2 out of every 5; 2:3; 2:5

Step-by-step explanation:

2 out of every 5 means that out of 5, he/she picks two (leftover 3)

the other choices are a ratio of if he/she has 2 of that then they will also have 5 of this

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Use reduction of order to find a second linearly independent solution

Hoochie [10]

Given that exp(2x) is a solution, we assume another solution of the form

y(x) = v(x) exp(2x) = v exp(2x)

with derivatives

y' = v' exp(2x) + 2v exp(2x)

y'' = v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)

Substitute these into the equation:

(2x + 5) (v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)) - 4 (x + 3) (v' exp(2x) + 2v exp(2x)) + 4v exp(2x) = 0

Each term contains a factor of exp(2x) that can be divided out:

(2x + 5) (v'' + 4v' + 4v) - 4 (x + 3) (v' + 2v) + 4v = 0

Expanding and simplifying eliminates the v term:

(2x + 5) v'' + (4x + 8) v' = 0

Substitute w(x) = v'(x) to reduce the order of the equation, and you're left with a linear ODE:

(2x + 5) w' + (4x + 8) w = 0

w' + (4x + 8)/(2x + 5) w = 0

I'll use the integrating factor method. The IF is

µ(x) = exp( ∫ (4x + 8)/(2x + 5) dx ) = exp(2x - log|2x + 5|) = exp(2x)/(2x + 5)

Multiply through the ODE in w by µ :

µw' + µ (4x + 8)/(2x + 5) w = 0

The left side is the derivative of a product:

[µw]' = 0

Integrate both sides:

∫ [µw]' dx = ∫ 0 dx

µw = C

Replace w with v', then integrate to solve for v :

exp(2x)/(2x + 5) v' = C

v' = C (2x + 5) exp(-2x)

∫ v' dx = ∫ C (2x + 5) exp(-2x) dx

v = C₁ (x + 3) exp(-2x) + C₂

Replace v with y exp(-2x) and solve for y :

y exp(-2x) = C₁ (x + 3) exp(-2x) + C₂

y = C₁ (x + 3) + C₂ exp(2x)

It follows that the second fundamental solution is y = x + 3. (The exp(2x) here is already accounted for as the first solution.)

3 0

3 years ago

Please help question in the picture

torisob [31]

Answer:

Step-by-step explanation:

triangles have to equal to 180 so 45+45 =90 +90=180

5 0

3 years ago

I don’t understand how to do it ?

Temka [501]

We know that Sum of Angles in a Triangle is Equal to 180°

Here EBF is a Triangle

⇒ m∠EBF + m∠BEF + m∠EFB = 180°

⇒ 60° + 40° + m∠EFB = 180°

⇒ 100° + m∠EFB = 180°

⇒ m∠EFB = 180° - 100°

⇒ m∠EFB = 80°

As Line m and Line p are Parallel Lines :

Alternate Interior Angles are Equal, here Alternate Interior Angles are m∠BEF and m∠ABE

⇒ m∠BEF = m∠ABE

⇒ m∠ABE = 40°

We know that Vertically Opposite Angles are Equal, Here m∠GFI and m∠EFB are Vertically Opposite Angles.

⇒ m∠GFI = m∠EFB

⇒ m∠GFI = 80°

We can notice that m∠DEB and m∠BEF form a Linear Pair

⇒ m∠DEB + m∠BEF = 180°

⇒ m∠DEB + 40° = 180°

⇒ m∠DEB = 180° - 40°

⇒ m∠DEB = 140°

We can notice that Sum of Angles m∠CBF and m∠EBF and m∠ABE is 180°

⇒ m∠CBF + m∠EBF + m∠ABE = 180°

⇒ m∠CBF + 60° + 40° = 180°

⇒ m∠CBF + 100° = 180°

⇒ m∠CBF = 180° - 100°

⇒ m∠CBF = 80°

We can notice that m∠BFG and m∠EFB form a Linear Pair

⇒ m∠BFG + m∠EFB = 180°

⇒ m∠BFG + 80° = 180°

⇒ m∠BFG = 180° - 80°

⇒ m∠BFG = 100°

We know that Vertically Opposite Angles are Equal, Here m∠BFG and m∠IFE are Vertically Opposite Angles.

⇒ m∠BFG = m∠IFE

⇒ m∠IFE = 100°

3 0

3 years ago

A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 45% of the cameras sold

Hitman42 [59]

The probability that has a basic model purchase extended warranty will be 0.1935 or 19.35%.

<h3>What is probability?</h3>

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

A company that manufactures video cameras produces a basic model and a deluxe model.

Over the past year, 45% of the cameras sold have been of the basic model.

Of those buying the basic model, 43% purchase an extended warranty, whereas 50% of all deluxe purchasers do so.

If you learn that a randomly selected purchaser has an extended warranty.

Then the probability that has a basic model purchase extended warranty will be

P = 0.45 × 0.43

P = 0.1935

P = 19.35%

More about the probability link is given below.

brainly.com/question/795909

#SPJ1

6 0

2 years ago

Please help me i need help please

Varvara68 [4.7K]

Server: Content Deleted; Error (673)

5 0

3 years ago