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dexar [7]
3 years ago
5

Find the function of which is the solution of 36y"-48y'-48y=0 with initial conditions y1(0)=1. y1'(0)=0

Mathematics
1 answer:
lilavasa [31]3 years ago
4 0

Answer:

y=\frac{1}{4} e^{2x}+\frac{3}{4} e^{-\frac{2}{3}x }

Step-by-step explanation:

Let,  D=\frac{d}{dx}

Now, us simplify the given differential equation and write it in terms of D,

36y''-48y'-48y=0

or, 3y''-4y'-4y=0

or, (3D^2-4D-4)y=0

We have our auxiliary equation:

3D^2-4D-4=0

or, (3D+2)(D-2)=0

or, D=2, - \frac{2}{3}

Therefore our solution is,

y=Ae^{2x}+Be^{- \frac{2}{3}x}

and, y'=2Ae^{2x}-\frac{2}{3}Be^{\frac{2}{3}x }

Applying the boundary conditions, we get,

A+B=1

2A-\frac{2}{3}B=0

Solving them gives us,

A=\frac{1}{4} ,B=\frac{3}{4}

Hence,

y=\frac{1}{4} e^{2x}+\frac{3}{4} e^{-\frac{2}{3}x }

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Please help quick!!!!!!!!
Semmy [17]

Answer:

a. V = 10*8*x

b. V= 10*8*22.5

Step-by-step explanation:

b. V= 1800

3 0
2 years ago
Based on the work shown on the right, check all of the possible solutions of the equation.
Mazyrski [523]

Incomplete question. However, here is a similar question attached.

Solve 3x^2 + 17x - 6 = 0.

Based on the work shown to the left, which of these values are possible solutions of the equation? Check all of the boxes that apply

A X=-6

B X=6

C X=-1/3

D X=1/3

E X=0

Answer:

A and D

Step-by-step explanation:

Note that such question requires using completing the square method of solving equations. By using the values X= -6 and X= 1/3 we arrive at a solution.

7 0
3 years ago
Triangle ABC is reflected across the line y=2x to map onto triangle RST. Select all statements that are true.
Anettt [7]

The reflection transformation in the question is a rigid transformation,

therefore, the image and the preimage are congruent.

The statements that are true are;

  • <u>AB = RS</u>
  • <u>∠ABC ~ ∠RST</u>
  • <u>ΔABC = ΔRST</u>
  • <u>m∠BAC = m∠SRT</u>

Reasons:

The given parameter are;

Triangle ΔABC is reflected across the line 2·X, to map onto triangle ΔRST

Required:

To select the true statements

Solution:

A reflection is a rigid transformation, therefore, the distance between corresponding points on the image and the preimage are equal.

Therefore;

AB = RS

BC = ST

AC = RT

Given that the image formed by a reflection is congruent to the preimage, we have;

ΔABC ≅ ΔRST

∠ABC ≅ ∠RST

m∠ABC = m∠RST by the definition of congruency

∠BCA ≅ ∠STR

m∠BCA = m∠STR by the definition of congruency

∠BAC ≅ ∠SRT

m∠BAC = m∠SRT by the definition of congruency

Therefore, the true statements are;

  • <u>AB = RS</u>; Image formed by rigid transformation
  • <u>∠ABC ~ ∠RST</u>; Definition of similarity
  • <u>ΔABC = ΔRST</u>; By definition of congruency
  • <u>m∠BAC = m∠SRT</u>; by the definition of congruency

Learn more here:

brainly.com/question/11787764

7 0
3 years ago
Goods bought for $800 had to be sold off at a loss of 8% the selling price was​
Vikentia [17]

Answer:

8% of 800 is 64

800-64=736

Step-by-step explanation:

4 0
3 years ago
Please help me! I REALLLY need my math grade to go up!!! PLEASE HELP!!!!
melomori [17]

Answer:

Hi I only know part be yes the figures are congruent

Step-by-step explanation:

There the same shape, same size so yes they are congruent

6 0
3 years ago
Read 2 more answers
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