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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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Which of the following questions describes the equation 4n = -24?
Alona [7]

Answer:

n = -6

Step-by-step explanation:

<u>Step 1:  Divide both sides by 4</u>

4n / 4 = -24 / 4

n = -6

Answer:  n = -6

3 0
3 years ago
The first time that Arnold ran for mayor in a small town, he received 5% of the votes. This year, when Arnold ran for mayor agai
sammy [17]

Answer:

20 votes

Step-by-step explanation:

You start with the percents: You always start with 100%

100-5=95

Then you multiply

95 x 4

4 is how many votes he received the 2nd time

95 x 4= 380

Then you subtract

380-360= 20

Your Welcome :)

6 0
2 years ago
Is this thesis OK for my schizophrenia essay? Schizophrenia is a severe mental illness that deeply affects the patient's daily l
sattari [20]
I don't know how many paragraphs your professor needs you to develop, but if your essay consists on just 3 paragraphs (introduction, body and conclusion) your thesis is OK.
Now, if your essay needs to have, lets say 4 or 5 paragraphs (introduction, body 1, body 2, body 3, and conclusion) I'd recommend you to add two more details to your essay. For example,

Schizophrenia is a severe mental illness that deeply affects not only the patient's daily life, but also his family and friends.

paragraph 1 is to develop how schizophrenia affects the patient daily life only. Paragraph 2 is to develop how schizophrenia affects the patient's family and paragraph 3 to develop how it affects his or her family.

Don't forget to put examples, professors love when you put examples.
Good luck, and if you need help, you can ask me.
3 0
3 years ago
A=1/2 bh (base/height)<br> =.5(12)4<br> a=24ft<br> how did i get the answer a=24?
vampirchik [111]
That’s what i got
step by step explanation
4 0
2 years ago
she has 6 cherry candies, 3 grape candies, and 3 lime candies. If Charlotte randomly pulls one piece of candy out of the bag, wh
yKpoI14uk [10]

Answer:     \dfrac{1}{2}

Step-by-step explanation:

We know that probability for any event = \dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}

Given : Charlotte has 6 cherry candies, 3 grape candies, and 3 lime candies.

I..e Total pieces of candies she has = 6+3+3=  12

Now , If Charlotte randomly pulls one piece of candy out of the bag, what is the probability that it will be cherry is given by :-

\text{P(cherry)}=\dfrac{\text{Number of cherries}}{\text{Total candies}}\\\\=\dfrac{6}{12}\\\\=\dfrac{1}{2}

Hence, the  probability that it will be cherry is \dfrac{1}{2} .

7 0
3 years ago
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