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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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The linear function m=55-8.5b represents the amount m (in dollars) of money that you have after buying b books. Find the domain
Amiraneli [1.4K]

Answer:

The domain is (-∞ , ∞)

The domain is continuous

Step-by-step explanation:

Here, we want to identify the domain of the linear function

The domain in this case can be represented by the set of all real numbers.

When we talk of the domain of a function, we are simply referring to the the range of values between the smallest value on the x-axis and the largest number on the x-axis

Hence, mathematically, we are simply considering the smallest value of b up to the largest value of b in this case. Where b simply represents the number of books

Thus, the domain here will be (-∞ , ∞)

On if the domain is discrete or continuous, we can see that the domain is continuous.

The domain is continuous simply because, the domain we have contains all the values and not some in the set of real numbers. If it had contain only some, then it would have been discrete. But since it contains all, it is continuous

8 0
3 years ago
Help please it is due in 10 min<br> will give brinly
Effectus [21]

Answer:

its H

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What is the value of the expression 2^2+4^2 divided by 2^2
N76 [4]

Use PEMDAS:

Parentheses

Exponents

Multiply and Divide from left to right.

Add and Subtract from left to right.

-------------------------------------------------------

Evaluate the exponents.

2^2+4^2/2^2

Divide from left to right.

4 + 16/4

Add from left to right.

4 + 4

Solution.

8

5 0
3 years ago
What is the equation of the line that is parallel to line y = -3x – 8 and passes
qwelly [4]

Answer:

y = -3x + 3

Step-by-step explanation:

Since the line is parallel, it has the same slope. Plug the point you have into the equation y - y1 = slope (x -x1) to get your answer, which should be y = -3x +3

Hopefully this helps - let me know if you have any questions!

6 0
3 years ago
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Enter the finite geometric series from its given description, and then enter its sum.
Mama L [17]

Answer:

a_n= 4(-5)^{(n-1)}

-10416

Step-by-step explanation:

a = 4

r = -5

geometric series:  a_n=ar^{(n-1)} = 4(-5)^{(n-1)}

Determine which term = -12500:

a_n=-12500

4(-5)^{(n-1)}=-12500

(-5)^{(n-1)} = -3125

(5)^{(n-1)} = 3125

(n-1)ln(5) = ln(3125)

n-1 = ln(3125)/ln(5) = 5

n = 5 + 1 = 6

a_6=-12500

Using geometric sum series formula: S_n=\frac{a(1-r^n)}{1-r}

Therefore, S_6=\frac{4(1-(-5)^6)}{1-(-5)} =\frac{-62496}{6} =-10416

4 0
2 years ago
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