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forsale [732]
3 years ago
10

52:44

Mathematics
1 answer:
bagirrra123 [75]3 years ago
8 0

Answer:

1          

Step-by-step explanation:

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Find the function of which is the solution of 36y"-48y'-48y=0 with initial conditions y1(0)=1. y1'(0)=0
lilavasa [31]

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 }

4 0
3 years ago
The perimeter of the rectangle is 114 units. what's the length of 5x​
kotykmax [81]
22.8 I think because you divide them?? Idk
6 0
3 years ago
Which sequences of transformations confirm the congruence of shape II and shape I?
mylen [45]

Answer:

1. When we reflect the shape I along X axis it will take the shape I in first quadrant, and then if we rotate the shape I by 90° clockwise, it will take the shape again in second quadrant . So we are not getting shape II. This Option is Incorrect.

2. Second Option is correct , because by reflecting the shape I across  X axis and then by 90° counterclockwise rotation will take the Shape I in second quadrant ,where we are getting shape II.

3. a reflection of shape I across the y-axis followed by a 90° counterclockwise rotation about the origin takes the shape I in fourth Quadrant. →→ Incorrect option.

4. This option is correct, because after reflecting the shape through Y axis ,and then rotating the shape through an angle of 90° in clockwise direction takes it in second quadrant.

5. A reflection of shape I across the x-axis followed by a 180° rotation about the origin takes the shape I in third quadrant.→→Incorrect option

6 0
3 years ago
Read 2 more answers
(45pts) An elevator holds at most 1,400 pounds. A team of movers and their cart have a combined weight of 1,200 pounds. If each
emmainna [20.7K]
Let x be the number of boxes the team brings with them. Their weight combined with the boxes can't exceed the capacity of 1400. Assuming the elevator runs fine at that exact weight, you want to find the number of boxes, each of which contributes 40 pounds. This is given by the equation

1400=1200+40x

Solving for x, you have

1400=1200-40x
200=40x
x=5

So the team can bring *at most* 5 boxes at a time.
4 0
3 years ago
Simplify the expression to a + bi form:<br> (9+7i)(6 + i)
Scorpion4ik [409]

(9 + 7i)(6 + i) \\  = 54 + 9i + 42i + 7 {i}^{2}  \\  = 54 + 51i  - 7 \\  = 47 + 51i

I hope I helped you^_^

6 0
3 years ago
Read 2 more answers
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