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Rus_ich [418]
3 years ago
5

The differential equation of a certain system is 20⁢y′⁢′+c⁢y′+80⁢y=0

Mathematics
1 answer:
Sholpan [36]3 years ago
5 0

Answer:

c=80

Step-by-step explanation:

Based on my reading the critical damping occurs when the discriminant of the quadratic characteristic equation is 0.

So let's see that characteristic equation:

20⁢r^2+c⁢r+80⁢=0

The discriminant can be found by calculating b^2-4aC of ar^2+br+C=0.

a=20

b=c

C=80

c^2-4(20)(80)

We want this to be 0.

c^2-4(20)(80)=0

Simplify:

c^2-6400=0

Add 6400 on both sides:

c^2=6400

Take square root of both sides:

c=80 or c=-80

Based on further reading damping equations in form

a⁢y′⁢′+b⁢y′+C⁢y=0

should have positive coefficients with b also having the possibility of being zero.

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Use a graphing utility to graph the function and the damping factor of the function in the same viewing window.
Bas_tet [7]

Answer:

The function touches the damping factor

at x=\frac{(4n-3)\pi}{2} and x=\frac{(4n-1)\pi}{2}

The x-intercept of f(x) is

at x=n\pi

Step-by-step explanation:

Given function is f(x)=e^{-3x} sin(x) and damping factor as y=e^{-3x} and y=(-1)e^{-3x}

To find when function touches the damping factor:

For f(x)=e^{-3x} sin(x) and y=e^{-3x}

Equating the both the equation,

e^{-3x} sin(x)=e^{-3x}

sin(x)=1

x=\frac{(4n-3)\pi}{2}

For f(x)=e^{-3x} sin(x) and y=(-1)e^{-3x}

Equating the both the equation,

e^{-3x} sin(x)=(-1)e^{-3x}

sin(x)=(-1)

x=\frac{(4n-1)\pi}{2}

Therefore, The function touches the damping factor x=\frac{(4n-3)\pi}{2} and x=\frac{(4n-1)\pi}{2}

To find x-intercept of f(x):

For x-intercept, y=0

f(x)=e^{-3x} sin(x)

y=e^{-3x} sin(x)

e^{-3x} sin(x)=0

Hence, e^{-3x} is always greater than zero.

Therefore,sin(x)=0

x=n\pi

Thus,

The x-intercept of f(x) is at x=n\pi

7 0
3 years ago
The ratio of the number of adults to the number of children in a library is 12:5. If there are 45 children in the library, how m
zysi [14]
The answer would be 108. 108:45 can be simplified to 12:5.
4 0
3 years ago
Read 2 more answers
8/4 divided by 100 equals what
dexar [7]
\frac{8}{4} (8/4) divided by 100 equals .02
6 0
3 years ago
Read 2 more answers
50 POINTS !!<br><br> PLEASE HELP ILL GIVE BRAINLIEST !!
dybincka [34]

Answer:

3.9 miles

Step-by-step explanation:

Use phytagoras theorem

c²=a²+b²

4²=1²+b²

16=1+b²

b²=16-1

b²=15

b=

\sqrt{15}

b= 3.872

≈3.9miles

6 0
3 years ago
How do I do this????
statuscvo [17]
3,107\div 350\approx8.9

So she need at least 9 cans.
5 0
3 years ago
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