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AlekseyPX
2 years ago
10

Which estimate is closest to the answer of this number sentence?

Mathematics
1 answer:
spayn [35]2 years ago
3 0
The answer is 11 :)))))
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All of these ODEs model a system with a spring, mass and dashpot.
Wewaii [24]

Answer:

− 3 y ' ' − 3 y ' + 3 y = 0 : over-damped

− 2 y ' ' − 4 y ' + 1 y = 0 : over-damped

1 y ' ' + 7 y ' + 5 y = 0: over-damped

Step-by-step explanation:

Using the characteristic equation you can express a differential equation of order n as an algebraic equation of degree n:

a_ny^n+a_n_-_1y^{n-1}+...+a_1y'+a_oy=0

This differential equation will have a characteristic equation of the form:

a_nr^n+a_n_-_1r^{n-1}+...+a_1r+a_o=0

Now, you can classify the solution for a differential equation using a simple method. In order to do it, you just need to use the discriminant.

  • If the discriminant is greater than zero, the solution is over-damped

  • If the discriminant is less than zero, the solution is under-damped

  • If the discriminant is equal to zero, the solution is critically damped

So, given the differential equation:

-3y''-3y+3y=0

Which has characteristic equation of the form:

-3r^2-3r+3=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=-3\\b=-3\\c=3

So:

Disc=(-3)^2-4(-3)(3)=9-(-36)=45

In this case:

Disc=45>0

Therefore the solution is over-damped.

Now, given the differential equation:

-2y''-4y'+1y=0

Which has characteristic equation of the form:

-2r^2-4r+1=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=-2\\b=-4\\c=1

So:

Disc=(-4)^2-4(-2)(1)=16+8=24

In this case:

Disc=24>0

Therefore the solution is over-damped.

Finally, given the differential equation:

1y''+7y'+5y=0

Which has characteristic equation of the form:

1r^2+7r+5=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=1\\b=7\\c=5

So:

Disc=(7)^2-4(1)(5)=49-20=29

In this case:

Disc=29>0

Therefore the solution is over-damped.

6 0
3 years ago
Trevor ran a race in 1 4/5 hours. He ran a total of 8 1/3 miles. How far did he run in one hour?
gulaghasi [49]

Answer:

4.63

Step-by-step explanation:

4/5 of an hour is 48 minutes

1 4/5 hour is 60 + 48

which is

108 minutes

he ran 8 1/3 miles in 108 minutes

so

(8 1/3 times 60 ) ÷ 108

which =

4.6296296296 miles in one hour

6 0
2 years ago
Read 2 more answers
No links please ASAP!!! Find the slope of the line that passes through (5,3) and (4,2).
hodyreva [135]

Answer:

1

Step-by-step explanation:

y2 - y1/ x2 - x1

3-2/ 5-4 = 1/1 = 1

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

5 0
2 years ago
Help with this one please
ivann1987 [24]

with what? you need to explain whats going on in order to get the help you need!

4 0
3 years ago
The law of cosines can only be applied to right triangles ? True or false
LenaWriter [7]
False it can work with non right angles triangles too
6 0
3 years ago
Read 2 more answers
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