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jok3333 [9.3K]
3 years ago
7

The tree diagram below shows all of the possible outcomes for flipping three coins.

Mathematics
1 answer:
Pepsi [2]3 years ago
3 0

Answer:

5

Step-by-step explanation:

Ghhjj fun in jjhv GUI gh

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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
What is the value of y?
Lelu [443]

Answer:

y=66

Step-by-step explanation:

(y-31)+(180-(y+35))+y=180

y-31+145-y+y=180

y=180-114

y=66

3 0
3 years ago
Which expressions are equivalent to the one below? Check all that apply. 53 • 5x
weeeeeb [17]
<span>

</span>Calculate 3 x 5, which is 15.Since 15 is two-digit, we carry the first digit 1 to the next column.

Calculate 5 x 5, which is 25. Now add the carry digit of 1, which is 26.Since 26 is two-digit, we carry the first digit 2 to the next column.

Bring down the carry digit of 2.


<span>Therefore, 53 x 5 = 265.</span>

4 0
3 years ago
Read 2 more answers
73.50 divided by 21. Ishsdbdh
valina [46]
3.5 is the answer!!!
5 0
2 years ago
Read 2 more answers
Pienso en un número lo multiplicó por 2 y el resultado es lo mismo cuando le sumó 1
MrRa [10]
Translate that to english please?

5 0
3 years ago
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