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Dvinal [7]
2 years ago
7

Can i get some help with #6

Mathematics
2 answers:
lara31 [8.8K]2 years ago
8 0
Just break it up
4x^2 needs to equal 240
So find what equals 240 when multiplied by 4
ollegr [7]2 years ago
6 0
4(x^2) + 2 - (242) ➡0
(2^2 x^2 + 2) - 242 ➡0
4 (x^2 - 60)
Now factor: x^2 -60
4 (x^2 - 60) ➡0
4 ➡0[solve]
x^2➡±60 [by the way]
X ➡ ±  √15 [⬅this might be your answer if you're working with square roots]
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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
3. Solve for y: -5x + 2y = 14
Schach [20]

Answer:

y= -1

Explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

8 0
2 years ago
Read 2 more answers
The amount of a radioactive isotope decays in half every year the amount of the isotope can be modeled by f(x)=3461/2x and f(1)=
pychu [463]

Answer:

1 represents the number of years passed.

step -by-step explanation:

The amount of a radioactive isotope decays in half every year. The amount of the isotope can be modeled by f(x) = 346 (1/2)x and f(1) = 173

Here 1 represents the number of years that passed.

So 1 represents the number of years.

Hope this will helpful.

Thank you.

4 0
3 years ago
Tell me about what you know about "Rounding"
user100 [1]
It is finding the closest estimate to number. Rounding is used in everyday calculations and in many different fields of work
4 0
3 years ago
Read 2 more answers
He found a quotient of 7 which division problem was he using?
marshall27 [118]
The answer is 3 1/2 divided by 1 1/2 because those equal 7.
~Silver
6 0
2 years ago
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