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sashaice [31]
2 years ago
12

3(1) to the power of 2

Mathematics
1 answer:
love history [14]2 years ago
7 0

Answer:

9

Step-by-step explanation:

Raising a number to the second means multiplying that number.  3 * 3 = 9

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A mass of 3.25 kg is attached to the end of a spring that is stretched 22 cm by a force of 15 N. It is set in motion with an ini
mylen [45]

Answer:

Step-by-step explanation:

Given that,

Mass of object=3.25kg

The extension e=22cm=0.22m

Force applied to cause extension F=15N

Initial position Xo=0

Initial velocity Vo=-12m/s

We can get the spring constant from Hooke's law

F=ke

Then, k=F/e

k=15/0.22

k=68.182N/m

Also our natural frequency w is given as

w=√(k/m)

Therefore,

w=√(68.182/3.24)

w=√20.98

w=√21

w=4.58rad/s

w=4.6rad/s

There is no damping in this situation, no outside force acting on the system and the equation that governs the system is

mx''+kx=0

3.25x''+68.182x=0

Divide through by 3.25

x''+20.98x=0

We can approximate 20.98 to 21

x"+21x=0

The solution to this differential equation using D operator

D²+21=0

D²=-21

D= ±√-21

D=±√21 •i

Then the solution is

x(t)=A•Sinwt +B•Coswt

x(t)=A•Sin√21 t +B•Cos√21 t

Note that x'(t)=v(t)

and at t=0 Vo=-12m/s

x(t)=A•Sin√21 t +B•Cos√21 t

x'(t)=v(t)=A√21•Cos√21 t - B√21•Sin√21 t

v(t)=A√21•Cos√21 t - B√21•Sin√21 t

Then, using the two initial conditions

v(0)=-12

And X(0)=0

x(t)=A•Sin√21 t +B•Cos√21 t

X(0)=A•Sin√21•0 +B•Cos√21•0

X(0)=A•Sin0+B•Cos0

0=B

B=0

Also,, V(0)=-12m/s

v(t)=A√21•Cos√21 t - B√21•Sin√21 t

V(0)=A√21•Cos√21•0- B√21•Sin√21•0

V(0)=A√21•Cos0- B√21•Sin0

-12=A√21

Therefore,

A=-12/√21

A=-2.62

Therefore the general equation becomes

x(t)=A•Sin√21 t +B•Cos√21 t

x(t)=-2.62Sin√21 t +0•Cos√21 t

x(t)=-2.62Sin√21 t

a. The amplitude

Comparing x(t) to wave equations

x(t)=-Asin(wt+2λ/t)

Then,

A=2.62m

b. We know the natural frequency already to be

w=√21

w=4.58rad/s

c. Period

Comparing the equation again

wt=√21t

Given that w=2πf

Therefore, 2πft=√21t

Then, f=√21t / 2πt

f=√21/2π

f=0.73Hz

Then, period is the reciprocal of frequency

T=1/f

T=1/0.73

T=1.37seconds

The period is 1.37sec,

5 0
3 years ago
If the probability of selecting, without replacement, 2 red marbles from a bag containing only red and blue marbles is 3 55 and
Marat540 [252]

Answer:

Step-by-step explanation:

Let T = the TOTAL number of marbles in the bag.

We are told that 3 of those marbles are red

P(select a red marble first) = 3/T

Once we've removed the first red marble, there are T-1 marbles remaining and 2 of them are red

So, P(select a red marble second) = 2/(T-1)

Okay, now let's use probability rules to answer the question....

P(select 2 red marbles) = P(select a red marble first AND select a red marble second)

= P(select a red marble first) x P(select a red marble second)

= 3/T x 2/(T-1)

= 6/(T² - T)

We're told that P(select 2 red marbles) = 3/55

So, we can write: 6/(T² - T) = 3/55

Cross multiply to get: 3(T² - T) = (6)(55)

Divide both sides by 3 to get: T² - T = (2)(55)

Evaluate: T² - T = 110

Rearrange: T² - T - 110 = 0

Factor: (T - 11)(T + 10) = 0

So, EITHER T = 11 OR T = -10

Since T cannot be negative, it must be the case that T = 11

6 0
3 years ago
Is answer choice D correct help please ??
SpyIntel [72]
O wpuld say that d is correct
4 0
3 years ago
Read 2 more answers
What is -5(7x + 2) =200
blondinia [14]
Your answer is going to be X=-6

3 0
3 years ago
Read 2 more answers
Need help...!! plzzz
kipiarov [429]
This is true sometimes and false sometimes, depending on the numbers.
3 0
3 years ago
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