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Misha Larkins [42]
3 years ago
6

For the first 6% of Carlene's salary, her employer matches 100% of her 401(k) contributions, and from 6% to 12%, Carlene's emplo

yer matches 50% of her 401(k) contributions. Carlene's salary is $40,000, and last year, she contributed $4000 to her 401(k) plan. What was her employer's contribution to the 401(k)?​
Mathematics
1 answer:
Hoochie [10]3 years ago
5 0

Answer:

4000 that is the answer

and i believe

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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
PLZ HELP I NEED BY 2:00 PM ATY LEAST!!! WILL GIVE BRAINLYIST<br> Find the value of in each case:
Pie

Answer:

23°

Step-by-step explanation:

Step 1:

< GEC + < ECG + < CGE = Δ ECG    Sum of a Δ

Step 2:

< IGF = < GCE    Corresponding ∠ 's

Step 3:

14° + 180° - 4x + 78° = 180°   Substitution

Step 4:

272° - 4x = 180°     Add / Algebra

Step 5:

- 4x = - 92   Subtract 272° on both sides

Step 6:

- 92 ÷ - 4   Divide

Answer:

x = 23°

Hope This Helps :)

7 0
3 years ago
Read 2 more answers
If y varies directly with x, and y= 10 when x = 4, find y when x = 10.​
mixer [17]

Answer:

17

Step-by-step explanation:

bc

6 0
3 years ago
What is -5 2/3 divided by -3?
sweet [91]
The answer to this question is 1.88888888889 or rounded to 2.0
6 0
3 years ago
Which expression is equivalent to 64y18 – 1000z6?
const2013 [10]
(16y6)3 - (10z2)3 I think is the right answer
3 0
3 years ago
Read 2 more answers
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