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iVinArrow [24]
3 years ago
14

Rewrite it as a function and isolate Y. ​

Mathematics
1 answer:
hodyreva [135]3 years ago
8 0

Answer: y= -2x + 12

or f (y ) = 6 - \frac{y}{2}

Step-by-step explanation:

just subtract the 2x to get the y alone

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Rowan baked 17 chocolate chip cookies and 9 sugar cookies for her class how many cookies does she have left
frez [133]

Answer: She has 8 cookies left

Step-by-step explanation:

17-9=8

6 0
3 years ago
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
In each figure, a|| b . Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain
stellarik [79]

Answer should be:

b. No; it is a reflection followed by a translation.

Hope it helps.

4 0
3 years ago
Read 2 more answers
A car rental company charges $34 per day for a rented car and $0.50 for every mile driven. A second rental company charges $20 p
Dahasolnce [82]

Answer:

A

Step-by-step explanation:

If you multiply the price for each mule x the amount of miles + the daily rental, you get the price. If you do this for each option and each car rental then you can see when the answers add up.

.75x56+20=62

.50x56+34=62

8 0
4 years ago
Read 2 more answers
Grace bought a season pass to galactic quest amusement park last summer. With the pass, she got 4 visits to the park at a discou
defon
Answer: 59$

Step-by-Step Explanation:

Let the discounted rate be ‘x’
No. of visits = 4
Total Amount for the visits = 4 * x = 4x
Additional cost = 25$
Total Amount = 261$

Therefore,
= 4x + 25 = 261
= 4x = 261 - 25 = 236
=> x = 236/4 = 59

Therefore, x = 59
Hence, discounted rate = 59$
3 0
2 years ago
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