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Sauron [17]
3 years ago
8

What is the best first step for solving the given system using substitution while avoiding fractions -9x+4y=10 -9x+3y=3

Mathematics
2 answers:
Setler [38]3 years ago
8 0

Answer:

B is the answer

Step-by-step explanation:

Sever21 [200]3 years ago
7 0

Answer:

Solve for x in the first equation. ⇒ the first answer

Step-by-step explanation:

* Lets study how to solve the system of the equation using

 the substitution method

- The first equation is ax + by = c

- The second equation is dx + ey = f

* To chose the first step

- Solve for x or y depends on the integer answer

EX: ax = c - by ⇒ x = c/a - (b/a)y

      b/a = integer , c/a = integer ⇒ best choice

- If not solve for next variable

EX: by = c - ax ⇒ y = c/b - (a/b)y

      a/b = integer , c/b = integer ⇒ best choice

- If not repeat with the second equation to find the best choice

* Lets check our equations:

∵ -9x + 4y = 10 ⇒ (1)

∵ -9x + 3y = 3 ⇒ (2)

* If we start with the first equation and solve for x

∵ -9x = 10 - 4y ⇒ (2)

- It will be difficult if we divide by -9, but the second equation

 has -9x, so we will solve of -9x not for x and substitute the value

 of -9x in the second equation

* Substitute (3) in (2)

∴ 10 - 4y + 3y = 3 ⇒ collect the like terms

∴ -y = -7 ⇒ y = 7

substitute the value of in (3)

∴ -9x = 10 - 4(7) ⇒ -9x = -18 ⇒ ÷ -9 in both sides

∴ x = 3

∴ The best choice to avoid fraction is:

  Solve for x in the first equation.

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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

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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)

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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

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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

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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

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f=√21/2π

f=0.73Hz

Then, period is the reciprocal of frequency

T=1/f

T=1/0.73

T=1.37seconds

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luda_lava [24]

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Step-by-step explanation:

If you simplify you should get 2 x  +  3y −  6

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