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3 years ago

5a-z=8 -2a+5z =-6 What is the answer

Mathematics

1 answer:

timurjin [86]3 years ago

8 0

Answer:

122 = 7(z + 8) + -5(6 + z) >z = 48

Step-by-step explanation:

122 = 7(8 + z) + -5(6 + z)

122 = (8 * 7 + z * 7) + -5(6 + z)

122 = (56 + 7z) + -5(6 + z)

122 = 56 + 7z + (6 * -5 + z * -5)

122 = 56 + 7z + (-30 + -5z)

Reorder the terms:

122 = 56 + -30 + 7z + -5z

Combine like terms: 56 + -30 = 26

122 = 26 + 7z + -5z

Combine like terms: 7z + -5z = 2z

122 = 26 + 2z

Solving

122 = 26 + 2z

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '-2z' to each side of the equation.

122 + -2z = 26 + 2z + -2z

Combine like terms: 2z + -2z = 0

122 + -2z = 26 + 0

122 + -2z = 26

Add '-122' to each side of the equation.

122 + -122 + -2z = 26 + -122

Combine like terms: 122 + -122 = 0

0 + -2z = 26 + -122

-2z = 26 + -122

Combine like terms: 26 + -122 = -96

-2z = -96

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4 years ago

Find the general solution of<br><br> dz/dt=5ze^(sint)cost+2e^(sint)cost

gizmo_the_mogwai [7]

Answer:

The general solution of given differential equation is $\frac{1}{5}ln|5z+2|=e^{\sin t}+C$ .

Step-by-step explanation:

The given differential equation is

$\frac{dz}{dt}=5ze^{\sin t}\cos t+2e^{\sin t}\cos t$

Taking out common factors.

$\frac{dz}{dt}=(5z+2)e^{\sin t}\cos t$

Using variable separable method, we get

$\frac{dz}{5z+2}=e^{\sin t}\cos t dt$

Integrate both sides.

$\int\frac{dz}{5z+2}=\int e^{\sin t}\cos t dt$

$I_1=I_2$ .... (1)

First solve LHS,

$I_1=\int\frac{dz}{5z+2}$

Substitute $5z+2=u$

$5\frac{dz}{du}=1$

$dz=\frac{1}{5}du$

$I_1=\frac{1}{5}\int\frac{du}{u}$

$I_1=\frac{1}{5}ln|u|+C_1$

$I_1=\frac{1}{5}ln|5z+2|+C_1$

Now, solve RHS,

$I_2=\int e^{\sin t}\cos t dt$

Substitute $\sin t=v$ ,

$\cos t\frac{dt}{dv}=1$

$\cos tdt=dv$

$I_2=\int e^{v}dv$

$I_2=e^{v}+C_2$

$I_2=e^{\sin t}+C_2$

Subtitle the values of I₁ and I₂ in equation (1).

$\frac{1}{5}ln|5z+2|+C_1=e^{\sin t}+C_2$

$\frac{1}{5}ln|5z+2|=e^{\sin t}+C_2-C_1$

$\frac{1}{5}ln|5z+2|=e^{\sin t}+C$

Therefore the general solution of given differential equation is $\frac{1}{5}ln|5z+2|=e^{\sin t}+C$ .

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3 years ago