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3 years ago

1-2n) - 7n(12-2) simplify this and show work

Mathematics

1 answer:

Natasha2012 [34]3 years ago

5 0

For this case we must simplify the following expression:

$(1-2n) -7n (12-2) =$

We solve the operation of the second parenthesis, taking into account that different signs are subtracted and the sign of the major is placed:

$(1-2n) -7n (10) =$

We multiply:

$(1-2n) -70n =$

We eliminate the parentheses:

$1-2n-70n =$

We add similar terms, taking into account that equal signs are added and the same sign is placed:

$1-72n$

Answer:

The simplified expression is: $1-72n$

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Combine like terms:

7x + 12 = 180

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3 years ago

The base of a triangle is nine centimeters longer than the perpendicular height. If the area of the triangle is 180 square centi

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Answer:

Step-by-step explanation:

<u>Equations</u>

Let's call

b= base of the triangle

h=height of the triangle

The base is 9 cm longer than the height, thus:

b = h + 9

The area of the triangle is:

$\displaystyle A=\frac{bh}{2}$

$\displaystyle A=\frac{(h+9)h}{2}$

And its value is 180:

$\displaystyle \frac{(h+9)h}{2}=180$

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Operating:

$h^2+9h-360=0$

Factoring:

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The only valid positive solution is:

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D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

3 years ago

1-2n) - 7n(12-2) simplify this and show work​

1-2n) - 7n(12-2) simplify this and show work