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3 years ago

3x^2 (x^2 - 4x - 2) + (5x^3 + 7x^2+2x+11) plz show work

Mathematics

1 answer:

matrenka [14]3 years ago

5 0

Let's simplify step-by-step.

3x2(x2−4x−4)+5x3+7x2+2x+11

Distribute:

=(3x2)(x2)+(3x2)(−4x)+(3x2)(−4)+5x3+7x2+2x+11

=3x4+−12x3+−12x2+5x3+7x2+2x+11

Combine Like Terms:

=3x4+−12x3+−12x2+5x3+7x2+2x+11

=(3x4)+(−12x3+5x3)+(−12x2+7x2)+(2x)+(11)

=3x4+−7x3+−5x2+2x+11

Answer:

=3x4−7x3−5x2+2x+11

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Answer:

The complete solution is

$\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43$

Step-by-step explanation:

Given differential equation is

3y"- 8y' - 3y =4

The trial solution is

$y = e^{mx}$

Differentiating with respect to x

$y'= me^{mx}$

Again differentiating with respect to x

$y''= m ^2 e^{mx}$

Putting the value of y, y' and y'' in left side of the differential equation

$3m^2e^{mx}-8m e^{mx}- 3e^{mx}=0$

$\Rightarrow 3m^2-8m-3=0$

The auxiliary equation is

$3m^2-8m-3=0$

$\Rightarrow 3m^2 -9m+m-3m=0$

$\Rightarrow 3m(m-3)+1(m-3)=0$

$\Rightarrow (3m+1)(m-3)=0$

$\Rightarrow m = 3, -\frac13$

The complementary function is

$y= Ae^{3x}+Be^{-\frac13 x}$

y''= D², y' = D

The given differential equation is

(3D²-8D-3D)y =4

⇒(3D+1)(D-3)y =4

Since the linear operation is

L(D) ≡ (3D+1)(D-3)

For particular integral

$y_p=\frac 1{(3D+1)(D-3)} .4$

$=4.\frac 1{(3D+1)(D-3)} .e^{0.x}$ [since $e^{0.x}=1$ ]

$=4\frac{1}{(3.0+1)(0-3)}$ [ replace D by 0 , since L(0)≠0]

$=-\frac43$

The complete solution is

y= C.F+P.I

$\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43$

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3 years ago

Svet_ta [14]

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3 Select the correct answer. How can you write the expression 7(b – 2) in words? A. two subtracted from the quotient of seven di

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Answer:

E. the product of seven and the difference of b minus two

Step-by-step explanation:

7(b-2)

seven is being multiplied by the difference of b minus 2

So this can be written as the product of seven and the difference of b minus two.

Reasons its not the other answer choices

A. two subtracted from the quotient of seven divided by b would be (7/b) - 2

B. seven added to difference of b minus two would be 7 + (b-2)

C. the quotient of seven divided by b minus two would be 7/(b-2)

D. two subtracted from seven times b would be 7b - 2

Key Vocabulary:

Difference = Subtraction

Product = Multiplication

Quotient = Division

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