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3 years ago

Select ALL the correct answers.

Mathematics

1 answer:

stiv31 [10]3 years ago

4 0

Answer:

Statements 3, 4 and 5 are true.

Step-by-step explanation:

x^2 - 8x + 4

Using the quadratic formula:

x = [ -(-8) +/- √((-8)^2 - 4*1*4)] / 2

= (8 +/- √(64 - 16)) / 2

= 4 +/- √48 / 2

= 4 +/- 4√3/2

= 4 +/- 2√3.

So the third statement is true.

Converting to vertex form:

x^2 - 8x + 4

= (x - 4)^2 - 16 + 4

= (x - 4)^2 -12

So the extreme value is at (4, -12)

So the fourth statement is true.

The coefficient of the term in x^2 is 1 (positive) so the graph has a minimum.

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What is the coeffieent of (x^4)(y^4) in the expansion of (x+y)^8

kap26 [50]

ANSWER

The coefficient is 70.

EXPLANATION

The given binomial expression is

$(x+y)^8$

The specific term of a binomial expansion can be determined using the formula,

$T_{r+1}= nC_ra^{n-r}b^r$
where

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We substitute these values into the formula to get,

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3 years ago

Write the given differential equation in the form L(y) = g(x), where L is a linear differential operator with constant coefficie

melamori03 [73]

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

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

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The auxiliary equation is

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

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

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

$\Rightarrow m = 3, -\frac13$

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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DerKrebs [107]

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3 years ago

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3 years ago