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2 years ago

Subtract. 44.3 – 2.74 = ?

Mathematics

2 answers:

larisa86 [58]2 years ago

6 0

Your answer would be 41.56x

IrinaVladis [17]2 years ago

4 0

44.3 subtracted by 2.74 would be equal to 41.56.

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Consider the function f(x, y) = x2 + xy + y2 defined on the unit disc, namely, d = {(x, y)| x2 + y2 ≤ 1}. use the method of lagr

Pani-rosa [81]

First we note that the partial derivatives vanish simultaneously at one point:

$\begin{cases}f_x=2x+y=0\\f_y=x+2y=0\end{cases}\implies(x,y)=(0,0)$

so there is one critical point within the region $D$ .

The Lagrangian is

$L(x,y,\lambda)=x^2+xy+y^2+\lambda(x^2+y^2-1)$

and has partial derivatives

$L_x=2x+y+2\lambda x$
$L_y=x+2y+2\lambda y$
$L_\lambda=x^2+y^2-1$

Set each partial derivative to 0 to find the possible critical points within the disk $D$ . Then we notice that

$yL_x=2xy+y^2+2\lambda xy=0$
$xL_y=x^2+2xy+2\lambda xy=0$
$L_\lambda=0\implies x^2+y^2=1$

$\implies xL_y-yL_x=x^2-y^2=0$

Since $x^2+y^2=1$ , we have

$x^2-y^2=x^2+y^2-2y^2=0\implies1=2y^2\implies y^2=\dfrac12\implies y=\pm\dfrac1{\sqrt2}$

And since $x^2-y^2=0$ , or $x^2=y^2$ , we also have

$x=\pm\dfrac1{\sqrt2}$

So we have four possible additional critical points to consider:

$f(0,0)=0$
$f\left(-\dfrac1{\sqrt2},-\dfrac1{\sqrt2}\right)=\dfrac32$
$f\left(-\dfrac1{\sqrt2},\dfrac1{\sqrt2}\right)=\dfrac12$
$f\left(\dfrac1{\sqrt2},-\dfrac1{\sqrt2}\right)=\dfrac12$
$f\left(\dfrac1{\sqrt2},\dfrac1{\sqrt2}\right)=\dfrac32$

It should be clear enough which of these correspond to the absolute extrema of $f$ over $D$ .

8 0

2 years ago

4) A right triangle has a hypotenuse length of 10 and one of its legs has a

Rudiy27

Answer: 8

Step-by-step explanation:

8 0

2 years ago

A patio is rectangular. Its length is 6.21 meters, and its width is 5.7 meters. What is the approximate perimeter of the patio?

Nikolay [14]

Answer:

Step-by-step explanation:

6.21+6.21=5.7+5.7=23.82

23.82 rounds to 24

(perimeter is all of the sides combined)

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2 years ago

Can you please help me on question number 16 ASAP.

nadezda [96]

EOF Is A 80 Degree Angle FOB Is A 180 Degree Angle BOC Is A 90 Degree Angle.

4 0

3 years ago

Read 2 more answers

Amuseumcharges forgeneraladmission and exhibitions. Admission and 3 exhibitionscosts $45. Admission and 5 exhibitionscosts $65.

leonid [27]

Answer:

The price of the admission is 15.

Step-by-step explanation:

From the information given, you can write the following equations:

a+3e=45 (1)

a+5e=65 (2), where:

a is the admission cost

e is the exhibition cost

First, you can solve for a in (1):

a=45-3e (3)

Second, you can replace (3) in (2):

45-3e+5e=65

45+2e=65

2e=65-45

2e=20

e=20/2

e=10

Finally, you can replace the value of e in (3):

a=45-3e

a=45-3(10)

a=45-30

a=15

According to this, the price of the admission is 15.

3 0

2 years ago