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3 years ago

8.14÷20 please show work

Mathematics

2 answers:

saul85 [17]3 years ago

6 0

Answer:

0.407

Step-by-step explanation:

0. 4 0 7

2 0 /8. 1 4 0

− 0

8 1

− 8 0

1 4

− 0

1 4 0

− 1 4 0

12345 [234]3 years ago

5 0

Answer: 0.407

Step-by-step explanation:

8.14/20= 0.402

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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

3 years ago

If the third term in a geometric sequence is 20, and the fifth term in the

Gwar [14]

Answer: A) 1/2

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

If the third term is 20, it means that

T3 = 20 = ar^(3 - 1)

20 = ar²- - - - - - - - - - 1

If the third term is 20, it means that

T5 = 5 = ar^(5 - 1)

5 = ar⁴- - - - - - - - - - 2

Dividing equation 2 by equation 1, it becomes

5/20 = r⁴/r²

1/4 = r^(4 - 2)

(1/2)² = r²

r = 1/2

6 0

3 years ago

A semi circle has a radius 8.2 cm

zaharov [31]

Answer:

Step-by-step explanation:

$Area=\frac{1}{2}*\pi *r^{2}\\\\=\frac{1}{2}*3.14*8.2*8.2\\\\=3.14*4.1*8.2\\$

= 105.57

= 105.6 cm²

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3 years ago

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David drove the first six hours of his journey at 65 km/ hour and the last 3 hours of his journey at 80 km/hour how far is the w

zzz [600]

630 kilometers for the whole journey

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3 years ago

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Whats 3 3/4 divided by 1/2

sasho [114]

3 3/4 divided by 1/2 is 7 1/2.

5 0

3 years ago

8.14÷20 please show work​

8.14÷20 please show work