What is 20 yards in meters? pls explain how you got the answer

Sue ran the first 12 miles of the 24-mile Fun Run in 72 minutes. Her rate decreased by 2 miles per hour in the second half of th

densk [106]

Answer:

90 minutes or 1.30 hours

Step-by-step explanation:

In 72 minutes, Sue ran 12 miles per hour

In 1 minute, Sue ran 12/72 miles per hour

In 60 minutes, Sue ran (12/72)*60 miles per hour

= 10 miles per hour

Remaining miles after completing 12 miles in 72 minutes = (24-12) = 12 miles.

If the mileage decreases to 2 miles per hour, he will now run = (10 - 2) = 8 miles per hour.

Now,

1 hour = 60 minutes

Sue can run 8 miles in 60 minutes

Sue can run 1 miles in 60/8 minutes

Sue can run 12 miles in (60/8)*12 minutes

= 90 minutes or 1.30 hours

6 0

3 years ago

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

Find the surface area of the triangular prism shown below.

VikaD [51]

Answer:

136

Step-by-step explanation:

5*7 = 35

4*6/2 = 12

7*6 = 42

Add them all up

5 0