360 miles in 6 hours

Mathematics

1 answer:

Ahat [919]2 years ago

7 0

6=360<span>
60=3600
600=36000
6000=360000
60000=3600000

And so on and so on.
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Circle D is below what is the arc measure of BC in degrees

maks197457 [2]

Answer:

84°

Step-by-step explanation:

$\because (13n - 16) \degree + (7n + 12) \degree + (6n)\degree \\= 360\degree \\ \\ \therefore \: (26n - 4) \degree= 360\degree \\ \\ \therefore \: 26n - 4= 360 \\ \\ \therefore \: 26n = 360 + 4 \\ \\ \therefore \: 26n = 364 \\ \\ \therefore \: n = \frac{364}{26} \\ \\ \therefore \: n = 14 \\ \\\because m\overset { \frown}{BC} = (6n)°\\ \\\therefore \:m \overset { \frown}{BC} =(6\times 14)° \\ \\ \huge \purple {\boxed {\therefore \:m\overset { \frown}{BC}= 84°}} \\$

4 0

3 years ago

Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.

irina1246 [14]

Lagrange multipliers:

$L(x,y,z,\lambda)=xy^2z^2+\lambda(x+y+z-5)$

$L_x=y^2z^2+\lambda=0$
$L_y=2xyz^2+\lambda=0$
$L_z=2xy^2z+\lambda=0$
$L_\lambda=x+y+z-5=0$

$\lambda=-y^2z^2=-2xyz^2=-2xy^2z$

$-y^2z^2=-2xyz^2\implies y=2x$ (if $y,z\neq0$ )

$-y^2z^2=-2xy^2z\implies z=2x$ (if $y,z\neq0$ )

$-2xyz^2=-2xy^2z\implies z=y$ (if $x,y,z\neq0$ )

In the first octant, we assume $x,y,z>0$ , so we can ignore the caveats above. Now,

$x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2$

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of $f(1,2,2)=16$ .

We also need to check the boundary of the region, i.e. the intersection of $x+y+z=5$ with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force $f(x,y,z)=0$ , so the point we found is the only extremum.