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2 years ago

Plss helpppp 1/3 ÷ 4 3/4

Mathematics

1 answer:

Fynjy0 [20]2 years ago

3 0

Answer:

1/16

Step-by-step explanation:

Hope this helps

If you have hard time with math I use an app called photo math

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Find the maximum and minimum values attained by f(x, y, z) = 5xyz on the unit ball x2 + y2 + z2 ≤ 1.

Allushta [10]

Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
$f_x=5yz=0\implies y=0\text{ or }z=0$
$f_y=5xz=0\implies x=0\text{ or }z=0$
$f_z=5xy=0\implies x=0\text{ or }y=0$

Taken together, we find that (0, 0, 0) appears to be the only critical point on $f$ within the ball. At this point, we have $f(0,0,0)=0$ .

Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian

$L(x,y,z,\lambda)=5xyz+\lambda(x^2+y^2+z^2-1)$

with partial derivatives (set to 0)

$L_x=5yz+2\lambda x=0$
$L_y=5xz+2\lambda y=0$
$L_z=5xy+2\lambda z=0$
$L_\lambda=x^2+y^2+z^2-1=0$

We then observe that

$xL_x+yL_y+zL_z=0\implies15xyz+2\lambda=0\implies\lambda=-\dfrac{15xyz}2$

So, ignoring the critical point we've already found at (0, 0, 0),

$5yz+2\left(-\dfrac{15xyz}2\right)x=0\implies5yz(1-3x^2)=0\implies x=\pm\dfrac1{\sqrt3}$
$5xz+2\left(-\dfrac{15xyz}2\right)y=0\implies5xz(1-3y^2)=0\implies y=\pm\dfrac1{\sqrt3}$
$5xy+2\left(-\dfrac{15xyz}2\right)z=0\implies5xy(1-3z^2)=0\implies z=\pm\dfrac1{\sqrt3}$

So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of $\left(\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3}\right)$ , at which points we get a value of either of $\pm\dfrac5{\sqrt3}$ , with the maximum being the positive value and the minimum being the negative one.

5 0

2 years ago

Write the following situation in slope intercept form - y=mx+b

cestrela7 [59]

I think the answer is C

3 0

2 years ago

When running a 100 meter race matt reaches his maximum speed when he is 40 meters from the starting line, and 7 seconds have ela

ch4aika [34]

Answer:

Step-by-step explanation:

time after 40 meters to 80 meters=12-7=5 s

distance=80-40=40 m

max. speed=40/5=8 m/s

4 0

2 years ago

Read 2 more answers

Sarah answered 24 questions on her test correctly and earned an 80%. How many questions were on the test?

MaRussiya [10]

Answer:

43 questions in total

Step-by-step explanation:

the original equation with the unknown (total number of questions on the test) will look like this

$\frac{total \: number \: of \: questions \: on \: exam}{24 \: answered \: questions} = 80\%$

we know this because to work out a percentage in the 1st place you need the total ÷ number (in this case it's ÷ how many questions out of the total she did answer)

now you rearrange.

you need to move the 24 to get the total on it's own here's how you do it

$\frac{tot \: num \: of \: qs}{24} \times 24 = 80\% \times 24$

what you do to one side of equation you have to do to the other. the 24 and 24 on the left will cancel because 24÷24=1 and we don't write

got mum of Q's x 1= 80 x 24

now you convert % to decimal

$80\% \times 100 = 0.80$

replace

$tot \: num \: qs \: = 24 \times 0.80 = 19$

now you take the original and + the 19

$24 + 19 = 43$

therefore there are a total of 43 questions on the exam

5 0

3 years ago

PLEASE HELP I will mark brailist

WARRIOR [948]

Answer:

72m^2

Step-by-step explanation:

Conevert the lengths into what they really are

Length of Patio:12

width of patio:6

Soooo.....

multiply

12x6=72

8 0

2 years ago