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4 years ago

Which lists the fractions from least to greatest?

Mathematics

2 answers:

Andre45 [30]4 years ago

5 0

The answer is D because negative numbers are behind zero

kumpel [21]4 years ago

3 0

the correct answer is answer Choice E

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Use Lagrange multipliers to find the maximum and minimum values of (i) f(x,y)-81x^2+y^2 subject to the constraint 4x^2+y^2=9. (i

sp2606 [1]

i. The Lagrangian is

$L(x,y,\lambda)=81x^2+y^2+\lambda(4x^2+y^2-9)$

with critical points whenever

$L_x=162x+8\lambda x=0\implies2x(81+4\lambda)=0\implies x=0\text{ or }\lambda=-\dfrac{81}4$

$L_y=2y+2\lambda y=0\implies2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1$

$L_\lambda=4x^2+y^2-9=0$

If $x=0$ , then $L_\lambda=0\implies y=\pm3$ .
If $y=0$ , then $L_\lambda=0\implies x=\pm\dfrac32$ .
Either value of $\lambda$ found above requires that either $x=0$ or $y=0$ , so we get the same critical points as in the previous two cases.

We have $f(0,-3)=9$ , $f(0,3)=9$ , $f\left(-\dfrac32,0\right)=\dfrac{729}4=182.25$ , and $f\left(\dfrac32,0\right)=\dfrac{729}4$ , so $f$ has a minimum value of 9 and a maximum value of 182.25.

ii. The Lagrangian is

$L(x,y,z,\lambda)=y^2-10z+\lambda(x^2+y^2+z^2-36)$

with critical points whenever

$L_x=2\lambda x=0\implies x=0$ (because we assume $\lambda\neq0$ )

$L_y=2y+2\lambda y=0\implies 2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1$

$L_z=-10+2\lambda z=0\implies z=\dfrac5\lambda$

$L_\lambda=x^2+y^2+z^2-36=0$

If $x=y=0$ , then $L_\lambda=0\implies z=\pm6$ .
If $\lambda=-1$ , then $z=-5$ , and with $x=0$ we have $L_\lambda=0\implies y=\pm\sqrt{11}$ .

We have $f(0,0,-6)=60$ , $f(0,0,6)=-60$ , $f(0,-\sqrt{11},-5)=61$ , and $f(0,\sqrt{11},-5)=61$ . So $f$ has a maximum value of 61 and a minimum value of -60.

5 0

3 years ago

What is the intersection of plane TUYX and plane VUYZ??

Alexandra [31]

Thats not enough information

4 0

3 years ago

Read 2 more answers

Factorise <br> 3xy2− 6x2y+ 12xy

d1i1m1o1n [39]

Answer:

terms=3xy2,-6x2y,12xy

factor=3xy2=3,x,y2

=-6x2y=-6,x2,y

=12xy=12,x,y

Step-by-step explanation:

Pls mark as branliest thanks.

7 0

3 years ago

Read 2 more answers

What is the area of parallelogram <br> H=4 in b=7 in

Wittaler [7]

Answer:

A = 28 in²

Step-by-step explanation:

Equation for the area of a parallelogram: <em>A = b * h</em>

Plug in: A = 7 in * 4 in

Solve: A = 28 in²

7 0

3 years ago

Does anyone know Experimental Probability?

PIT_PIT [208]

If you roll a fair 6-sided die you can get 1, 2, 3, 4, 5 or 6. In total there are 6 possibilities for the outcomes. The theoretical probability to roll each number of 6 possible is the same and equal to 1/6.

If you roll a fair 6-sided die 600 times, you can expect that near 1/6 of these attempts will get you 3's. Then you expect about 600·1/6=100 3’s (you can't suppose to get exactly 100 3's, because the experimental probability may differ from theoretical).

Answer: correct choice is A.

7 0

3 years ago