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2 years ago

Use the table below to answer this question:

1 answer:

8 0

In the interval from x=-1 to x=2, x increases by 3. In that same interval, y increases by 6 from -3 to +3. The average rate of change is
.. average rate of change = (increase in y)/(increase in x) = 6/3 = 2

The average rate of change is 2 over the given interval.

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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

2 years ago

Please help me, I'll give brainliest!!

kumpel [21]

Answer:

irrational and regular

Step-by-step explanation:

i looked it up

8 0

2 years ago

The bus fare without a coupon book is $1.50 a coupon book cost $30.00, with the coupon book the fare is reduced $0.50. How many

valentina_108 [34]

Answer: the bus would be used 30 times for the monthly costs to be the same.

Step-by-step explanation:

Let x represent the number of times in a month for which the bus must be used so the total monthly cost is the same with the book as it is without it.

The bus fare without a coupon book is $1.50. This means that the total monthly cost of using the bus for x times without a coupon book is 1.5x

A coupon book cost $30.00 and with the coupon book, the fare is reduced $0.50. This means that the total monthly cost of using the bus for x times with a coupon book is

0.5x + 30

For the monthly costs to be the same,

1.5x = 0.5x + 30

1.5x - 0.5x = 30

x = 30

3 0

2 years ago

7 - 36 - 2(b + 3 - 2b)

ale4655 [162]

Answer:

Step-by-step explanation:

utstistidtizfizitsgitisgisigsgisgi

4 0

2 years ago

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Slope-intercept intro<br> What is the slope of y = -1 + 3x?

miss Akunina [59]

Answer:

look up something called desmos and type in the equation

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers