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3 years ago

5

Buzz is buying 143 sodas for his pool party.They sold in packs of 12 and 35. pack of 35 is $12.58 and pack of 12 is $7.19.How ma

ny packs of 35 should she buy and how many pcks of 12 she buy so she spend least amount of moneu?

2 answers:

stich3 [128]3 years ago

8 0

He should buy 4 packs of 35ct.And 1 pack of 12ct he may have some extra

madam [21]3 years ago

3 0

Buzz should buy 3 35 packs and 4 12 packs.

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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

3 years ago

How do you round 949999 to the nearest ten thousand

3241004551 [841]

Answer:

950000

Step-by-step explanation:

the rule with rounding is if the number to the direct left is under 5, it stays the same but if it is 5 or above, you round up and everything behind becomes zeroes.

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3 years ago

The league championship 800 meter race has 9 runners. In how many different ways they place first, second and third?

uysha [10]

Answer:

504 different ways

Step-by-step explanation:

There are 9 people competing

9 Different people can come in 1st

We have a winner

Now there are only 8 people left to come in second

8 different people can come in 2nd

There is 1 second place winner

Now there are only 7 people left to come in second

7 different people can come in 3rd

9*8*7 =504

There are 504 different ways

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4 years ago

Drew works at a laundromat. Every day for two weeks, he records the total number of loads of laundry washed at the laundromat. T

Afina-wow [57]

Answer:

B

Step-by-step explanation:

The first quartile of his data is 60.

The median of his data is 82.

The first quartile Q1 is the median of the lower half of the data set. This means that about 25% of the numbers in the data set lie below Q1 and about 75% lie above Q1.

The median Q2 is the median of the data set. This means that about 50% of the numbers in the data set lie below Q2 and about 50% lie above Q2.

Between Q1 and Q2 lie exactly 25% of the numbers in the data set.

25% of 200 is exactly 50, so option B is true.

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3 years ago

Help me find domain? Please

dedylja [7]

This graph is that of a parabola, which in turn represents a quadratic (2nd order) equation, also a polynomial. The domain of any and all polynomial(s) is "the set of all real numbers," or (-infinity, infinity).

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3 years ago