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DanielleElmas [232]

2 years ago

6

Kip is using a recipe that calls for 1/4 cup of lemon juice. He has a 6-fluid- ounce bottle of lemon juice. There are 8 fluid ou

nces of lemon juice in 1 cup. How many batches of the recipe can Kip make?

1 answer:

umka2103 [35]2 years ago

4 0

Answer:

3

Step-by-step explanation:

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This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the ex

olga nikolaevna [1]

$f(x_1,\ldots,x_n)=x_1+\cdots+x_n=\displaystyle\sum_{i=1}^nx_i$

${x_1}^2+\cdots+{x_n}^2=\displaystyle\sum_{i=1}^n{x_i}^2=4$

The Lagrangian is

$L(x_1,\ldots,x_n,\lambda)=\displaystyle\sum_{i=1}^nx_i+\lambda\left(\sum_{i=1}^n{x_i}^2-4\right)$

with partial derivatives (all set equal to 0)

$L_{x_i}=1+2\lambda x_i=0\implies x_i=-\dfrac1{2\lambda}$

for $1\le i\le n$ , and

$L_\lambda=\displaystyle\sum_{i=1}^n{x_i}^2-4=0$

Substituting each $x_i$ into the second sum gives

$\displaystyle\sum_{i=1}^n\left(-\frac1{2\lambda}\right)^2=4\implies\dfrac n{4\lambda^2}=4\implies\lambda=\pm\frac{\sqrt n}4$

Then we get two critical points,

$x_i=-\dfrac1{2\frac{\sqrt n}4}=-\dfrac2{\sqrt n}$

or

$x_i=-\dfrac1{2\left(-\frac{\sqrt n}4\right)}=\dfrac2{\sqrt n}$

At these points we get a value of $f(x_1,\cdots,x_n)=\pm2\sqrt n$ , i.e. a maximum value of $2\sqrt n$ and a minimum value of $-2\sqrt n$ .

6 0

3 years ago

4x7=(4x3)+(4x4) is an example of what property?

RideAnS [48]

That is an example of the Distributive Property!

4 0

3 years ago

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After 5 years, Marcel's account earned $900 in interest. If the interest rate (in decimal form) is 0.06, how much did Marcel ini

Natasha2012 [34]

Answer:

$3000

Step-by-step explanation:

I= PRT÷100

where,

I = interest = 900

T= 5

R/100 = 0.06

P = ?

I= PRT/100

900= P × 5 × 0.06

P = 900÷ 0.3

P= 3000

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3 years ago

Reflect the following points over the<br> x-axis. (-5, -3) (-2,-6) (-4,-8)

viktelen [127]

Reflect over x-axis rule: (x,y) -> (x,-y)

(-5,3) --> (-5,-3)

(-2,-6) --> (-2,6)

(-4,-8) --> (-4,8)

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3 years ago

Need help asap hurry please

Kobotan [32]

Answer:

B

Step-by-step explanation:

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3 years ago

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