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4 years ago

5

What percent of 1/4 is 2/3 and what percent of 1/6 is 2/3 ?

2 answers:

vfiekz [6]4 years ago

6 0

400% and 266.666667

vlada-n [284]4 years ago

3 0

Answer:

The percentages are 267% and 400% respectively.

Step-by-step explanation:

To find the answers of these, you need to divide the second number by the first. This will give you the percentage.

2/3 ÷ 1/4 = 8/3 = 2.67 = 267%

You can do the same for the second one.

2/3 ÷ 1/6 = 12/3 = 4 = 400%

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Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer d

eduard

The Lagrangian is

$L(x_1,\ldots,x_n,\lambda_1,\ldots,\lambda_n)=x_1+\cdots+x_n+\lambda_1({x_1}^2+\cdots+{x_n}^2)+\cdots+\lambda_n({x_1}^2+\cdots+{x_n}^2)$

with partial derivatives (set equal to 0)

$\dfrac{\partial L}{\partial x_i}=1+2x_i(\lambda_1+\cdots+\lambda_n)=0$

$\dfrac{\partial L}{\partial\lambda_i}={x_1}^2+\cdots+{x_n}^2-36=0$

for each $1\le i\le n$ .

Let $\Lambda$ be the sum of all the multipliers $\lambda_i$ ,

$\Lambda=\displaystyle\sum_{k=1}^n\lambda_k=\lambda_1+\cdots+\lambda_n$

We notice that

$x_i\dfrac{\partial L}{\partial x_i}=x_i+2{x_i}^2\Lambda=0$

so that

$\displaystyle\sum_{i=1}^nx_i\dfrac{\partial L}{\partial x_i}=\sum_{i=1}^nx_i+2\Lambda\sum_{i=1}^n{x_i}^2=0$

We know that $\sum\limits_{i=1}^n{x_i}^2=36$ , so

$\displaystyle\sum_{i=1}^nx_i+2\Lambda\sum_{i=1}^n{x_i}^2=0\implies\sum_{i=1}^nx_i=-72\Lambda$

Solving the first $n$ equations for $x_i$ gives

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

and in particular

$\displaystyle\sum_{i=1}^nx_i=-\dfrac n{2\Lambda}$

It follows that

$-\dfrac n{2\Lambda}+72\Lambda=0\implies\Lambda^2=\dfrac n{144}\implies\Lambda=\pm\dfrac{\sqrt n}{12}$

which gives us

$x_i=-\dfrac1{2\left(\pm\frac{\sqrt n}{12}\right)}=\pm\dfrac6{\sqrt n}$

That is, we've found two critical points,

$\pm\left(\dfrac6{\sqrt n},\ldots,\dfrac6{\sqrt n}\right)$

At the critical point with positive signs, $f(x_1,\ldots,x_n)$ attains a maximum value of

$\displaystyle\sum_{i=1}^nx_i=\dfrac{6n}{\sqrt n}=6\sqrt n$

and at the other, a minimum value of

$\displaystyle\sum_{i=1}^nx_i=-\dfrac{6n}{\sqrt n}=-6\sqrt n$

4 0

4 years ago

How to graph 2 (X+4)^2-6?

raketka [301]

Direction: Opens UpVertex: <span><span>(<span><span>−4</span>,<span>−6</span></span>)</span><span><span>-4</span>,<span>-6</span></span></span>Focus: <span><span>(<span><span>−4</span>,<span>−<span>478</span></span></span>)</span><span><span>-4</span>,<span>-<span>478</span></span></span></span>Axis of Symmetry: <span><span>x=<span>−4</span></span><span>x=<span>-4</span></span></span>Directrix: <span>y=<span>−<span><span>498</span></span></span></span>

6 0

4 years ago

Read 2 more answers

Jenny sleeps for 8 hours every day. How many days does she spend over the course

ankoles [38]

Answer:

56 Hours A Week... how long is the course though?

Step-by-step explanation:

3 0

3 years ago

If 130 is invested in a savings account that earns 4% interest per year, which of the following is closest to the amount in the

kykrilka [37]

The answer would be 182
4% of 130 = 5.2
5.2 x 10yrs = 52
130 + 52 = 182

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4 years ago

(11x – 6x2 – 8)/(3x – 1)

kozerog [31]

Answer:

46.6

Step-by-step explanation:

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3 years ago