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3 years ago

10

8/9 - 4/6 - (-1/4) SOME ONE HELP

1 answer:

Luden [163]3 years ago

7 0

Answer:

17/36

Step-by-step explanation:

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hodyreva [135]

199 *0.05 = 9.95

4750 * 0.06 = 285

99.50 * 0.047 = 4.68

19.88 * 0.069 = 1.37

8.95 * 0.072 = 0.64

14.27 * 0.068 = 0.97

544.38 * 0.042 = 22.86

7.49 * 0.081 = 0.61

28.56 * 0.075 = 2.14

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6 0

3 years ago

The scale of a map is 1 inch = 70 miles. If two cities are 5 ½ inches apart on the map, how many miles apart are they?

kondaur [170]

70x5 1/2=385

385 miles

4 0

3 years ago

Solve for x:<br> <img src="https://tex.z-dn.net/?f=x-2%28x-%5Cfrac%7B3%7D%7B2%7Dx%29%3D2%284-x%29%2B10" id="TexFormula1" title="

Arlecino [84]

Answer:

$x = \frac{9}{2}$

Step-by-step explanation:

x - 2 (x - $\frac{3x}{2}$ ) = 2 (4 - x) + 10

x − 2 × $\frac{-x}{2}$ =2(4−x)+10

x−(−x)=2(4−x)+10

x+x=2(4−x)+10

2x=2(4−x)+10

2x=8−2x+10

2x=−2x+18

2x+2x=18

4x=18

$x = \frac{18}{4}$

$x = \frac{9}{2}$

7 0

3 years ago

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

8/9 divided by 7/5 x 3/16

nadya68 [22]

This might be wrong but I got 120/1008

4 0

3 years ago