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3 years ago

Write brackets () in this statement to make it correct 6 + 4 x 5 - 3 = 14

Mathematics

2 answers:

S_A_V [24]3 years ago

8 0

Answer: 6 + 4 × (5-3)

Explanation:

6 + 4 × (5-3) = 14

6 + 4 × 2 = 14

6 + 8 = 14

14 = 14

Must click thanks and mark brainliest

bekas [8.4K]3 years ago

5 0

Answer:

6+4*(5-3)

Step-by-step explanation:

Because of PEMDAS l, we first solve in the parantheses. So 5-3 would be 2, then we multiply 2 by 4 which would be 8 obviously. Then we do the final step, add 6 and 8 which would be 14. Cheers!

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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

Susie has planned a trip to a city 60 miles away. She wishes to have an average speed of 60 miles/hour for the trip. Due to a tr

Nutka1998 [239]

Answer:

90 mi/h

Step-by-step explanation:

Given,

For first 30 miles, her speed is 30 miles per hour,

Let x be her speed in miles per hour for another 30 miles,

Since, here the distance are equal in each interval,

So, the average speed of the entire journey

$=\frac{\text{Average speed for first 30 miles + Average speed for another 30 miles}}{2}$

$=\frac{30+x}{2}$

According to the question,

$\frac{30+x}{2}=60$

$30+x=120$

$\implies x = 90$

Hence, she needs to go 90 miles per hour for remaining 30 miles.

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4 years ago

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cluponka [151]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

The difference of two numbers is 18, and their sum is 90.<br> Find the two numbers

sladkih [1.3K]

Answer:

54 and 36

Step-by-step explanation:

when we add 54 and 36 we get 90 and when we subtract 54 from 36 we get the difference 18

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3 years ago

Solve 21.85 x (-6.2)

liubo4ka [24]

Answer:

= −135.47x

Step-by-step explanation:

^^^^^^^^^^^^^^^

7 0

3 years ago