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3 years ago

I need help with this assignment

Mathematics

1 answer:

Slav-nsk [51]3 years ago

4 0

Answer and Step-by-step explanation:

This is negative slope (or a downwards negative slope).

When the slope is negative, the line goes from right to left from top to bottom.

<em><u>#teamtrees #PAW (Plant And Water)</u></em>

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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,

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

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

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

4 years ago

Miss Green tells you that a right triangle has a hypotenuse of 13 and a leg of 5 she asked you to find the other leg of the tria

Natalka [10]

Answer:

The other leg of the triangle is 12.

Step-by-step explanation:

Given:

Hypotenuse of triangle is 13 and a leg(Leg1) is 5.

Let, the other leg of the triangle (Leg2) be $x$ .

Now, putting the formula:

$(Hypotenuse)^{2}=(Leg1)^{2}+(Leg2)^{2}$

⇒ $13^{2} =5^{2} +x^{2}$

⇒ $169=25+x^{2}$

⇒ $169-25=x^{2}$

⇒ $144=x^{2}$

Taking square root both sides

⇒ $12=x$

⇒ $x=12$ .

Therefore, the other leg of the triangle is 12.

7 0

4 years ago

Please help all i know is 10,000x 12/100=1,200+99=1,299

Liono4ka [1.6K]

Answer: Because 1 10,000 is the amount he earns a year so where does $99 come in?

Step-by-step explanation:

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3 years ago

In the library at Lenape Elementary School, there are

Phoenix [80]

Solution:

we are given that

In the library at Lenape Elementary School, there are 3/8 as many fiction books as there are nonfiction books.

There are 44 books in the school library.

we have been asked to find How many books are fiction books?

Let there are x non fiction books in the library. Then there will be $\frac{3}{8}x$ fiction books.

Hence we can write

$x+\frac{3}{8}x=44\\\\\text{Now solve for x}\\\\\frac{8x+3x}{8}=44\\\\\frac{11x}{8}=44\\\\11x=44*8\\\\x=\frac{44*8}{11}\\\\x=4*8=32\\$

Hence there are 32 non-fiction books in the library.

and 44-32=12 fiction books in the library.

6 0

3 years ago

The number of adult passengers on a bus (excluding the driver) is three times the number of children. If there are a adult passe

Fiesta28 [93]

C because you need to multiply the adults by 3 to know how many children there are and then you need to exclude the driver which is a-1 meaning taking out 1 adult.

5 0

3 years ago