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3 years ago

9

Factor the following.

1 answer:

a_sh-v [17]3 years ago

3 0

The answer would be (y + 14) (y - 8) because when multiplied it gives you
y^2 + 6y - 112

Hope this helps :)
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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 $-2\sqrt n$ .

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3 years ago

You store square notepaper in a cube shape box with an inside edge length of 3 inches. What is the volume of the box

Ber [7]

A cube has sides that are all equal lengths .

Volume of a cube is S^3, where S is the length of the side.

Volume = 3^3 = 3 x 3 x 3 = 27 cubic inches.

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3 years ago

Simplify the expression:<br><br> 5x + 8 – 13y – 4x – 18 + 16y

aleksandrvk [35]

$\text{Hey there!}$

$\text{Simply the equation: 5x + 8 - 13y - 4x - 18 + 16y}$

$\text{First you have to combine the \bf{like-terms}}$

$\text{5x-4x = 1x}$

$\text{-13y + 16y = 3y}$

$\text{8 + (-18) = -10}$

$\boxed{\boxed{\bf{Answer: 1x + 3y - 10}}}\checkmark$

~ $\frak{LoveYourselfFirst:)}$

4 0

3 years ago

Twice a number plus 6 times the number is -72.

katen-ka-za [31]

Answer:

The number is -9

Look at the attachment

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3 years ago

What coefficient would you get for the x terms on the right side of 3x+15=2x+10+x+5

Zielflug [23.3K]

Answer:

x=0

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers