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3 years ago

What two integers have a sum of zero and why

Mathematics

1 answer:

pantera1 [17]3 years ago

4 0

Answer:

The number 0 is called the additive identity because when you add it to a number, the result you get is the same number.

Step-by-step explanation:

Example : 3 + (-3) = 0

Hope this helps!! :))

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the following statement, express the first number as a percentage of the second number. A certain candidate won 337 electoral v

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Step-by-step explanation:

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3 years ago

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Select the correct answer.

romanna [79]

Employees salary [$}: 30,000, 30,000, 35,000, 35,000, 40,000, 40,000.

CEO Salary: $70,000.

The correct answer is this: BOTH JAN AND MARCY ARE CORRECT.

Jan says the employee average salary is $35,000. This is correct as shown below:

Average employee salary = 30,000 + 30,000 + 35,000 +35,000 + 40,000 + 40,000 / 6 = 210 / 6 = $35,000.

Marcy says the average salary of all company members is $40,000. This is also true as shown below.

Average salary of all company members = 30,000 + 30,000 +35,000 + 35,000 + 40,000 + 40,000 + 70,000 / 7 = 280 / 7 = $40,000.

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3 years ago

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FromTheMoon [43]

I don’t understand your question

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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

aliya0001 [1]

The Lagrangian

$L(x,y,z,\lambda)=x^2+y^2+z^2+\lambda(x^4+y^4+z^4-13)$

has critical points where the first derivatives vanish:

$L_x=2x+4\lambda x^3=2x(1+2\lambda x^2)=0\implies x=0\text{ or }x^2=-\dfrac1{2\lambda}$

$L_y=2y+4\lambda y^3=2y(1+2\lambda y^2)=0\implies y=0\text{ or }y^2=-\dfrac1{2\lambda}$

$L_z=2z+4\lambda z^3=2z(1+2\lambda z^2)=0\implies z=0\text{ or }z^2=-\dfrac1{2\lambda}$

$L_\lambda=x^4+y^4+z^4-13=0$

We can't have $x=y=z=0$ , since that contradicts the last condition.

(0 critical points)

If two of them are zero, then the remaining variable has two possible values of $\pm\sqrt[4]{13}$ . For example, if $y=z=0$ , then $x^4=13\implies x=\pm\sqrt[4]{13}$ .

(6 critical points; 2 for each non-zero variable)

If only one of them is zero, then the squares of the remaining variables are equal and we would find $\lambda=-\frac1{\sqrt{26}}$ (taking the negative root because $x^2,y^2,z^2$ must be non-negative), and we can immediately find the critical points from there. For example, if $z=0$ , then $x^4+y^4=13$ . If both $x,y$ are non-zero, then $x^2=y^2=-\frac1{2\lambda}$ , and

$xL_x+yL_y=2(x^2+y^2)+52\lambda=-\dfrac2\lambda+52\lambda=0\implies\lambda=\pm\dfrac1{\sqrt{26}}$

$\implies x^2=\sqrt{\dfrac{13}2}\implies x=\pm\sqrt[4]{\dfrac{13}2}$

and for either choice of $x$ , we can independently choose from $y=\pm\sqrt[4]{\frac{13}2}$ .

(12 critical points; 3 ways of picking one variable to be zero, and 4 choices of sign for the remaining two variables)

If none of the variables are zero, then $x^2=y^2=z^2=-\frac1{2\lambda}$ . We have

$xL_x+yL_y+zL_z=2(x^2+y^2+z^2)+52\lambda=-\dfrac3\lambda+52\lambda=0\implies\lambda=\pm\dfrac{\sqrt{39}}{26}$

$\implies x^2=\sqrt{\dfrac{13}3}\implies x=\pm\sqrt[4]{\dfrac{13}3}$

and similary $y,z$ have the same solutions whose signs can be picked independently of one another.

(8 critical points)

Now evaluate $f$ at each critical point; you should end up with a maximum value of $\sqrt{39}$ and a minimum value of $\sqrt{13}$ (both occurring at various critical points).