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Ede4ka [16]
3 years ago
10

Find the global maximum and global minimum values (if they exist) of x 2 + y 2 in the region x + y = 1. If there is no global ma

x, justify why. If there is no global minimum, justify why.
Mathematics
1 answer:
Grace [21]3 years ago
5 0

Given that x+y=1, we have y=1-x, so that

f(x,y)=x^2+y^2\iff g(x)=x^2+(1-x)^2

Take the derivative and find the critical points of g:

g'(x)=2x-2(1-x)=4x-2=0\implies x=\dfrac12

Take the second derivative and evaluate it at the critical point:

g''(x)=4>0

Since g'' is positive for all x, the critical point is a minimum.

At the critical point, we get the minimum value g\left(\frac12\right)=f\left(\frac12,\frac12\right)=\frac12.

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Find the product of the expression:<br> (5p^3) (-1m^8p^2)
Rainbow [258]

Answer:

We conclude that:

  • \left(5p^3\right)\:\left(-1m^8p^2\right)=-5p^5m^8

Step-by-step explanation:

Given the expression

\left(5p^3\right)\:\left(-1m^8p^2\right)

Apply the rule:

a\left(-b\right)=-ab

so the expression becomes

\left(5p^3\right)\left(-1\cdot \:m^8p^2\right)=-5p^3\cdot \:1\cdot \:m^8p^2

Apply the rule:

a^b\cdot \:a^c=a^{b+c}

so the expression becomes

                             =-5p^{3+2}\cdot \:1\cdot \:m^8         ∵ p^3p^2=p^{3+2}

                             =-5p^5\cdot \:1\cdot \:m^8

                             =-5p^5m^8

Therefore, we conclude that:

  • \left(5p^3\right)\:\left(-1m^8p^2\right)=-5p^5m^8
7 0
3 years ago
PLS HELP Solve for n. -3 + n = 8
Tamiku [17]

Answer:

-3 + 11 = 8

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
What is the place value of 7<br>in 1,709?​
Wittaler [7]

Answer:

7 is in the ten-thousands place.

Step-by-step explanation:

5 0
3 years ago
If 12 children represents 12.5% of the people attending a concert, how many people are attending the concert
NeTakaya

96 people are attending the concert.

Step-by-step explanation:

Given,

Number of children at concert = 12

This represents 12.5% of the people attending concert.

Let,

p be the total people attending concert.

12.5% of p = 12

\frac{12.5}{100}*p=12\\0.125p=12

Dividing both sides by 0.125

\frac{0.125p}{0.125}=\frac{12}{0.125}\\p=96

96 people are attending the concert.

Keywords: percentage, division

Learn more about division at:

  • brainly.com/question/317601
  • brainly.com/question/306772

#LearnwithBrainly

7 0
3 years ago
Can anyone help me asap plzz.
zloy xaker [14]

Answer:

answer : D)

Step-by-step explanation:

y – 5 ≥ 11

add 5 :   y – 5 + 5 ≥ 11 + 5

y ≥  16   ...answer : D)

3 0
3 years ago
Read 2 more answers
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