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gladu [14]
4 years ago
14

Question 3 (1 point)

Mathematics
1 answer:
Virty [35]4 years ago
7 0

Answer:

The answer to your question is (4, 6)

Step-by-step explanation:

Data

E ( 9 , 7 )

F ( - 1, 5)

Formula

Xm = \frac{x1 + x2}{2}

Ym = \frac{y1 + y2}{2}

Substitution and simplification

Xm = \frac{9 -1}{2}

Xm = \frac{8}{2}

      Xm = 4

Ym = \frac{7 + 5}{2}

Ym = \frac{12}{2}

      Ym = 6

Result

            (4 , 6)  

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We are given the equation: g(s,t) = t^2 e^s

Which is subject to the constraint: s^2 + t^2=3

 

The points (x,y) that will maximize g(s,t) will be the points that will satisfy the equation ∇f(x, y, z) = λ∇g(x, y, z), therefore:

2 t e^s = λ (2 t), so  e^s = λ           --> 1

t^2 e^s = λ (2 s)                                                --> 2

s^2 + t^2 = 3                                       -->3

 

To solve this problem, note that λ cannot be zero by equation 1 since e^s can never be zero. Therefore plug in equation 1 to 2:

t^2 e^s = (e^s) (2 s)       

t^2 = 2 s                                               --> 4

 

Plug in equation 4 to 3:

s^2 + 2s = 3

 

By completing the square:

s^2 + 2s + 1 = 4

(s + 1)^2 = 4

s + 1 = ±2

s = -3, 1

 

Calculating for t using equation 4:

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Step-by-step explanation:

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