If you're just focusing on the boundary, it's the circle $x^2+y^2=1$ . Parameterize it by taking $x=\cos t$ and $y=\sin t$ , with $0\le t\le2\pi$ . Then $f(x,y)$ reduces to a univariate function $g(t)$ :

$f(x,y)=10x^2+11y\iff g(t)=f(\cos t,\sin t)=10\cos^2t+11\sin t$

Then you can find any extrema on the boundary by checking the critical points of $g$ .

8 0

3 years ago

Maurice's family put a pool into their backyard. It is rectangular in shape and its dimension are 20 feet by 10 feet by 10 feet.

s344n2d4d5 [400]

Answer:

C. $150

Step-by-step explanation:

6 0

3 years ago

What is the vertex of the graph y = x^2 + 6x - 5 ?

Dafna11 [192]

Given: y = x^2 + 6x - 5. Then a = 1, b = 6 and c = -5.

The x-coord. of the vertex is given by x = -b / (2a), which here is x = -6 / (2*1) = -3.

Use the given formula y = x^2 + 6x - 5 to find the value of y when x = -3:

y = (-3)^2 + 6(-3) - 5 = 9 - 18 - 5 = -14

Then the vertex is (-3, -14).

6 0

3 years ago